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-0
-00:00:00,000 --> 00:00:15,840
-
-
-1
-00:00:15,840 --> 00:00:20,260
-PROFESSOR: Well, I hope you
-appreciate that we have
-
-2
-00:00:20,260 --> 00:00:26,690
-inducted you into some real
-magic, the magic of building
-
-3
-00:00:26,690 --> 00:00:29,730
-languages, really building
-new languages.
-
-4
-00:00:29,730 --> 00:00:30,430
-What have we looked at?
-
-5
-00:00:30,430 --> 00:00:39,390
-We've looked at an Escher
-picture language: this
-
-6
-00:00:39,390 --> 00:00:42,360
-language invented by
-Peter Henderson.
-
-7
-00:00:42,360 --> 00:00:46,260
-We looked at digital
-logic language.
-
-8
-00:00:46,260 --> 00:00:53,260
-
-
-9
-00:00:53,260 --> 00:00:53,570
-Let's see.
-
-10
-00:00:53,570 --> 00:00:55,360
-We've looked at the
-query language.
-
-11
-00:00:55,360 --> 00:00:59,700
-
-
-12
-00:00:59,700 --> 00:01:01,570
-And the thing you should realize
-is, even though these
-
-13
-00:01:01,570 --> 00:01:06,760
-were toy examples, they really
-are the kernels of really
-
-14
-00:01:06,760 --> 00:01:08,250
-useful things.
-
-15
-00:01:08,250 --> 00:01:12,520
-So, for instance, the Escher
-picture language was taken by
-
-16
-00:01:12,520 --> 00:01:17,320
-Henry Wu, who's a student at
-MIT, and developed into a real
-
-17
-00:01:17,320 --> 00:01:21,840
-language for laying out PC
-boards based just on extending
-
-18
-00:01:21,840 --> 00:01:23,300
-those structures.
-
-19
-00:01:23,300 --> 00:01:25,320
-And the digital logic language,
-Jerry mentioned when
-
-20
-00:01:25,320 --> 00:01:28,550
-he showed it to you, was really
-extended to be used as
-
-21
-00:01:28,550 --> 00:01:32,050
-the basis for a simulator
-that was used to
-
-22
-00:01:32,050 --> 00:01:33,460
-design a real computer.
-
-23
-00:01:33,460 --> 00:01:34,900
-And the query language,
-of course, is kind
-
-24
-00:01:34,900 --> 00:01:37,510
-of the germ of prologue.
-
-25
-00:01:37,510 --> 00:01:39,830
-So we built all of these
-languages, they're
-
-26
-00:01:39,830 --> 00:01:41,080
-all based on LISP.
-
-27
-00:01:41,080 --> 00:01:43,630
-
-
-28
-00:01:43,630 --> 00:01:48,010
-A lot of people ask what
-particular problems is LISP
-
-29
-00:01:48,010 --> 00:01:48,820
-good for solving for?
-
-30
-00:01:48,820 --> 00:01:52,150
-The answer is LISP is not good
-for solving any particular
-
-31
-00:01:52,150 --> 00:01:56,340
-problems. What LISP is good for
-is constructing within it
-
-32
-00:01:56,340 --> 00:01:58,140
-the right language to solve
-the problems you want to
-
-33
-00:01:58,140 --> 00:02:01,470
-solve, and that's how you
-should think about it.
-
-34
-00:02:01,470 --> 00:02:04,326
-So all of these languages
-were based on LISP.
-
-35
-00:02:04,326 --> 00:02:07,270
-Now, what's LISP based on?
-
-36
-00:02:07,270 --> 00:02:07,920
-Where's that come from?
-
-37
-00:02:07,920 --> 00:02:09,400
-Well, we looked at that too.
-
-38
-00:02:09,400 --> 00:02:12,740
-
-
-39
-00:02:12,740 --> 00:02:23,760
-We looked at the meta-circular
-evaluator and said well, LISP
-
-40
-00:02:23,760 --> 00:02:25,810
-is based on LISP.
-
-41
-00:02:25,810 --> 00:02:28,910
-And when we start looking at
-that, we've got to do some
-
-42
-00:02:28,910 --> 00:02:29,950
-real magic, right?
-
-43
-00:02:29,950 --> 00:02:31,660
-So what does that mean, right?
-
-44
-00:02:31,660 --> 00:02:37,730
-Why operators, and fixed points,
-and the idea that what
-
-45
-00:02:37,730 --> 00:02:40,460
-this means is that LISP is
-somehow the fixed-point
-
-46
-00:02:40,460 --> 00:02:44,600
-equation for this funny set of
-things which are defined in
-
-47
-00:02:44,600 --> 00:02:47,470
-terms of themselves.
-
-48
-00:02:47,470 --> 00:02:49,070
-Now, it's real magic.
-
-49
-00:02:49,070 --> 00:02:53,000
-Well, today, for a final piece
-of magic, we're going to make
-
-50
-00:02:53,000 --> 00:02:54,250
-all the magic go away.
-
-51
-00:02:54,250 --> 00:03:06,430
-
-
-52
-00:03:06,430 --> 00:03:09,770
-We already know how
-to do that.
-
-53
-00:03:09,770 --> 00:03:11,970
-The idea is, we're going to
-take the register machine
-
-54
-00:03:11,970 --> 00:03:14,380
-architecture and show
-how to implement
-
-55
-00:03:14,380 --> 00:03:15,500
-LISP on terms of that.
-
-56
-00:03:15,500 --> 00:03:22,640
-And, remember, the idea of the
-register machine is that
-
-57
-00:03:22,640 --> 00:03:24,800
-there's a fixed and finite
-part of the machine.
-
-58
-00:03:24,800 --> 00:03:27,050
-There's a finite-state
-controller, which does some
-
-59
-00:03:27,050 --> 00:03:30,510
-particular thing with a
-particular amount of hardware.
-
-60
-00:03:30,510 --> 00:03:32,470
-There are particular data
-paths: the operation the
-
-61
-00:03:32,470 --> 00:03:33,550
-machine does.
-
-62
-00:03:33,550 --> 00:03:35,780
-And then, in order to implement
-recursion and
-
-63
-00:03:35,780 --> 00:03:38,460
-sustain the illusion of
-infinity, there's some large
-
-64
-00:03:38,460 --> 00:03:42,060
-amount of memory, which
-is the stack.
-
-65
-00:03:42,060 --> 00:03:47,280
-So, if we implement LISP in
-terms of a register machine,
-
-66
-00:03:47,280 --> 00:03:48,900
-then everything ought to
-become, at this point,
-
-67
-00:03:48,900 --> 00:03:49,850
-completely concrete.
-
-68
-00:03:49,850 --> 00:03:51,650
-All the magic should go away.
-
-69
-00:03:51,650 --> 00:03:55,140
-And, by the end of this talk,
-I want you get the feeling
-
-70
-00:03:55,140 --> 00:03:58,400
-that, as opposed to this very
-mysterious meta-circular
-
-71
-00:03:58,400 --> 00:04:01,630
-evaluator, that a LISP evaluator
-really is something
-
-72
-00:04:01,630 --> 00:04:03,740
-that's concrete enough that
-you can hold in the
-
-73
-00:04:03,740 --> 00:04:04,720
-palm of your hand.
-
-74
-00:04:04,720 --> 00:04:06,950
-You should be able to
-imagine holding a
-
-75
-00:04:06,950 --> 00:04:09,546
-LISP interpreter there.
-
-76
-00:04:09,546 --> 00:04:10,950
-All right, how are we
-going to do this?
-
-77
-00:04:10,950 --> 00:04:13,960
-We already have all
-the ingredients.
-
-78
-00:04:13,960 --> 00:04:18,300
-See, what you learned last time
-from Jerry is how to take
-
-79
-00:04:18,300 --> 00:04:23,980
-any particular couple of LISP
-procedures and hand-translate
-
-80
-00:04:23,980 --> 00:04:28,210
-them into something that runs
-on a register machine.
-
-81
-00:04:28,210 --> 00:04:30,900
-So, to implement all of LISP on
-a register machine, all we
-
-82
-00:04:30,900 --> 00:04:34,010
-have to do is take the
-particular procedures that are
-
-83
-00:04:34,010 --> 00:04:37,450
-the meta-circular evaluator and
-hand-translate them for a
-
-84
-00:04:37,450 --> 00:04:39,120
-register machine.
-
-85
-00:04:39,120 --> 00:04:42,320
-And that does all
-of LISP, right?
-
-86
-00:04:42,320 --> 00:04:45,380
-So, in principle, we already
-know how to do this.
-
-87
-00:04:45,380 --> 00:04:51,640
-And, indeed, it's going to be
-no different, in kind, from
-
-88
-00:04:51,640 --> 00:04:53,430
-translating, say, recursive
-factorial
-
-89
-00:04:53,430 --> 00:04:54,670
-or recursive Fibonacci.
-
-90
-00:04:54,670 --> 00:04:56,840
-It's just bigger and
-there's more of it.
-
-91
-00:04:56,840 --> 00:04:58,760
-So it'd just be more details,
-but nothing really
-
-92
-00:04:58,760 --> 00:05:01,730
-conceptually new.
-
-93
-00:05:01,730 --> 00:05:03,600
-All right, also, when we've done
-that, and the thing is
-
-94
-00:05:03,600 --> 00:05:06,990
-completely explicit, and we see
-how to implement LISP in
-
-95
-00:05:06,990 --> 00:05:10,510
-terms of the actual sequential
-register operations, that's
-
-96
-00:05:10,510 --> 00:05:13,230
-going to be our final most
-explicit model of
-
-97
-00:05:13,230 --> 00:05:14,810
-LISP in this course.
-
-98
-00:05:14,810 --> 00:05:16,410
-And, remember, that's
-a progression
-
-99
-00:05:16,410 --> 00:05:16,950
-through this course.
-
-100
-00:05:16,950 --> 00:05:18,790
-We started out with
-substitution, which is sort of
-
-101
-00:05:18,790 --> 00:05:20,370
-like algebra.
-
-102
-00:05:20,370 --> 00:05:22,070
-And then we went to the
-environment model, which
-
-103
-00:05:22,070 --> 00:05:24,230
-talked about the actual
-frames and how
-
-104
-00:05:24,230 --> 00:05:26,390
-they got linked together.
-
-105
-00:05:26,390 --> 00:05:28,100
-And then we made that
-more concrete in the
-
-106
-00:05:28,100 --> 00:05:31,080
-meta-circular evaluator.
-
-107
-00:05:31,080 --> 00:05:33,120
-There are things the
-meta-circular evaluator
-
-108
-00:05:33,120 --> 00:05:34,360
-doesn't tell us.
-
-109
-00:05:34,360 --> 00:05:36,090
-You should realize that.
-
-110
-00:05:36,090 --> 00:05:40,420
-For instance, it left unanswered
-the question of how
-
-111
-00:05:40,420 --> 00:05:46,100
-a procedure, like recursive
-factorial here , somehow takes
-
-112
-00:05:46,100 --> 00:05:47,210
-space that grows.
-
-113
-00:05:47,210 --> 00:05:51,160
-On the other hand, a procedure
-which also looks syntactically
-
-114
-00:05:51,160 --> 00:05:56,760
-recursive, called fact-iter,
-somehow doesn't take space.
-
-115
-00:05:56,760 --> 00:06:01,040
-We justify that it doesn't need
-to take space by showing
-
-116
-00:06:01,040 --> 00:06:01,960
-the substitution model.
-
-117
-00:06:01,960 --> 00:06:05,550
-But we didn't really say how
-it happens that the machine
-
-118
-00:06:05,550 --> 00:06:09,210
-manages to do that, that that
-has to do with the details of
-
-119
-00:06:09,210 --> 00:06:12,520
-how arguments are passed
-to procedures.
-
-120
-00:06:12,520 --> 00:06:14,710
-And that's the thing we didn't
-see in the meta-circular
-
-121
-00:06:14,710 --> 00:06:17,930
-evaluator precisely because the
-way arguments got passed
-
-122
-00:06:17,930 --> 00:06:21,840
-to procedures in this LISP
-depended on the way arguments
-
-123
-00:06:21,840 --> 00:06:23,510
-got passed to procedures
-in this LISP.
-
-124
-00:06:23,510 --> 00:06:26,070
-
-
-125
-00:06:26,070 --> 00:06:30,740
-But, now, that's going to become
-extremely explicit.
-
-126
-00:06:30,740 --> 00:06:31,230
-OK.
-
-127
-00:06:31,230 --> 00:06:35,000
-Well, before going on to the
-evaluator, let me just give
-
-128
-00:06:35,000 --> 00:06:37,940
-you a sense of what a whole LISP
-system looks like so you
-
-129
-00:06:37,940 --> 00:06:39,730
-can see the parts we're going
-to talk about and the parts
-
-130
-00:06:39,730 --> 00:06:43,250
-we're not going to talk about.
-
-131
-00:06:43,250 --> 00:06:49,240
-Let's see, over here is a happy
-LISP user, and the LISP
-
-132
-00:06:49,240 --> 00:06:52,525
-user is talking to something
-called the reader.
-
-133
-00:06:52,525 --> 00:07:00,360
-
-
-134
-00:07:00,360 --> 00:07:14,170
-The reader's job in life is to
-take characters from the user
-
-135
-00:07:14,170 --> 00:07:17,960
-and turn them into data
-structures in something called
-
-136
-00:07:17,960 --> 00:07:19,210
-a list structure memory.
-
-137
-00:07:19,210 --> 00:07:29,783
-
-
-138
-00:07:29,783 --> 00:07:33,110
-All right, so the reader is
-going to take symbols,
-
-139
-00:07:33,110 --> 00:07:36,600
-parentheses, and A's and B's,
-and ones and threes that you
-
-140
-00:07:36,600 --> 00:07:39,460
-type in, and turn these into
-actual list structure: pairs,
-
-141
-00:07:39,460 --> 00:07:42,340
-and pointers, and things.
-
-142
-00:07:42,340 --> 00:07:44,180
-And so, by the time evaluator
-is going, there are no
-
-143
-00:07:44,180 --> 00:07:45,850
-characters in the world.
-
-144
-00:07:45,850 --> 00:07:49,480
-And, of course, in more modern
-list systems, there's sort of
-
-145
-00:07:49,480 --> 00:07:51,770
-a big morass here that might sit
-between the user and the
-
-146
-00:07:51,770 --> 00:07:55,390
-reader: Windows systems, and top
-levels, and mice, and all
-
-147
-00:07:55,390 --> 00:07:56,280
-kinds of things.
-
-148
-00:07:56,280 --> 00:07:59,590
-But conceptually, characters
-are coming in.
-
-149
-00:07:59,590 --> 00:08:06,240
-All right, the reader transforms
-these into pointers
-
-150
-00:08:06,240 --> 00:08:09,940
-to stuff in this memory,
-and that's what the
-
-151
-00:08:09,940 --> 00:08:17,090
-evaluator sees, OK?
-
-152
-00:08:17,090 --> 00:08:19,780
-The evaluator has a
-bunch of helpers.
-
-153
-00:08:19,780 --> 00:08:23,080
-It has all possible primitive
-operators you might want.
-
-154
-00:08:23,080 --> 00:08:29,610
-So there's a completely separate
-box, a floating point
-
-155
-00:08:29,610 --> 00:08:33,340
-unit, or all sorts of
-things, which do
-
-156
-00:08:33,340 --> 00:08:35,960
-the primitive operators.
-
-157
-00:08:35,960 --> 00:08:38,240
-And, if you want more special
-primitives, you build more
-
-158
-00:08:38,240 --> 00:08:39,309
-primitive operators,
-but they're
-
-159
-00:08:39,309 --> 00:08:42,080
-separate from the evaluator.
-
-160
-00:08:42,080 --> 00:08:46,150
-The evaluator finally gets an
-answer and communicates that
-
-161
-00:08:46,150 --> 00:08:47,400
-to the printer.
-
-162
-00:08:47,400 --> 00:08:50,780
-
-
-163
-00:08:50,780 --> 00:08:52,980
-And now, the printer's job in
-life is to take this list
-
-164
-00:08:52,980 --> 00:08:56,150
-structure coming from the
-evaluator, and turn it back
-
-165
-00:08:56,150 --> 00:09:03,630
-into characters, and communicate
-them to the user
-
-166
-00:09:03,630 --> 00:09:05,540
-through whatever interface
-there is.
-
-167
-00:09:05,540 --> 00:09:08,050
-
-
-168
-00:09:08,050 --> 00:09:08,810
-OK.
-
-169
-00:09:08,810 --> 00:09:10,100
-Well, today, what we're
-going to talk
-
-170
-00:09:10,100 --> 00:09:12,670
-about is this evaluator.
-
-171
-00:09:12,670 --> 00:09:14,900
-The primitive operators have
-nothing particular to do with
-
-172
-00:09:14,900 --> 00:09:17,430
-LISP, they're however you like
-to implement primitive
-
-173
-00:09:17,430 --> 00:09:19,440
-operations.
-
-174
-00:09:19,440 --> 00:09:22,370
-The reader and printer are
-actually complicated, but
-
-175
-00:09:22,370 --> 00:09:24,420
-we're not going to
-talk about them.
-
-176
-00:09:24,420 --> 00:09:27,410
-They sort of have to do with
-details of how you might build
-
-177
-00:09:27,410 --> 00:09:29,900
-up list structure
-from characters.
-
-178
-00:09:29,900 --> 00:09:31,650
-So that is a long story,
-but we're not going
-
-179
-00:09:31,650 --> 00:09:32,490
-to talk about it.
-
-180
-00:09:32,490 --> 00:09:36,930
-The list structure memory, we'll
-talk about next time.
-
-181
-00:09:36,930 --> 00:09:39,170
-So, pretty much, except for
-the details of reading and
-
-182
-00:09:39,170 --> 00:09:41,860
-printing, the only mystery
-that's going to be left after
-
-183
-00:09:41,860 --> 00:09:44,950
-you see the evaluator is how
-you build list structure on
-
-184
-00:09:44,950 --> 00:09:46,295
-conventional memories.
-
-185
-00:09:46,295 --> 00:09:50,580
-But we'll worry about
-that next time too.
-
-186
-00:09:50,580 --> 00:09:51,830
-OK.
-
-187
-00:09:51,830 --> 00:09:53,350
-
-
-188
-00:09:53,350 --> 00:09:56,110
-Well, let's start talking
-about the evaluator.
-
-189
-00:09:56,110 --> 00:09:59,970
-The one that we're going to show
-you, of course, is not, I
-
-190
-00:09:59,970 --> 00:10:01,120
-think, nothing special
-about it.
-
-191
-00:10:01,120 --> 00:10:03,040
-It's just a particular register
-
-192
-00:10:03,040 --> 00:10:04,810
-machine that runs LISP.
-
-193
-00:10:04,810 --> 00:10:08,280
-And it has seven registers,
-and here
-
-194
-00:10:08,280 --> 00:10:09,890
-are the seven registers.
-
-195
-00:10:09,890 --> 00:10:16,430
-There's a register, called EXP,
-and its job is to hold
-
-196
-00:10:16,430 --> 00:10:18,370
-the expression to
-be evaluated.
-
-197
-00:10:18,370 --> 00:10:22,660
-And by that, I mean it's going
-to hold a pointer to someplace
-
-198
-00:10:22,660 --> 00:10:24,040
-in list structure memory
-that holds the
-
-199
-00:10:24,040 --> 00:10:26,550
-expression to be evaluated.
-
-200
-00:10:26,550 --> 00:10:29,490
-There's a register, called
-ENV, which holds the
-
-201
-00:10:29,490 --> 00:10:34,070
-environment in which this
-expression is to be evaluated.
-
-202
-00:10:34,070 --> 00:10:34,940
-And, again, I made a pointer.
-
-203
-00:10:34,940 --> 00:10:38,240
-The environment is some
-data structure.
-
-204
-00:10:38,240 --> 00:10:41,390
-There's a register, called
-FUN, which will hold the
-
-205
-00:10:41,390 --> 00:10:44,630
-procedure to be applied when you
-go to apply a procedure.
-
-206
-00:10:44,630 --> 00:10:48,210
-A register, called ARGL,
-which wants the list
-
-207
-00:10:48,210 --> 00:10:50,630
-of evaluated arguments.
-
-208
-00:10:50,630 --> 00:10:52,060
-What you can start seeing
-here is the basic
-
-209
-00:10:52,060 --> 00:10:53,140
-structure of the evaluator.
-
-210
-00:10:53,140 --> 00:10:54,490
-Remember how evaluators work.
-
-211
-00:10:54,490 --> 00:10:57,670
-There's a piece that takes
-expressions and environments,
-
-212
-00:10:57,670 --> 00:10:59,880
-and there's a piece that
-takes functions, or
-
-213
-00:10:59,880 --> 00:11:03,480
-procedures and arguments.
-
-214
-00:11:03,480 --> 00:11:05,360
-And going back and forth
-around here is
-
-215
-00:11:05,360 --> 00:11:07,740
-the eval/apply loop.
-
-216
-00:11:07,740 --> 00:11:10,270
-So those are the basic pieces
-of the eval and apply.
-
-217
-00:11:10,270 --> 00:11:11,610
-Then there's some other things,
-there's continue.
-
-218
-00:11:11,610 --> 00:11:15,340
-You just saw before how the
-continue register is used to
-
-219
-00:11:15,340 --> 00:11:19,000
-implement recursion and
-stack discipline.
-
-220
-00:11:19,000 --> 00:11:21,510
-There's a register that's going
-to hold the result of
-
-221
-00:11:21,510 --> 00:11:24,190
-some evaluation.
-
-222
-00:11:24,190 --> 00:11:25,890
-And then, besides that,
-there's one temporary
-
-223
-00:11:25,890 --> 00:11:29,280
-register, called UNEV, which
-typically, in the evaluator,
-
-224
-00:11:29,280 --> 00:11:32,980
-is going to be used to hold
-temporary pieces of the
-
-225
-00:11:32,980 --> 00:11:34,690
-expression you're working on,
-which you haven't gotten
-
-226
-00:11:34,690 --> 00:11:37,150
-around to evaluate yet, right?
-
-227
-00:11:37,150 --> 00:11:40,646
-So there's my machine: a
-seven-register machine.
-
-228
-00:11:40,646 --> 00:11:43,300
-And, of course, you might want
-to make a machine with a lot
-
-229
-00:11:43,300 --> 00:11:46,040
-more registers to get better
-performance, but this is just
-
-230
-00:11:46,040 --> 00:11:48,480
-a tiny, minimal one.
-
-231
-00:11:48,480 --> 00:11:49,780
-Well, how about the
-data paths?
-
-232
-00:11:49,780 --> 00:11:55,100
-This machine has a lot of
-special operations for LISP.
-
-233
-00:11:55,100 --> 00:12:00,120
-So, here are some typical
-data paths.
-
-234
-00:12:00,120 --> 00:12:03,410
-A typical one might be, oh,
-assign to the VAL register the
-
-235
-00:12:03,410 --> 00:12:06,710
-contents of the EXP register.
-
-236
-00:12:06,710 --> 00:12:10,190
-In terms of those diagrams you
-saw, that's a little button on
-
-237
-00:12:10,190 --> 00:12:11,900
-some arrow.
-
-238
-00:12:11,900 --> 00:12:14,040
-Here's a more complicated one.
-
-239
-00:12:14,040 --> 00:12:18,810
-It says branch, if the thing in
-the expression register is
-
-240
-00:12:18,810 --> 00:12:21,820
-a conditional to some label
-here, called the
-
-241
-00:12:21,820 --> 00:12:23,850
-ev-conditional.
-
-242
-00:12:23,850 --> 00:12:25,680
-And you can imagine this
-implemented in a lot of
-
-243
-00:12:25,680 --> 00:12:26,230
-different ways.
-
-244
-00:12:26,230 --> 00:12:28,950
-You might imagine this
-conditional test as a special
-
-245
-00:12:28,950 --> 00:12:32,180
-purpose sub-routine, and
-conditional might be
-
-246
-00:12:32,180 --> 00:12:34,400
-represented as some data
-abstraction that you don't
-
-247
-00:12:34,400 --> 00:12:36,610
-care about at this
-level of detail.
-
-248
-00:12:36,610 --> 00:12:37,980
-So that might be done
-as a sub-routine.
-
-249
-00:12:37,980 --> 00:12:41,200
-This might be a machine with
-hardware-types, and
-
-250
-00:12:41,200 --> 00:12:42,910
-conditional might be testing
-some bits for
-
-251
-00:12:42,910 --> 00:12:45,350
-a particular code.
-
-252
-00:12:45,350 --> 00:12:47,280
-There are all sorts of ways
-that's beneath the level of
-
-253
-00:12:47,280 --> 00:12:50,190
-abstraction we're looking at.
-
-254
-00:12:50,190 --> 00:12:52,610
-Another kind of operation, and
-there are a lot of different
-
-255
-00:12:52,610 --> 00:12:55,880
-operations assigned to
-EXP, the first clause
-
-256
-00:12:55,880 --> 00:12:56,840
-of what's in EXP.
-
-257
-00:12:56,840 --> 00:12:59,260
-This might be part of processing
-a conditional.
-
-258
-00:12:59,260 --> 00:13:03,810
-And, again, first clause is some
-selector whose details we
-
-259
-00:13:03,810 --> 00:13:04,470
-don't care about.
-
-260
-00:13:04,470 --> 00:13:06,670
-And you can, again, imagine that
-as a sub-routine which'll
-
-261
-00:13:06,670 --> 00:13:09,180
-do some list operations, or
-you can imagine that as
-
-262
-00:13:09,180 --> 00:13:12,170
-something that's built directly
-into hardware.
-
-263
-00:13:12,170 --> 00:13:14,580
-The reason I keep saying you can
-imagine it built directly
-
-264
-00:13:14,580 --> 00:13:18,360
-into hardware is even though
-there are a lot of operations,
-
-265
-00:13:18,360 --> 00:13:19,740
-there are still a fixed
-number of them.
-
-266
-00:13:19,740 --> 00:13:22,370
-I forget how many, maybe 150.
-
-267
-00:13:22,370 --> 00:13:24,360
-So, it's plausible to think
-of building these
-
-268
-00:13:24,360 --> 00:13:26,400
-directly into hardware.
-
-269
-00:13:26,400 --> 00:13:28,500
-Here's a more complicated one.
-
-270
-00:13:28,500 --> 00:13:29,940
-You can see this has to
-do with looking up
-
-271
-00:13:29,940 --> 00:13:31,710
-the values of variables.
-
-272
-00:13:31,710 --> 00:13:34,370
-It says assign to the VAL
-register the result of looking
-
-273
-00:13:34,370 --> 00:13:39,310
-up the variable value of some
-particular expression, which,
-
-274
-00:13:39,310 --> 00:13:41,330
-in this case, is supposed
-to be a variable in some
-
-275
-00:13:41,330 --> 00:13:42,850
-environment.
-
-276
-00:13:42,850 --> 00:13:46,650
-And this'll be some operation
-that searches through the
-
-277
-00:13:46,650 --> 00:13:49,860
-environment structure, however
-it is represented, and goes
-
-278
-00:13:49,860 --> 00:13:52,240
-and looks up that variable.
-
-279
-00:13:52,240 --> 00:13:54,360
-And, again, that's below the
-level of detail that we're
-
-280
-00:13:54,360 --> 00:13:55,790
-thinking about.
-
-281
-00:13:55,790 --> 00:13:58,350
-This has to do with the details
-of the data structures
-
-282
-00:13:58,350 --> 00:14:00,380
-for representing environments.
-
-283
-00:14:00,380 --> 00:14:04,410
-But, anyway, there is this fixed
-and finite number of
-
-284
-00:14:04,410 --> 00:14:05,940
-operations in the register
-machine.
-
-285
-00:14:05,940 --> 00:14:08,500
-
-
-286
-00:14:08,500 --> 00:14:11,720
-Well, what's its overall
-structure?
-
-287
-00:14:11,720 --> 00:14:14,930
-Those are some typical
-operations.
-
-288
-00:14:14,930 --> 00:14:17,060
-Remember what we have to
-do, we have to take the
-
-289
-00:14:17,060 --> 00:14:20,172
-meta-circular evaluator--
-
-290
-00:14:20,172 --> 00:14:22,890
-and here's a piece of the
-meta-circular evaluator.
-
-291
-00:14:22,890 --> 00:14:28,310
-This is the one using abstract
-syntax that's in the book.
-
-292
-00:14:28,310 --> 00:14:30,500
-It's a little bit different
-from the one
-
-293
-00:14:30,500 --> 00:14:33,500
-that Jerry shows you.
-
-294
-00:14:33,500 --> 00:14:37,950
-And the main thing to remember
-about the evaluator is that
-
-295
-00:14:37,950 --> 00:14:40,310
-it's doing some sort of case
-analysis on the kinds of
-
-296
-00:14:40,310 --> 00:14:46,120
-expressions: so if it's either
-self-evaluated, or quoted, or
-
-297
-00:14:46,120 --> 00:14:48,560
-whatever else.
-
-298
-00:14:48,560 --> 00:14:51,620
-And then, in the general case
-where the expression it's
-
-299
-00:14:51,620 --> 00:14:54,280
-looking at is an application,
-there's some tricky
-
-300
-00:14:54,280 --> 00:14:55,750
-recursions going on.
-
-301
-00:14:55,750 --> 00:15:00,730
-First of all, eval has to call
-itself both to evaluate the
-
-302
-00:15:00,730 --> 00:15:05,880
-operator and to evaluate
-all the operands.
-
-303
-00:15:05,880 --> 00:15:08,470
-So there's this sort of red
-recursion of values walking
-
-304
-00:15:08,470 --> 00:15:12,270
-down the tree that's really
-the easy recursion.
-
-305
-00:15:12,270 --> 00:15:14,750
-That's just a val walking down
-this tree of expressions.
-
-306
-00:15:14,750 --> 00:15:16,600
-Then, in the evaluator, there's
-a hard recursion.
-
-307
-00:15:16,600 --> 00:15:18,200
-There's the red to green.
-
-308
-00:15:18,200 --> 00:15:19,450
-Eval calls apply.
-
-309
-00:15:19,450 --> 00:15:22,470
-
-
-310
-00:15:22,470 --> 00:15:26,132
-That's the case where evaluating
-a procedure or
-
-311
-00:15:26,132 --> 00:15:28,920
-argument reduces to applying
-the procedure
-
-312
-00:15:28,920 --> 00:15:30,370
-to the list of arguments.
-
-313
-00:15:30,370 --> 00:15:31,700
-And then, apply comes
-over here.
-
-314
-00:15:31,700 --> 00:15:34,770
-
-
-315
-00:15:34,770 --> 00:15:39,270
-Apply takes a procedure and
-arguments and, in the general
-
-316
-00:15:39,270 --> 00:15:41,950
-case where there's a compound
-procedure, apply goes around
-
-317
-00:15:41,950 --> 00:15:44,560
-and green calls red.
-
-318
-00:15:44,560 --> 00:15:48,170
-Apply comes around and
-calls eval again.
-
-319
-00:15:48,170 --> 00:15:51,330
-Eval's the body of the procedure
-in the result of
-
-320
-00:15:51,330 --> 00:15:54,600
-extending the environment with
-the parameters of the
-
-321
-00:15:54,600 --> 00:15:56,605
-procedure by binding
-the arguments.
-
-322
-00:15:56,605 --> 00:15:59,620
-
-
-323
-00:15:59,620 --> 00:16:01,560
-Except in the primitive case,
-where it just calls something
-
-324
-00:16:01,560 --> 00:16:03,550
-else primitive-apply, which
-is not really the
-
-325
-00:16:03,550 --> 00:16:05,980
-business of the evaluator.
-
-326
-00:16:05,980 --> 00:16:11,630
-So this sort of red to green,
-to red to green, that's the
-
-327
-00:16:11,630 --> 00:16:15,130
-eval/apply loop, and that's the
-thing that we're going to
-
-328
-00:16:15,130 --> 00:16:17,186
-want to see in the evaluator.
-
-329
-00:16:17,186 --> 00:16:19,840
-
-
-330
-00:16:19,840 --> 00:16:19,970
-All right.
-
-331
-00:16:19,970 --> 00:16:22,570
-Well, it won't surprise you at
-all that the two big pieces of
-
-332
-00:16:22,570 --> 00:16:27,470
-this evaluator correspond
-to eval and apply.
-
-333
-00:16:27,470 --> 00:16:30,070
-There's a piece called
-eval-dispatch, and a piece
-
-334
-00:16:30,070 --> 00:16:32,110
-called apply-dispatch.
-
-335
-00:16:32,110 --> 00:16:34,520
-And, before we get into the
-details of the code, the way
-
-336
-00:16:34,520 --> 00:16:37,760
-to understand this is to think,
-again, in terms of
-
-337
-00:16:37,760 --> 00:16:40,430
-these pieces of the evaluator
-having contracts with the rest
-
-338
-00:16:40,430 --> 00:16:41,870
-of the world.
-
-339
-00:16:41,870 --> 00:16:44,320
-What do they do from the outside
-before getting into
-
-340
-00:16:44,320 --> 00:16:45,780
-the grungy details?
-
-341
-00:16:45,780 --> 00:16:50,080
-Well, the contract for
-eval-dispatch--
-
-342
-00:16:50,080 --> 00:16:51,300
-remember, it corresponds
-to eval.
-
-343
-00:16:51,300 --> 00:16:54,100
-It's got to evaluate an
-expression in an environment.
-
-344
-00:16:54,100 --> 00:16:56,840
-So, in particular, what this
-one is going to do,
-
-345
-00:16:56,840 --> 00:16:59,920
-eval-dispatch will assume that,
-when you call it, that
-
-346
-00:16:59,920 --> 00:17:01,460
-the expression you
-want to evaluate
-
-347
-00:17:01,460 --> 00:17:03,640
-is in the EXP register.
-
-348
-00:17:03,640 --> 00:17:07,680
-The environment in which you
-want the evaluation to take
-
-349
-00:17:07,680 --> 00:17:09,569
-place is in the ENV register.
-
-350
-00:17:09,569 --> 00:17:12,040
-And continue tells you the place
-where the machine should
-
-351
-00:17:12,040 --> 00:17:13,880
-go next when the evaluation
-is done.
-
-352
-00:17:13,880 --> 00:17:17,440
-
-
-353
-00:17:17,440 --> 00:17:20,210
-Eval-dispatch's contract is that
-it'll actually perform
-
-354
-00:17:20,210 --> 00:17:23,930
-that evaluation, and, at the end
-of which, it'll end up at
-
-355
-00:17:23,930 --> 00:17:26,619
-the place specified
-by continue.
-
-356
-00:17:26,619 --> 00:17:29,950
-The result of the evaluation
-will be in the VAL register.
-
-357
-00:17:29,950 --> 00:17:33,100
-And it just warns you, it makes
-no promises about what
-
-358
-00:17:33,100 --> 00:17:35,230
-happens to the registers.
-
-359
-00:17:35,230 --> 00:17:37,490
-All other registers might
-be destroyed.
-
-360
-00:17:37,490 --> 00:17:41,790
-So, there's one piece, OK?
-
-361
-00:17:41,790 --> 00:17:43,640
-Together, the pieces,
-apply-dispatch that
-
-362
-00:17:43,640 --> 00:17:47,650
-corresponds to apply, it's got
-to apply a procedure to some
-
-363
-00:17:47,650 --> 00:17:52,060
-arguments, so it assumes that
-this register, ARGL, contains
-
-364
-00:17:52,060 --> 00:17:54,540
-a list of the evaluated
-arguments.
-
-365
-00:17:54,540 --> 00:17:57,220
-FUN contains the procedure.
-
-366
-00:17:57,220 --> 00:17:59,500
-Those correspond to the
-arguments to the apply
-
-367
-00:17:59,500 --> 00:18:01,055
-procedure in the meta-circular
-evaluator.
-
-368
-00:18:01,055 --> 00:18:03,970
-
-
-369
-00:18:03,970 --> 00:18:06,520
-And apply, in this particular
-evaluator, we're going to use
-
-370
-00:18:06,520 --> 00:18:10,790
-a discipline which says the
-place the machine should go to
-
-371
-00:18:10,790 --> 00:18:14,480
-next when apply is done is, at
-the moment apply-dispatch is
-
-372
-00:18:14,480 --> 00:18:18,850
-called at the top of the stack,
-that's just discipline
-
-373
-00:18:18,850 --> 00:18:21,840
-for the way this particular
-machine's organized.
-
-374
-00:18:21,840 --> 00:18:23,950
-And now apply's contract
-is given all that.
-
-375
-00:18:23,950 --> 00:18:25,540
-It'll perform the application.
-
-376
-00:18:25,540 --> 00:18:28,890
-The result of that application
-will end up in VAL.
-
-377
-00:18:28,890 --> 00:18:31,120
-The stack will be popped.
-
-378
-00:18:31,120 --> 00:18:33,460
-And, again, the contents of all
-the other registers may be
-
-379
-00:18:33,460 --> 00:18:35,110
-destroyed, all right?
-
-380
-00:18:35,110 --> 00:18:39,760
-So that's the basic organization
-of this machine.
-
-381
-00:18:39,760 --> 00:18:41,110
-Let's break for a little bit
-and see if there are any
-
-382
-00:18:41,110 --> 00:18:42,700
-questions, and then we'll
-do a real example.
-
-383
-00:18:42,700 --> 00:19:47,850
-
-
-384
-00:19:47,850 --> 00:19:51,300
-Well, let's take the register
-machine now, and actually step
-
-385
-00:19:51,300 --> 00:19:57,950
-through, and really, in real
-detail, so you see completely
-
-386
-00:19:57,950 --> 00:20:03,400
-concrete how some expressions
-are evaluated, all right?
-
-387
-00:20:03,400 --> 00:20:06,435
-So, let's start with a very
-simple expression.
-
-388
-00:20:06,435 --> 00:20:09,620
-
-
-389
-00:20:09,620 --> 00:20:13,320
-Let's evaluate the
-expression 1.
-
-390
-00:20:13,320 --> 00:20:18,880
-
-
-391
-00:20:18,880 --> 00:20:21,620
-And we need an environment, so
-let's imagine that somewhere
-
-392
-00:20:21,620 --> 00:20:23,085
-there's an environment,
-we'll call it E,0.
-
-393
-00:20:23,085 --> 00:20:30,260
-
-
-394
-00:20:30,260 --> 00:20:36,230
-And just, since we'll use these
-later, we obviously
-
-395
-00:20:36,230 --> 00:20:38,360
-don't really need anything
-to evaluate 1.
-
-396
-00:20:38,360 --> 00:20:40,810
-But, just for reference later,
-let's assume that E,0 has in
-
-397
-00:20:40,810 --> 00:20:49,140
-it an X that's bound to 3 and
-a Y that's bound to 4, OK?
-
-398
-00:20:49,140 --> 00:20:53,700
-And now what we're going to do
-is we're going to evaluate 1
-
-399
-00:20:53,700 --> 00:20:59,650
-in this environment, and so the
-ENV register has a pointer
-
-400
-00:20:59,650 --> 00:21:03,560
-to this environment,
-E,0, all right?
-
-401
-00:21:03,560 --> 00:21:05,650
-So let's watch that thing go.
-
-402
-00:21:05,650 --> 00:21:08,260
-What I'm going to do is
-step through the code.
-
-403
-00:21:08,260 --> 00:21:10,080
-And, let's see, I'll
-be the controller.
-
-404
-00:21:10,080 --> 00:21:12,980
-And now what I need, since this
-gets rather complicated,
-
-405
-00:21:12,980 --> 00:21:16,830
-is a very little
-execution unit.
-
-406
-00:21:16,830 --> 00:21:22,624
-So here's the execution
-unit, OK?
-
-407
-00:21:22,624 --> 00:21:23,874
-OK.
-
-408
-00:21:23,874 --> 00:21:27,088
-
-
-409
-00:21:27,088 --> 00:21:28,590
-OK.
-
-410
-00:21:28,590 --> 00:21:30,690
-All right, now we're
-going to start.
-
-411
-00:21:30,690 --> 00:21:31,710
-We're going to start
-the machine at
-
-412
-00:21:31,710 --> 00:21:33,660
-eval-dispatch, right?
-
-413
-00:21:33,660 --> 00:21:36,120
-That's the beginning of this.
-
-414
-00:21:36,120 --> 00:21:39,320
-Eval-dispatch is going to look
-at the expression in dispatch,
-
-415
-00:21:39,320 --> 00:21:42,010
-just like eval where we look
-at the very first thing.
-
-416
-00:21:42,010 --> 00:21:46,990
-We branch on whether or
-not this expression is
-
-417
-00:21:46,990 --> 00:21:47,950
-self-evaluating.
-
-418
-00:21:47,950 --> 00:21:50,170
-Self-evaluating is some
-abstraction we
-
-419
-00:21:50,170 --> 00:21:52,550
-put into the machine--
-
-420
-00:21:52,550 --> 00:21:53,690
-it's going to be true
-for numbers--
-
-421
-00:21:53,690 --> 00:21:57,040
-to a place called ev-self-eval,
-right?
-
-422
-00:21:57,040 --> 00:22:00,260
-So me, being the controller,
-looks at ev-self-eval, so
-
-423
-00:22:00,260 --> 00:22:02,780
-we'll go over to there.
-
-424
-00:22:02,780 --> 00:22:09,050
-Ev-self-eval says fine, assign
-to val whatever is in the
-
-425
-00:22:09,050 --> 00:22:15,220
-expression unit, OK?
-
-426
-00:22:15,220 --> 00:22:19,930
-And I have a bug because what I
-didn't do when I initialized
-
-427
-00:22:19,930 --> 00:22:23,610
-this machine is also say what's
-supposed to happen when
-
-428
-00:22:23,610 --> 00:22:27,640
-it's done, so I should have
-started out the machine with
-
-429
-00:22:27,640 --> 00:22:32,050
-done being in the continue
-register, OK?
-
-430
-00:22:32,050 --> 00:22:33,640
-So we assign to VAL.
-
-431
-00:22:33,640 --> 00:22:35,790
-And now go to fetch
-of continue, and
-
-432
-00:22:35,790 --> 00:22:38,000
-now change--
-
-433
-00:22:38,000 --> 00:22:40,000
-OK.
-
-434
-00:22:40,000 --> 00:22:42,160
-OK, let's try something
-harder.
-
-435
-00:22:42,160 --> 00:22:47,900
-Let's reset the machine here,
-and we'll put in the
-
-436
-00:22:47,900 --> 00:22:56,710
-expression register, X, OK?
-
-437
-00:22:56,710 --> 00:22:59,610
-Start again at eval-dispatch.
-
-438
-00:22:59,610 --> 00:23:01,690
-Check, is it self-evaluating?
-
-439
-00:23:01,690 --> 00:23:02,650
-No.
-
-440
-00:23:02,650 --> 00:23:04,630
-Is it a variable?
-
-441
-00:23:04,630 --> 00:23:05,560
-Yes.
-
-442
-00:23:05,560 --> 00:23:08,380
-We go off to ev-variable.
-
-443
-00:23:08,380 --> 00:23:14,700
-It says assign to VAL, look up
-the variable value in the
-
-444
-00:23:14,700 --> 00:23:21,620
-expression register, OK?
-
-445
-00:23:21,620 --> 00:23:23,625
-Go to fetch of continue.
-
-446
-00:23:23,625 --> 00:23:24,875
-PROFESSOR: Done.
-
-447
-00:23:24,875 --> 00:23:27,252
-
-
-448
-00:23:27,252 --> 00:23:28,950
-PROFESSOR: OK.
-
-449
-00:23:28,950 --> 00:23:29,430
-All right.
-
-450
-00:23:29,430 --> 00:23:31,330
-Well, that's the basic idea.
-
-451
-00:23:31,330 --> 00:23:32,920
-That's a simple operation
-of the machine.
-
-452
-00:23:32,920 --> 00:23:34,600
-Now, let's actually do something
-a little bit more
-
-453
-00:23:34,600 --> 00:23:36,070
-interesting.
-
-454
-00:23:36,070 --> 00:23:49,678
-Let's look at the expression
-the sum of x and y.
-
-455
-00:23:49,678 --> 00:23:50,130
-OK.
-
-456
-00:23:50,130 --> 00:23:53,240
-And now we'll see how you
-start unrolling these
-
-457
-00:23:53,240 --> 00:23:57,100
-expression trees, OK?
-
-458
-00:23:57,100 --> 00:24:00,645
-Well, start again at
-eval-dispatch, all right?
-
-459
-00:24:00,645 --> 00:24:04,610
-
-
-460
-00:24:04,610 --> 00:24:06,060
-Self-evaluating?
-
-461
-00:24:06,060 --> 00:24:06,810
-No.
-
-462
-00:24:06,810 --> 00:24:07,280
-Variable?
-
-463
-00:24:07,280 --> 00:24:07,850
-No.
-
-464
-00:24:07,850 --> 00:24:10,270
-All the other special forms
-which I didn't write down,
-
-465
-00:24:10,270 --> 00:24:12,480
-like quote, and lambda,
-and set, and whatever,
-
-466
-00:24:12,480 --> 00:24:13,260
-it's none of those.
-
-467
-00:24:13,260 --> 00:24:16,520
-It turns out to be an
-application, so we go off to
-
-468
-00:24:16,520 --> 00:24:19,970
-ev-application, OK?
-
-469
-00:24:19,970 --> 00:24:25,580
-Ev-application, remember what
-it's going to do overall.
-
-470
-00:24:25,580 --> 00:24:28,310
-It is going to evaluate
-the operator.
-
-471
-00:24:28,310 --> 00:24:32,950
-It's going to evaluate the
-arguments, and then it's going
-
-472
-00:24:32,950 --> 00:24:35,060
-to go apply them.
-
-473
-00:24:35,060 --> 00:24:38,140
-So, before we start, since we're
-being very literal, we'd
-
-474
-00:24:38,140 --> 00:24:40,610
-better remember that, somewhere
-in this environment,
-
-475
-00:24:40,610 --> 00:24:46,010
-it's linked to another
-environment in which plus is
-
-476
-00:24:46,010 --> 00:24:52,380
-bound to the primitive procedure
-plus before we get
-
-477
-00:24:52,380 --> 00:24:55,340
-an unknown variable
-in our machine.
-
-478
-00:24:55,340 --> 00:24:56,590
-OK, so we're at ev-application.
-
-479
-00:24:56,590 --> 00:24:59,850
-
-
-480
-00:24:59,850 --> 00:25:05,920
-OK, assign to UNEV the operands
-of what's in the
-
-481
-00:25:05,920 --> 00:25:07,920
-expression register, OK?
-
-482
-00:25:07,920 --> 00:25:09,230
-Those are the operands.
-
-483
-00:25:09,230 --> 00:25:11,920
-UNEV's a temporary register
-where we're
-
-484
-00:25:11,920 --> 00:25:12,916
-going to save them.
-
-485
-00:25:12,916 --> 00:25:13,860
-PROFESSOR: I'm assigning.
-
-486
-00:25:13,860 --> 00:25:18,070
-PROFESSOR: Assign to
-x the operator.
-
-487
-00:25:18,070 --> 00:25:22,140
-Now, notice we've destroyed that
-expression in x, but the
-
-488
-00:25:22,140 --> 00:25:25,820
-piece that we need is
-now in UNEV. OK.
-
-489
-00:25:25,820 --> 00:25:27,490
-Now, we're going to get
-set up to recursively
-
-490
-00:25:27,490 --> 00:25:28,750
-evaluate the operator.
-
-491
-00:25:28,750 --> 00:25:31,565
-Save the continue register
-on the stack.
-
-492
-00:25:31,565 --> 00:25:34,870
-
-
-493
-00:25:34,870 --> 00:25:36,120
-Save the environment.
-
-494
-00:25:36,120 --> 00:25:40,520
-
-
-495
-00:25:40,520 --> 00:25:53,210
-Save UNEV. OK, assign
-to continue a
-
-496
-00:25:53,210 --> 00:25:54,460
-label called eval-args.
-
-497
-00:25:54,460 --> 00:26:01,400
-
-
-498
-00:26:01,400 --> 00:26:01,980
-Now, what have we done?
-
-499
-00:26:01,980 --> 00:26:04,380
-We've set up for a
-recursive call.
-
-500
-00:26:04,380 --> 00:26:06,280
-We're about to go to
-eval-dispatch.
-
-501
-00:26:06,280 --> 00:26:10,230
-We've set up for a recursive
-call to eval-dispatch.
-
-502
-00:26:10,230 --> 00:26:11,020
-What did we do?
-
-503
-00:26:11,020 --> 00:26:15,240
-We took the things we're going
-to need later, those operands
-
-504
-00:26:15,240 --> 00:26:17,860
-that were in UNEV; the
-environment in which we're
-
-505
-00:26:17,860 --> 00:26:20,100
-going to eventually have to,
-maybe, evaluate those
-
-506
-00:26:20,100 --> 00:26:23,910
-operands; the place we
-eventually want to go to,
-
-507
-00:26:23,910 --> 00:26:27,120
-which, in this case, was done;
-we've saved them on the stack.
-
-508
-00:26:27,120 --> 00:26:29,120
-The reason we saved them
-on the stack is because
-
-509
-00:26:29,120 --> 00:26:31,860
-eval-dispatch makes no promises
-about what registers
-
-510
-00:26:31,860 --> 00:26:33,550
-it may destroy.
-
-511
-00:26:33,550 --> 00:26:35,020
-So all that stuff is
-saved on the stack.
-
-512
-00:26:35,020 --> 00:26:37,380
-Now, we've set up
-eval-dispatch's contract.
-
-513
-00:26:37,380 --> 00:26:41,220
-There's a new expression, which
-is the operator plus; a
-
-514
-00:26:41,220 --> 00:26:44,250
-new environment, although, in
-this case, it's the same one;
-
-515
-00:26:44,250 --> 00:26:45,670
-and a new place to
-go to when you're
-
-516
-00:26:45,670 --> 00:26:47,600
-done, which is eval-args.
-
-517
-00:26:47,600 --> 00:26:48,130
-So that's set up.
-
-518
-00:26:48,130 --> 00:26:50,890
-Now, we're going to go
-off to eval-dispatch.
-
-519
-00:26:50,890 --> 00:26:53,090
-Here we are back at
-eval-dispatch.
-
-520
-00:26:53,090 --> 00:26:54,490
-It's not self-evaluating.
-
-521
-00:26:54,490 --> 00:26:57,270
-Oh, it's a variable, so
-we'd better go off to
-
-522
-00:26:57,270 --> 00:27:00,260
-ev-variable, right?
-
-523
-00:27:00,260 --> 00:27:02,880
-Ev-variable is assigned
-to VAL.
-
-524
-00:27:02,880 --> 00:27:08,770
-Look up the variable value
-of the expression, OK?
-
-525
-00:27:08,770 --> 00:27:13,000
-So VAL is the primitive
-procedure plus, OK?
-
-526
-00:27:13,000 --> 00:27:15,020
-And go to fetch of continue.
-
-527
-00:27:15,020 --> 00:27:15,660
-PROFESSOR: Eval-args.
-
-528
-00:27:15,660 --> 00:27:19,340
-PROFESSOR: Right, which is
-now eval-args not done.
-
-529
-00:27:19,340 --> 00:27:23,210
-So we come back here at
-eval-args, and what do we do?
-
-530
-00:27:23,210 --> 00:27:25,620
-We're going to restore the stuff
-that we saved, so we
-
-531
-00:27:25,620 --> 00:27:31,710
-restore UNEV. And notice, there,
-it wasn't necessary,
-
-532
-00:27:31,710 --> 00:27:32,900
-although, in general,
-it would be.
-
-533
-00:27:32,900 --> 00:27:35,430
-It might be some arbitrary
-evaluation that happened.
-
-534
-00:27:35,430 --> 00:27:51,900
-We restore ENV. OK, we assign
-to FUN fetch of VAL.
-
-535
-00:27:51,900 --> 00:27:58,620
-
-
-536
-00:27:58,620 --> 00:28:01,650
-OK, now, we're going
-to go off and start
-
-537
-00:28:01,650 --> 00:28:04,340
-evaluating some arguments.
-
-538
-00:28:04,340 --> 00:28:08,330
-Well, first thing we'd better
-do is save FUN because some
-
-539
-00:28:08,330 --> 00:28:10,165
-arbitrary stuff might happen
-in that evaluation.
-
-540
-00:28:10,165 --> 00:28:15,330
-
-
-541
-00:28:15,330 --> 00:28:18,590
-We initialize the argument list.
-Assign to argl an empty
-
-542
-00:28:18,590 --> 00:28:25,460
-argument list, and go to
-eval-arg-loop, OK?
-
-543
-00:28:25,460 --> 00:28:29,580
-At eval-arg-loop, the idea
-of this is we're going to
-
-544
-00:28:29,580 --> 00:28:32,620
-evaluate the pieces of the
-expressions that are in UNEV,
-
-545
-00:28:32,620 --> 00:28:36,110
-one by one, and move them from
-unevaluated in UNEV to
-
-546
-00:28:36,110 --> 00:28:38,090
-evaluated in the arg list, OK?
-
-547
-00:28:38,090 --> 00:28:39,340
-So we save argl.
-
-548
-00:28:39,340 --> 00:28:43,950
-
-
-549
-00:28:43,950 --> 00:28:53,960
-We assign to x the first operand
-of the stuff in UNEV.
-
-550
-00:28:53,960 --> 00:28:55,890
-Now, we check and see if that
-was the last operand.
-
-551
-00:28:55,890 --> 00:28:59,190
-In this case, it is
-not, all right?
-
-552
-00:28:59,190 --> 00:29:01,235
-So we save the environment.
-
-553
-00:29:01,235 --> 00:29:09,170
-
-
-554
-00:29:09,170 --> 00:29:12,620
-We save UNEV because those
-are all things
-
-555
-00:29:12,620 --> 00:29:13,500
-we might need later.
-
-556
-00:29:13,500 --> 00:29:14,860
-We're going to need the
-environment to do some more
-
-557
-00:29:14,860 --> 00:29:15,800
-evaluations.
-
-558
-00:29:15,800 --> 00:29:18,420
-We're going to need UNEV to look
-at what the rest of those
-
-559
-00:29:18,420 --> 00:29:20,340
-arguments were.
-
-560
-00:29:20,340 --> 00:29:22,170
-We're going to assign continue
-a place called
-
-561
-00:29:22,170 --> 00:29:24,040
-accumulate-args, or
-accumulate-arg.
-
-562
-00:29:24,040 --> 00:29:30,898
-
-
-563
-00:29:30,898 --> 00:29:33,300
-OK, now, we've set up
-for another call to
-
-564
-00:29:33,300 --> 00:29:36,810
-eval-dispatch, OK?
-
-565
-00:29:36,810 --> 00:29:39,510
-All right, now, let me
-short-circuit this so we don't
-
-566
-00:29:39,510 --> 00:29:41,090
-go through the details
-of eval-dispatch.
-
-567
-00:29:41,090 --> 00:29:45,550
-Eval-dispatch's contract says
-I'm going to end up, the world
-
-568
-00:29:45,550 --> 00:29:48,480
-will end up, with the value of
-evaluating this expression in
-
-569
-00:29:48,480 --> 00:29:50,270
-this environment in
-the VAL register,
-
-570
-00:29:50,270 --> 00:29:51,320
-and I'll end up there.
-
-571
-00:29:51,320 --> 00:29:58,010
-So we short-circuit all of this,
-and a 3 ends up in VAL.
-
-572
-00:29:58,010 --> 00:30:00,050
-And, when we return from
-eval-dispatch, we're going to
-
-573
-00:30:00,050 --> 00:30:02,110
-return to accumulate-arg.
-
-574
-00:30:02,110 --> 00:30:03,555
-PROFESSOR: Accumulate-arg.
-
-575
-00:30:03,555 --> 00:30:08,720
-PROFESSOR: With 3 in the
-VAL register, OK?
-
-576
-00:30:08,720 --> 00:30:10,650
-So that short-circuited
-that evaluation.
-
-577
-00:30:10,650 --> 00:30:11,320
-Now, what do we do?
-
-578
-00:30:11,320 --> 00:30:13,230
-We're going to go back and
-look at the rest of the
-
-579
-00:30:13,230 --> 00:30:18,580
-arguments, so we restore
-UNEV. We restore
-
-580
-00:30:18,580 --> 00:30:28,650
-ENV. We restore argl.
-
-581
-00:30:28,650 --> 00:30:29,170
-One thing.
-
-582
-00:30:29,170 --> 00:30:30,750
-PROFESSOR: Oops!
-
-583
-00:30:30,750 --> 00:30:31,290
-Parity error.
-
-584
-00:30:31,290 --> 00:30:33,465
-[LAUGHTER]
-
-585
-00:30:33,465 --> 00:30:34,905
-PROFESSOR: Restore argl.
-
-586
-00:30:34,905 --> 00:30:41,650
-
-
-587
-00:30:41,650 --> 00:30:42,900
-PROFESSOR: OK.
-
-588
-00:30:42,900 --> 00:30:45,570
-
-
-589
-00:30:45,570 --> 00:30:51,880
-OK, we assign to argl consing on
-fetch of the value register
-
-590
-00:30:51,880 --> 00:30:53,130
-to what's in argl.
-
-591
-00:30:53,130 --> 00:30:58,985
-
-
-592
-00:30:58,985 --> 00:31:04,050
-OK, we assign to UNEV the rest
-of the operands in fetch of
-
-593
-00:31:04,050 --> 00:31:11,516
-UNEV, and we go back
-to eval-arg-loop.
-
-594
-00:31:11,516 --> 00:31:12,280
-PROFESSOR: Eval-arg-loop.
-
-595
-00:31:12,280 --> 00:31:13,530
-PROFESSOR: OK.
-
-596
-00:31:13,530 --> 00:31:15,880
-
-
-597
-00:31:15,880 --> 00:31:18,090
-Now, we're about to do the next
-argument, so the first
-
-598
-00:31:18,090 --> 00:31:19,340
-thing we do is save argl.
-
-599
-00:31:19,340 --> 00:31:25,400
-
-
-600
-00:31:25,400 --> 00:31:35,060
-OK, we assign to x the first
-operand of fetch of UNEV. OK,
-
-601
-00:31:35,060 --> 00:31:37,140
-we test and see if that's
-the last operand.
-
-602
-00:31:37,140 --> 00:31:40,320
-In this case, it is, so we're
-going to go to a special place
-
-603
-00:31:40,320 --> 00:31:43,930
-that says evaluate the last
-argument because, notice,
-
-604
-00:31:43,930 --> 00:31:45,600
-after evaluating the argument,
-we don't need the
-
-605
-00:31:45,600 --> 00:31:47,446
-environment any more.
-
-606
-00:31:47,446 --> 00:31:50,250
-That's going to be
-the difference.
-
-607
-00:31:50,250 --> 00:31:53,090
-So here, at eval-last-arg,
-which is assigned to
-
-608
-00:31:53,090 --> 00:32:06,220
-accumulate-last-arg, now,
-we're set up again for
-
-609
-00:32:06,220 --> 00:32:06,900
-eval-dispatch.
-
-610
-00:32:06,900 --> 00:32:08,620
-We've got a place to go
-to when we're done.
-
-611
-00:32:08,620 --> 00:32:09,840
-We've got an expression.
-
-612
-00:32:09,840 --> 00:32:11,330
-We've got an environment.
-
-613
-00:32:11,330 --> 00:32:14,370
-OK, so we'll short-circuit the
-call to eval-dispatch.
-
-614
-00:32:14,370 --> 00:32:18,090
-And what'll happen is there's
-a y there, it's 4 in that
-
-615
-00:32:18,090 --> 00:32:21,060
-environment, so VAL will
-end up with 4 in it.
-
-616
-00:32:21,060 --> 00:32:25,450
-And, then, we're going to end up
-at accumulate-last-arg, OK?
-
-617
-00:32:25,450 --> 00:32:30,150
-So, at accumulate-last-arg,
-we restore argl.
-
-618
-00:32:30,150 --> 00:32:41,490
-
-
-619
-00:32:41,490 --> 00:32:45,460
-We assign to argl cons of fetch
-of the new value onto
-
-620
-00:32:45,460 --> 00:32:49,850
-it, so we cons a 4 onto that.
-
-621
-00:32:49,850 --> 00:32:53,446
-We restore what was saved in
-the function register.
-
-622
-00:32:53,446 --> 00:32:56,590
-And notice, in this case, it had
-not been destroyed, but,
-
-623
-00:32:56,590 --> 00:32:59,420
-in general, it will be.
-
-624
-00:32:59,420 --> 00:33:02,850
-And now, we're ready to go off
-to apply-dispatch, all right?
-
-625
-00:33:02,850 --> 00:33:04,510
-So we've just gone
-through the eval.
-
-626
-00:33:04,510 --> 00:33:07,980
-We evaluated the argument, the
-operator, and the arguments,
-
-627
-00:33:07,980 --> 00:33:09,580
-and now, we're about
-to apply them.
-
-628
-00:33:09,580 --> 00:33:17,481
-So we come off to apply-dispatch
-here, OK?
-
-629
-00:33:17,481 --> 00:33:21,670
-We come off to apply-dispatch,
-and we're going to check
-
-630
-00:33:21,670 --> 00:33:23,450
-whether it's a primitive or
-a compound procedure.
-
-631
-00:33:23,450 --> 00:33:24,116
-PROFESSOR: Yes.
-
-632
-00:33:24,116 --> 00:33:24,830
-PROFESSOR: All right.
-
-633
-00:33:24,830 --> 00:33:27,870
-So, in this case, it's a
-primitive procedure, and we go
-
-634
-00:33:27,870 --> 00:33:29,790
-off to primitive-apply.
-
-635
-00:33:29,790 --> 00:33:34,130
-So we go off to primitive-apply,
-and it says
-
-636
-00:33:34,130 --> 00:33:38,360
-assign to VAL the result of
-applying primitive procedure
-
-637
-00:33:38,360 --> 00:33:40,940
-of the function to the
-argument list.
-
-638
-00:33:40,940 --> 00:33:42,540
-PROFESSOR: I don't
-know how to add.
-
-639
-00:33:42,540 --> 00:33:43,995
-I'm just an execution unit.
-
-640
-00:33:43,995 --> 00:33:45,350
-PROFESSOR: Well, I don't
-know how to add either.
-
-641
-00:33:45,350 --> 00:33:48,360
-I'm just the evaluator, so we
-need a primitive operator.
-
-642
-00:33:48,360 --> 00:33:51,290
-Let's see, so the primitive
-operator, what's the
-
-643
-00:33:51,290 --> 00:33:52,605
-sum of 3 and 4?
-
-644
-00:33:52,605 --> 00:33:53,205
-AUDIENCE: 7.
-
-645
-00:33:53,205 --> 00:33:54,580
-PROFESSOR: OK, 7.
-
-646
-00:33:54,580 --> 00:33:55,999
-PROFESSOR: Thank you.
-
-647
-00:33:55,999 --> 00:33:58,837
-
-
-648
-00:33:58,837 --> 00:34:12,330
-PROFESSOR: Now, we restore
-continue, and we go to fetch
-
-649
-00:34:12,330 --> 00:34:12,900
-of continue.
-
-650
-00:34:12,900 --> 00:34:13,880
-PROFESSOR: Done.
-
-651
-00:34:13,880 --> 00:34:14,929
-PROFESSOR: OK.
-
-652
-00:34:14,929 --> 00:34:18,659
-Well, that was in as much detail
-as you will ever see.
-
-653
-00:34:18,659 --> 00:34:21,590
-We'll never do it in as
-much detail again.
-
-654
-00:34:21,590 --> 00:34:25,780
-One very important thing to
-notice is that we just
-
-655
-00:34:25,780 --> 00:34:29,780
-executed a recursive
-procedure, right?
-
-656
-00:34:29,780 --> 00:34:31,500
-This whole thing, we used
-a stack and the
-
-657
-00:34:31,500 --> 00:34:33,070
-evaluator was recursive.
-
-658
-00:34:33,070 --> 00:34:36,480
-A lot of people think the reason
-that you need a stack
-
-659
-00:34:36,480 --> 00:34:39,090
-and recursion in an evaluator
-is because you might be
-
-660
-00:34:39,090 --> 00:34:40,810
-evaluating recursive
-procedures like
-
-661
-00:34:40,810 --> 00:34:42,150
-factorial or Fibonacci.
-
-662
-00:34:42,150 --> 00:34:43,670
-It's not true.
-
-663
-00:34:43,670 --> 00:34:46,110
-So you notice we did recursion
-here, and all we evaluated was
-
-664
-00:34:46,110 --> 00:34:48,010
-plus X, Y, all right?
-
-665
-00:34:48,010 --> 00:34:51,219
-The reason that you need
-recursion in the evaluator is
-
-666
-00:34:51,219 --> 00:34:53,550
-because the evaluation
-process, itself, is
-
-667
-00:34:53,550 --> 00:34:54,780
-recursive, all right?
-
-668
-00:34:54,780 --> 00:34:57,760
-It's not because the procedure
-that you might be evaluating
-
-669
-00:34:57,760 --> 00:34:59,270
-in LISP is a recursive
-procedure.
-
-670
-00:34:59,270 --> 00:35:01,130
-So that's an important
-thing that people get
-
-671
-00:35:01,130 --> 00:35:03,010
-confused about a lot.
-
-672
-00:35:03,010 --> 00:35:06,280
-The other thing to notice is
-that, when we're done here,
-
-673
-00:35:06,280 --> 00:35:07,120
-we're really done.
-
-674
-00:35:07,120 --> 00:35:12,600
-Not only are we at done, but
-there's no accumulated stuff
-
-675
-00:35:12,600 --> 00:35:13,810
-on the stack, right?
-
-676
-00:35:13,810 --> 00:35:17,170
-The machine is back to its
-initial state, all right?
-
-677
-00:35:17,170 --> 00:35:19,830
-So that's part of what
-it means to be done.
-
-678
-00:35:19,830 --> 00:35:26,410
-Another way to say that is the
-evaluation process has reduced
-
-679
-00:35:26,410 --> 00:35:33,460
-the expression, plus X, Y,
-to the value here, 7.
-
-680
-00:35:33,460 --> 00:35:36,010
-And by reduced, I mean a
-very particular thing.
-
-681
-00:35:36,010 --> 00:35:38,180
-It means that there's nothing
-left on the stack.
-
-682
-00:35:38,180 --> 00:35:41,480
-The machine is now in the same
-state, except there's
-
-683
-00:35:41,480 --> 00:35:42,760
-something in the
-value register.
-
-684
-00:35:42,760 --> 00:35:44,520
-It's not part of a sub-problem
-of anything.
-
-685
-00:35:44,520 --> 00:35:46,210
-There's nothing to go back to.
-
-686
-00:35:46,210 --> 00:35:46,440
-OK.
-
-687
-00:35:46,440 --> 00:35:47,690
-Let's break.
-
-688
-00:35:47,690 --> 00:35:49,712
-
-
-689
-00:35:49,712 --> 00:35:50,159
-Question?
-
-690
-00:35:50,159 --> 00:35:54,800
-AUDIENCE: The question here, in
-the stack, is because the
-
-691
-00:35:54,800 --> 00:35:55,820
-data may be recursive.
-
-692
-00:35:55,820 --> 00:35:59,312
-You may have embedded
-expressions, for instance.
-
-693
-00:35:59,312 --> 00:36:01,490
-PROFESSOR: Yes, because you
-might have embedded
-
-694
-00:36:01,490 --> 00:36:02,080
-expressions.
-
-695
-00:36:02,080 --> 00:36:06,400
-But, again, don't confuse that
-with what people sometimes
-
-696
-00:36:06,400 --> 00:36:08,660
-mean by the data may be
-recursive, which is to say you
-
-697
-00:36:08,660 --> 00:36:12,270
-have these list-structured,
-recursive data list
-
-698
-00:36:12,270 --> 00:36:12,930
-operations.
-
-699
-00:36:12,930 --> 00:36:13,980
-That has nothing
-to do with it.
-
-700
-00:36:13,980 --> 00:36:15,360
-It's simply that the
-expressions contain
-
-701
-00:36:15,360 --> 00:36:17,363
-sub-expressions.
-
-702
-00:36:17,363 --> 00:36:19,618
-Yeah?
-
-703
-00:36:19,618 --> 00:36:22,260
-AUDIENCE: Why is it that the
-order of the arguments in the
-
-704
-00:36:22,260 --> 00:36:23,225
-arg list got reversed?
-
-705
-00:36:23,225 --> 00:36:23,860
-PROFESSOR: Ah!
-
-706
-00:36:23,860 --> 00:36:27,260
-Yes, I should've
-mentioned that.
-
-707
-00:36:27,260 --> 00:36:28,755
-Here, the reason the
-order is reversed--
-
-708
-00:36:28,755 --> 00:36:32,507
-
-
-709
-00:36:32,507 --> 00:36:36,050
-it's a question of what
-you mean by reversed.
-
-710
-00:36:36,050 --> 00:36:40,624
-I believe it was Newton.
-
-711
-00:36:40,624 --> 00:36:43,800
-In the very early part of
-optics, people realized that,
-
-712
-00:36:43,800 --> 00:36:46,100
-when you look through the lens
-of your eye, the image was
-
-713
-00:36:46,100 --> 00:36:46,840
-up-side down.
-
-714
-00:36:46,840 --> 00:36:48,650
-And there was a lot of argument
-about why that didn't
-
-715
-00:36:48,650 --> 00:36:51,280
-mean you saw things
-up-side down.
-
-716
-00:36:51,280 --> 00:36:52,860
-So it's sort of the
-same issue.
-
-717
-00:36:52,860 --> 00:36:54,810
-Reversed from what?
-
-718
-00:36:54,810 --> 00:36:57,940
-So we just need some
-convention.
-
-719
-00:36:57,940 --> 00:37:01,730
-The reason that they're coming
-at 4, 3 is because we're
-
-720
-00:37:01,730 --> 00:37:04,520
-taking UNEV and consing
-the result onto argl.
-
-721
-00:37:04,520 --> 00:37:06,900
-So you have to realize you've
-made that convention.
-
-722
-00:37:06,900 --> 00:37:10,100
-The place that you have
-to realize that--
-
-723
-00:37:10,100 --> 00:37:11,230
-well, there's actually
-two places.
-
-724
-00:37:11,230 --> 00:37:12,910
-One is in
-apply-primitive-operator,
-
-725
-00:37:12,910 --> 00:37:16,610
-which has to realize that the
-arguments to primitives go in,
-
-726
-00:37:16,610 --> 00:37:19,490
-in the opposite order from the
-way you're writing them down.
-
-727
-00:37:19,490 --> 00:37:21,760
-And the other one is, we'll see
-later when you actually go
-
-728
-00:37:21,760 --> 00:37:24,720
-to bind a function's parameters,
-you should realize
-
-729
-00:37:24,720 --> 00:37:26,410
-the arguments are going to
-come in from the opposite
-
-730
-00:37:26,410 --> 00:37:28,870
-order of the variables to which
-you're binding them.
-
-731
-00:37:28,870 --> 00:37:31,830
-So, if you just keep track of
-that, there's no problem.
-
-732
-00:37:31,830 --> 00:37:34,560
-Also, this is completely
-arbitrary because, if we'd
-
-733
-00:37:34,560 --> 00:37:36,890
-done, say, an iteration through
-a vector assigning
-
-734
-00:37:36,890 --> 00:37:40,730
-them, they might come out
-in the other order, OK?
-
-735
-00:37:40,730 --> 00:37:42,700
-So it's just a convention of
-the way this particular
-
-736
-00:37:42,700 --> 00:37:45,085
-evaluator works.
-
-737
-00:37:45,085 --> 00:37:46,335
-All right, let's take a break.
-
-738
-00:37:46,335 --> 00:38:41,840
-
-
-739
-00:38:41,840 --> 00:38:46,050
-We just saw evaluating an
-expression and, of course,
-
-740
-00:38:46,050 --> 00:38:46,950
-that was very simple one.
-
-741
-00:38:46,950 --> 00:38:51,020
-But, in essence, it would be
-no different if it was some
-
-742
-00:38:51,020 --> 00:38:53,370
-big nested expression, so there
-would just be deeper
-
-743
-00:38:53,370 --> 00:38:55,130
-recursion on the stack.
-
-744
-00:38:55,130 --> 00:38:56,920
-But what I want to do now is
-show you the last piece.
-
-745
-00:38:56,920 --> 00:39:01,300
-I want to walk you around this
-eval and apply loop, right?
-
-746
-00:39:01,300 --> 00:39:03,000
-That's the thing we haven't
-seen, really.
-
-747
-00:39:03,000 --> 00:39:09,070
-We haven't seen any compound
-procedures where applying a
-
-748
-00:39:09,070 --> 00:39:11,110
-procedure reduces to evaluating
-the body of the
-
-749
-00:39:11,110 --> 00:39:15,810
-procedure, so let's just
-suppose we had this.
-
-750
-00:39:15,810 --> 00:39:29,340
-Suppose we were looking at the
-procedure define F of A and B
-
-751
-00:39:29,340 --> 00:39:36,520
-to be the sum of A and B. So, as
-we typed in that procedure
-
-752
-00:39:36,520 --> 00:39:41,120
-previously, and now we're going
-to evaluate F of X and
-
-753
-00:39:41,120 --> 00:39:46,030
-Y, again, in this environment,
-E,0, where X is bound to 3 and
-
-754
-00:39:46,030 --> 00:39:47,280
-Y is bound to 4.
-
-755
-00:39:47,280 --> 00:39:50,830
-
-
-756
-00:39:50,830 --> 00:39:53,120
-When the defined is executed,
-remember, there's a lambda
-
-757
-00:39:53,120 --> 00:39:55,950
-here, and lambdas create
-procedures.
-
-758
-00:39:55,950 --> 00:40:01,430
-And, basically, what will happen
-is, in E,0, we'll end
-
-759
-00:40:01,430 --> 00:40:07,440
-up with a binding for F, which
-will say F is a procedure, and
-
-760
-00:40:07,440 --> 00:40:18,180
-its args are A and B, and
-its body is plus a,b.
-
-761
-00:40:18,180 --> 00:40:21,460
-So that's what the environment
-would have looked like had we
-
-762
-00:40:21,460 --> 00:40:24,400
-made that definition.
-
-763
-00:40:24,400 --> 00:40:29,180
-Then, when we go to evaluate F
-of X and Y, we'll go through
-
-764
-00:40:29,180 --> 00:40:31,810
-exactly the same process
-that we did before.
-
-765
-00:40:31,810 --> 00:40:33,360
-It's even the same expression.
-
-766
-00:40:33,360 --> 00:40:36,030
-The only difference is that F,
-instead of having primitive
-
-767
-00:40:36,030 --> 00:40:41,040
-plus in it, will have
-this thing.
-
-768
-00:40:41,040 --> 00:40:43,600
-And so we'll go through exactly
-the same process,
-
-769
-00:40:43,600 --> 00:40:48,130
-except this time, when we end
-up at apply-dispatch, the
-
-770
-00:40:48,130 --> 00:40:50,590
-function register, instead of
-having primitive plus, will
-
-771
-00:40:50,590 --> 00:40:54,300
-have a thing that will represent
-it saying procedure,
-
-772
-00:40:54,300 --> 00:41:08,040
-where the args are A and B,
-and the body is plus A, B.
-
-773
-00:41:08,040 --> 00:41:10,420
-And, again, what I mean, by
-its ENV, I mean there's a
-
-774
-00:41:10,420 --> 00:41:12,530
-pointer to it, so don't worry
-that I'm writing a lot of
-
-775
-00:41:12,530 --> 00:41:13,280
-stuff there.
-
-776
-00:41:13,280 --> 00:41:17,170
-There's a pointer to this
-procedure data structure.
-
-777
-00:41:17,170 --> 00:41:20,960
-OK, so, we're in exactly
-the same situation.
-
-778
-00:41:20,960 --> 00:41:25,720
-We get to apply-dispatch,
-so, here, we come to
-
-779
-00:41:25,720 --> 00:41:26,480
-apply-dispatch.
-
-780
-00:41:26,480 --> 00:41:30,010
-Last time, we branched off
-to a primitive procedure.
-
-781
-00:41:30,010 --> 00:41:34,900
-Here, it says oh, we now have a
-compound procedure, so we're
-
-782
-00:41:34,900 --> 00:41:36,150
-going to go off to
-compound-apply.
-
-783
-00:41:36,150 --> 00:41:38,660
-
-
-784
-00:41:38,660 --> 00:41:39,910
-Now, what's compound-apply?
-
-785
-00:41:39,910 --> 00:41:42,100
-
-
-786
-00:41:42,100 --> 00:41:45,090
-Well, remember what the
-meta-circular evaluator did?
-
-787
-00:41:45,090 --> 00:41:50,790
-Compound-apply said we're going
-to evaluate the body of
-
-788
-00:41:50,790 --> 00:41:54,120
-the procedure in some
-new environment.
-
-789
-00:41:54,120 --> 00:41:56,730
-Where does that new environment
-come from?
-
-790
-00:41:56,730 --> 00:42:00,620
-We take the environment that
-was packaged with the
-
-791
-00:42:00,620 --> 00:42:06,080
-procedure, we bind the
-parameters of the procedure to
-
-792
-00:42:06,080 --> 00:42:10,760
-the arguments that we're passing
-in, and use that as a
-
-793
-00:42:10,760 --> 00:42:14,990
-new frame to extend the
-procedure environment.
-
-794
-00:42:14,990 --> 00:42:18,100
-And that's the environment
-in which we evaluate the
-
-795
-00:42:18,100 --> 00:42:21,630
-procedure body, right?
-
-796
-00:42:21,630 --> 00:42:24,470
-That's going around the
-apply/eval loop.
-
-797
-00:42:24,470 --> 00:42:27,988
-That's apply coming back to
-call eval, all right?
-
-798
-00:42:27,988 --> 00:42:30,910
-
-
-799
-00:42:30,910 --> 00:42:32,860
-OK.
-
-800
-00:42:32,860 --> 00:42:36,950
-So, now, that's all we have
-to do in compound-apply.
-
-801
-00:42:36,950 --> 00:42:37,720
-What are we going to do?
-
-802
-00:42:37,720 --> 00:42:40,730
-We're going to manufacture
-a new environment.
-
-803
-00:42:40,730 --> 00:42:43,720
-
-
-804
-00:42:43,720 --> 00:42:47,060
-And we're going to manufacture
-a new environment, let's see,
-
-805
-00:42:47,060 --> 00:42:48,310
-that we'll call E,1.
-
-806
-00:42:48,310 --> 00:42:53,100
-
-
-807
-00:42:53,100 --> 00:42:57,830
-E,1 is going to be some
-environment where the
-
-808
-00:42:57,830 --> 00:43:02,460
-parameters of the procedure,
-where A is bound to 3 and B is
-
-809
-00:43:02,460 --> 00:43:06,220
-bound to 4, and it's linked
-to E,0 because
-
-810
-00:43:06,220 --> 00:43:09,270
-that's where f is defined.
-
-811
-00:43:09,270 --> 00:43:11,090
-And, in this environment, we're
-going to evaluate the
-
-812
-00:43:11,090 --> 00:43:12,050
-body of the procedure.
-
-813
-00:43:12,050 --> 00:43:13,870
-So let's look at that,
-all right?
-
-814
-00:43:13,870 --> 00:43:16,730
-
-
-815
-00:43:16,730 --> 00:43:20,690
-All right, here we are at
-compound-apply, which says
-
-816
-00:43:20,690 --> 00:43:25,560
-assign to the expression
-register the body of the
-
-817
-00:43:25,560 --> 00:43:28,300
-procedure that's in the
-function register.
-
-818
-00:43:28,300 --> 00:43:31,470
-So I assign to the expression
-register the
-
-819
-00:43:31,470 --> 00:43:42,710
-procedure body, OK?
-
-820
-00:43:42,710 --> 00:43:46,300
-That's going to be evaluated
-in an environment which is
-
-821
-00:43:46,300 --> 00:43:53,040
-formed by making some bindings
-using information determined
-
-822
-00:43:53,040 --> 00:43:53,860
-by the procedure--
-
-823
-00:43:53,860 --> 00:43:55,320
-that's what's in FUN--
-
-824
-00:43:55,320 --> 00:43:57,800
-and the argument list.
-
-825
-00:43:57,800 --> 00:44:00,230
-And let's not worry about
-exactly what that does, but
-
-826
-00:44:00,230 --> 00:44:01,930
-you can see the information's
-there.
-
-827
-00:44:01,930 --> 00:44:06,420
-So make bindings will say oh,
-the procedure, itself, had an
-
-828
-00:44:06,420 --> 00:44:08,200
-environment attached to it.
-
-829
-00:44:08,200 --> 00:44:09,320
-I didn't write that
-quite here.
-
-830
-00:44:09,320 --> 00:44:11,810
-I should've said in environment
-because every
-
-831
-00:44:11,810 --> 00:44:13,660
-procedure gets built with
-an environment.
-
-832
-00:44:13,660 --> 00:44:17,400
-So, from that environment, it
-knows what the procedure's
-
-833
-00:44:17,400 --> 00:44:19,290
-definition environment is.
-
-834
-00:44:19,290 --> 00:44:21,830
-It knows what the
-arguments are.
-
-835
-00:44:21,830 --> 00:44:23,060
-It looks at argl, and
-then you see a
-
-836
-00:44:23,060 --> 00:44:24,280
-reversal convention here.
-
-837
-00:44:24,280 --> 00:44:27,830
-It just has to know that argl
-is reversed, and it builds
-
-838
-00:44:27,830 --> 00:44:29,990
-this frame, E,1.
-
-839
-00:44:29,990 --> 00:44:32,400
-All right, so, let's assume that
-that's what make bindings
-
-840
-00:44:32,400 --> 00:44:35,780
-returns, so it assigns to
-ENV this thing, E,1.
-
-841
-00:44:35,780 --> 00:44:41,490
-
-
-842
-00:44:41,490 --> 00:44:46,890
-All right, the next thing it
-says is restore continue.
-
-843
-00:44:46,890 --> 00:44:48,760
-Remember what continue
-was here?
-
-844
-00:44:48,760 --> 00:44:52,240
-It got put up in the
-last segment.
-
-845
-00:44:52,240 --> 00:44:54,020
-Continue got stored.
-
-846
-00:44:54,020 --> 00:44:56,180
-That was the original done,
-which said what are you going
-
-847
-00:44:56,180 --> 00:44:59,920
-to do after you're done with
-this particular application?
-
-848
-00:44:59,920 --> 00:45:01,980
-It was one of the very first
-things that happened when we
-
-849
-00:45:01,980 --> 00:45:03,920
-evaluated the application.
-
-850
-00:45:03,920 --> 00:45:06,860
-And now, finally, we're going
-to restore continue.
-
-851
-00:45:06,860 --> 00:45:09,290
-Remember apply-dispatch's
-contract.
-
-852
-00:45:09,290 --> 00:45:11,570
-It assumes that where it should
-go to next was on the
-
-853
-00:45:11,570 --> 00:45:13,590
-stack, and there it
-was on the stack.
-
-854
-00:45:13,590 --> 00:45:19,310
-Continue has done, and now
-we're going to go back to
-
-855
-00:45:19,310 --> 00:45:19,940
-eval-dispatch.
-
-856
-00:45:19,940 --> 00:45:20,970
-We're set up again.
-
-857
-00:45:20,970 --> 00:45:23,470
-We have an expression,
-an environment, and
-
-858
-00:45:23,470 --> 00:45:25,511
-a place to go to.
-
-859
-00:45:25,511 --> 00:45:28,690
-We're not going to go through
-that because it's sort of the
-
-860
-00:45:28,690 --> 00:45:29,940
-same expression.
-
-861
-00:45:29,940 --> 00:45:35,167
-
-
-862
-00:45:35,167 --> 00:45:39,590
-OK, but the thing, again, to
-notice is, at this point, we
-
-863
-00:45:39,590 --> 00:45:44,830
-have reduced the original
-expression, F,X,Y, right?
-
-864
-00:45:44,830 --> 00:45:50,150
-We've reduced evaluating F,X,Y
-in environment E,0 to evaluate
-
-865
-00:45:50,150 --> 00:45:52,670
-plus A, B in E,1.
-
-866
-00:45:52,670 --> 00:45:55,720
-And notice, nothing's
-on the stack, right?
-
-867
-00:45:55,720 --> 00:45:56,830
-It's a reduction.
-
-868
-00:45:56,830 --> 00:46:00,530
-At this point, the machine does
-not contain, as part of
-
-869
-00:46:00,530 --> 00:46:03,790
-its state, the fact that it's
-in the middle of evaluating
-
-870
-00:46:03,790 --> 00:46:08,090
-some procedure called f,
-that's gone, right?
-
-871
-00:46:08,090 --> 00:46:13,072
-There's no accumulated
-state, OK?
-
-872
-00:46:13,072 --> 00:46:14,370
-Again, that's a very
-important idea.
-
-873
-00:46:14,370 --> 00:46:17,590
-That's the meaning of, when
-we used to write in the
-
-874
-00:46:17,590 --> 00:46:20,430
-substitution model, this
-expression reduces to that
-
-875
-00:46:20,430 --> 00:46:21,350
-expression.
-
-876
-00:46:21,350 --> 00:46:22,660
-And you don't have to
-remember anything.
-
-877
-00:46:22,660 --> 00:46:24,500
-And here, you see the meaning
-of reduction.
-
-878
-00:46:24,500 --> 00:46:26,160
-At this point, there is
-nothing on the stack.
-
-879
-00:46:26,160 --> 00:46:31,590
-
-
-880
-00:46:31,590 --> 00:46:35,240
-See, that has very important
-consequences.
-
-881
-00:46:35,240 --> 00:46:37,180
-Let's go back and look
-at iterative
-
-882
-00:46:37,180 --> 00:46:40,590
-factorial, all right?
-
-883
-00:46:40,590 --> 00:46:45,130
-Remember, this was some sort
-of loop and doing iter.
-
-884
-00:46:45,130 --> 00:46:49,430
-And we kept saying that's an
-iterative procedure, right?
-
-885
-00:46:49,430 --> 00:46:52,570
-
-
-886
-00:46:52,570 --> 00:47:04,660
-And what we wrote, remember,
-are things like, we said,
-
-887
-00:47:04,660 --> 00:47:12,360
-fact-iter of 5.
-
-888
-00:47:12,360 --> 00:47:19,030
-We wrote things like reduces
-to iter of 1, and 1, and 5,
-
-889
-00:47:19,030 --> 00:47:26,550
-which reduces to iter of 1, and
-2, and 5, and so on, and
-
-890
-00:47:26,550 --> 00:47:27,210
-so on, and so on.
-
-891
-00:47:27,210 --> 00:47:29,360
-And we kept saying well, look,
-you don't have to build up any
-
-892
-00:47:29,360 --> 00:47:31,720
-storage to do that.
-
-893
-00:47:31,720 --> 00:47:33,730
-And we waved our hands, and said
-in principle, there's no
-
-894
-00:47:33,730 --> 00:47:35,040
-storage needed.
-
-895
-00:47:35,040 --> 00:47:36,170
-Now, you see no storage
-needed.
-
-896
-00:47:36,170 --> 00:47:39,090
-Each of these is a real
-reduction, right?
-
-897
-00:47:39,090 --> 00:47:49,280
-
-
-898
-00:47:49,280 --> 00:47:51,370
-As you walk through these
-expressions, what you'll see
-
-899
-00:47:51,370 --> 00:47:54,810
-are these expressions on the
-stack in some particular
-
-900
-00:47:54,810 --> 00:48:00,045
-environment, and then these
-expressions in the EXP
-
-901
-00:48:00,045 --> 00:48:01,650
-register in some particular
-environment.
-
-902
-00:48:01,650 --> 00:48:03,570
-And, at each point, there'll be
-no accumulated stuff on the
-
-903
-00:48:03,570 --> 00:48:09,135
-stack because each one's
-a real reduction, OK?
-
-904
-00:48:09,135 --> 00:48:11,520
-All right, so, for example,
-just to go through it in a
-
-905
-00:48:11,520 --> 00:48:15,510
-little bit more care, if I start
-out with an expression
-
-906
-00:48:15,510 --> 00:48:33,520
-that says something like, oh,
-say, fact-iter of 5 in some
-
-907
-00:48:33,520 --> 00:48:46,810
-environment that will, at some
-point, create an environment
-
-908
-00:48:46,810 --> 00:48:48,120
-in which n is down to 5.
-
-909
-00:48:48,120 --> 00:48:51,340
-
-
-910
-00:48:51,340 --> 00:48:52,590
-Let's call that--
-
-911
-00:48:52,590 --> 00:48:55,750
-
-
-912
-00:48:55,750 --> 00:49:02,120
-And, at some point, the machine
-will reduce this whole
-
-913
-00:49:02,120 --> 00:49:08,780
-thing to a thing that says
-that's really iter of 1, and
-
-914
-00:49:08,780 --> 00:49:16,550
-1, and n, evaluated in this
-environment, E,1 with nothing
-
-915
-00:49:16,550 --> 00:49:17,160
-on the stack.
-
-916
-00:49:17,160 --> 00:49:20,710
-See, at this moment, the machine
-is not remembering
-
-917
-00:49:20,710 --> 00:49:22,500
-that evaluating this
-expression, iter--
-
-918
-00:49:22,500 --> 00:49:25,000
-
-
-919
-00:49:25,000 --> 00:49:27,280
-which is the loop-- is
-part of this thing
-
-920
-00:49:27,280 --> 00:49:29,366
-called iterative factorial.
-
-921
-00:49:29,366 --> 00:49:30,590
-It's not remembering that.
-
-922
-00:49:30,590 --> 00:49:33,170
-It's just reducing the
-expression to that, right?
-
-923
-00:49:33,170 --> 00:49:38,390
-If we look again at the body of
-iterative factorial, this
-
-924
-00:49:38,390 --> 00:49:42,810
-expression has reduced
-to that expression.
-
-925
-00:49:42,810 --> 00:49:44,060
-Oh, I shouldn't have
-the n there.
-
-926
-00:49:44,060 --> 00:49:46,590
-
-
-927
-00:49:46,590 --> 00:49:48,495
-It's a slightly different
-convention from the slide to
-
-928
-00:49:48,495 --> 00:49:53,340
-the program, OK?
-
-929
-00:49:53,340 --> 00:49:56,310
-And, then, what's the
-body of iter?
-
-930
-00:49:56,310 --> 00:49:59,460
-Well, iter's going to be an it,
-and I won't go through the
-
-931
-00:49:59,460 --> 00:50:00,060
-details of if.
-
-932
-00:50:00,060 --> 00:50:02,540
-It'll evaluate the predicate.
-
-933
-00:50:02,540 --> 00:50:03,810
-In this case, it'll be false.
-
-934
-00:50:03,810 --> 00:50:14,490
-And this iter will now reduce
-to the expression iter of
-
-935
-00:50:14,490 --> 00:50:21,620
-whatever it says, star,
-counter product, and--
-
-936
-00:50:21,620 --> 00:50:22,650
-what does it say--
-
-937
-00:50:22,650 --> 00:50:30,820
-plus counter 1 in some other
-environment, by this time,
-
-938
-00:50:30,820 --> 00:50:38,840
-E,2, where E,2 will be set up
-having bindings for product
-
-939
-00:50:38,840 --> 00:50:43,200
-and counter, right?
-
-940
-00:50:43,200 --> 00:50:45,140
-And it'll reduce
-to that, right?
-
-941
-00:50:45,140 --> 00:50:47,925
-It won't be remembering that
-it's part of something that it
-
-942
-00:50:47,925 --> 00:50:49,340
-has to return to.
-
-943
-00:50:49,340 --> 00:50:51,500
-And when iter calls iter again,
-it'll reduce to another
-
-944
-00:50:51,500 --> 00:50:55,050
-thing that looks like this in
-some environment, E,3, which
-
-945
-00:50:55,050 --> 00:50:59,160
-has new bindings for product
-and counter.
-
-946
-00:50:59,160 --> 00:51:08,450
-So, if you're wondering, see,
-if you've always been queasy
-
-947
-00:51:08,450 --> 00:51:10,920
-about how it is we've been
-saying those procedures, that
-
-948
-00:51:10,920 --> 00:51:16,095
-look syntactically recursive,
-are, in fact, iterative, run
-
-949
-00:51:16,095 --> 00:51:19,230
-in constant space, well, I don't
-know if this makes you
-
-950
-00:51:19,230 --> 00:51:21,230
-less queasy, but at least it
-shows you what's happening.
-
-951
-00:51:21,230 --> 00:51:22,830
-There really isn't any
-buildup there.
-
-952
-00:51:22,830 --> 00:51:25,910
-
-
-953
-00:51:25,910 --> 00:51:28,830
-Now, you might ask well, is
-there buildup in principle in
-
-954
-00:51:28,830 --> 00:51:31,710
-these environment frames?
-
-955
-00:51:31,710 --> 00:51:33,240
-And the answer is yeah, you
-have to make these new
-
-956
-00:51:33,240 --> 00:51:35,560
-environment frames, but you
-don't have to hang onto them
-
-957
-00:51:35,560 --> 00:51:36,440
-when you're done.
-
-958
-00:51:36,440 --> 00:51:39,020
-They can be garbage collected,
-or the space can be reused
-
-959
-00:51:39,020 --> 00:51:40,720
-automatically.
-
-960
-00:51:40,720 --> 00:51:43,520
-But you see the control
-structure of the evaluator is
-
-961
-00:51:43,520 --> 00:51:47,020
-really using this idea that you
-actually have a reduction,
-
-962
-00:51:47,020 --> 00:51:50,132
-so these procedures really
-are iterative procedures.
-
-963
-00:51:50,132 --> 00:51:51,382
-All right, let's stop
-for questions.
-
-964
-00:51:51,382 --> 00:52:02,288
-
-
-965
-00:52:02,288 --> 00:52:03,538
-All right, let's break.
-
-966
-00:52:03,538 --> 00:52:48,770
-
-
-967
-00:52:48,770 --> 00:52:53,470
-Let me contrast the iterative
-procedure just so you'll see
-
-968
-00:52:53,470 --> 00:52:56,480
-where space does build up with
-a recursive procedure, so you
-
-969
-00:52:56,480 --> 00:52:58,030
-can see the difference.
-
-970
-00:52:58,030 --> 00:53:00,470
-Let's look at the evaluation
-of recursive
-
-971
-00:53:00,470 --> 00:53:02,880
-factorial, all right?
-
-972
-00:53:02,880 --> 00:53:07,220
-So, here's fact-recursive, or
-standard factorial definition.
-
-973
-00:53:07,220 --> 00:53:10,360
-We said this one is still a
-recursive procedure, but this
-
-974
-00:53:10,360 --> 00:53:13,750
-is actually a recursive
-process.
-
-975
-00:53:13,750 --> 00:53:17,210
-And then, just to link it back
-to the way we started, we said
-
-976
-00:53:17,210 --> 00:53:20,530
-oh, you can see that it's going
-to be recursive process
-
-977
-00:53:20,530 --> 00:53:24,520
-by the substitution model
-because, if I say recursive
-
-978
-00:53:24,520 --> 00:53:36,000
-factorial of 5, that turns
-into 5 times--
-
-979
-00:53:36,000 --> 00:53:37,989
-what is it, fact-rec,
-or record fact--
-
-980
-00:53:37,989 --> 00:53:42,620
-
-
-981
-00:53:42,620 --> 00:53:54,230
-5 times recursive factorial of
-4, which turns into 5 times 4
-
-982
-00:53:54,230 --> 00:54:08,090
-times fact-rec of 3, which
-returns into 5 times 4 times 3
-
-983
-00:54:08,090 --> 00:54:15,240
-times, and so on, right?
-
-984
-00:54:15,240 --> 00:54:18,100
-The idea is there was this chain
-of stuff building up,
-
-985
-00:54:18,100 --> 00:54:20,540
-which justified, in the
-substitution model, the fact
-
-986
-00:54:20,540 --> 00:54:21,520
-that it's recursive.
-
-987
-00:54:21,520 --> 00:54:24,180
-And now, let's actually see that
-chain of stuff build up
-
-988
-00:54:24,180 --> 00:54:27,465
-and where it is in
-the machine, OK?
-
-989
-00:54:27,465 --> 00:54:28,970
-All right, well, let's
-imagine we're going
-
-990
-00:54:28,970 --> 00:54:30,230
-to start out again.
-
-991
-00:54:30,230 --> 00:54:41,690
-We'll tell it to evaluate
-recursive factorial of 5 in
-
-992
-00:54:41,690 --> 00:54:46,360
-some environment, again, E,0
-where recursive factorial is
-
-993
-00:54:46,360 --> 00:54:49,580
-defined, OK?
-
-994
-00:54:49,580 --> 00:54:52,490
-Well, now we know what's
-eventually going to happen.
-
-995
-00:54:52,490 --> 00:54:55,670
-This is going to come along,
-it'll evaluate those things,
-
-996
-00:54:55,670 --> 00:54:58,860
-figure out it's a procedure,
-build somewhere over here an
-
-997
-00:54:58,860 --> 00:55:05,860
-environment, E,1, which has n
-bound to 5, which hangs off of
-
-998
-00:55:05,860 --> 00:55:09,620
-E,0, which would be, presumably,
-the definition
-
-999
-00:55:09,620 --> 00:55:14,610
-environment of recursive
-factorial, OK?
-
-1000
-00:55:14,610 --> 00:55:16,490
-And, in this environment,
-it's going to go off and
-
-1001
-00:55:16,490 --> 00:55:19,670
-evaluate the body.
-
-1002
-00:55:19,670 --> 00:55:27,860
-So, again, the evaluation here
-will reduce to evaluating the
-
-1003
-00:55:27,860 --> 00:55:30,240
-body in E,1.
-
-1004
-00:55:30,240 --> 00:55:32,880
-That's going to look at an if,
-and I won't go through the
-
-1005
-00:55:32,880 --> 00:55:33,530
-details of if.
-
-1006
-00:55:33,530 --> 00:55:34,880
-It'll look at the predicate.
-
-1007
-00:55:34,880 --> 00:55:37,840
-It'll decide it eventually has
-to evaluate the alternative.
-
-1008
-00:55:37,840 --> 00:55:43,122
-So this whole thing, again, will
-reduce to the alternative
-
-1009
-00:55:43,122 --> 00:55:47,870
-of recursive factorial, the
-alternative clause, which says
-
-1010
-00:55:47,870 --> 00:55:56,040
-that this whole thing reduces
-to times n of recursive
-
-1011
-00:55:56,040 --> 00:56:08,720
-factorial of n minus 1 in
-the environment E,1, OK?
-
-1012
-00:56:08,720 --> 00:56:11,200
-So the original expression,
-now, is going to reduce to
-
-1013
-00:56:11,200 --> 00:56:14,130
-evaluating that expression,
-all right?
-
-1014
-00:56:14,130 --> 00:56:16,280
-Now we have an application.
-
-1015
-00:56:16,280 --> 00:56:18,500
-We did an application before.
-
-1016
-00:56:18,500 --> 00:56:20,390
-Remember what happens
-in an application?
-
-1017
-00:56:20,390 --> 00:56:23,230
-The first thing you do is you go
-off and you save the value
-
-1018
-00:56:23,230 --> 00:56:25,350
-of the continue register
-on the stack.
-
-1019
-00:56:25,350 --> 00:56:27,365
-So the stack here is going
-to have done in it.
-
-1020
-00:56:27,365 --> 00:56:29,980
-
-
-1021
-00:56:29,980 --> 00:56:32,230
-And then you're going to
-set up to evaluate
-
-1022
-00:56:32,230 --> 00:56:35,130
-the sub-parts, OK?
-
-1023
-00:56:35,130 --> 00:56:36,710
-So here we go off to evaluate
-the sub-parts.
-
-1024
-00:56:36,710 --> 00:56:39,520
-
-
-1025
-00:56:39,520 --> 00:56:41,045
-First thing we're going to do
-is evaluate the operator.
-
-1026
-00:56:41,045 --> 00:56:44,490
-
-
-1027
-00:56:44,490 --> 00:56:47,250
-What happens when we evaluate
-an operator?
-
-1028
-00:56:47,250 --> 00:56:49,940
-Well, we arrange things so that
-the operator ends up in
-
-1029
-00:56:49,940 --> 00:56:51,480
-the expression register.
-
-1030
-00:56:51,480 --> 00:56:54,630
-The environments in the ENV
-register continue someplace
-
-1031
-00:56:54,630 --> 00:56:56,590
-where we're going to go evaluate
-the arguments.
-
-1032
-00:56:56,590 --> 00:56:59,520
-And, on the stack, we've saved
-the original continue, which
-
-1033
-00:56:59,520 --> 00:57:01,720
-is where we wanted to be
-when we're all done.
-
-1034
-00:57:01,720 --> 00:57:04,510
-And then the things we needed
-when we're going to get done
-
-1035
-00:57:04,510 --> 00:57:07,190
-evaluating the operator, the
-things we'll need to evaluate
-
-1036
-00:57:07,190 --> 00:57:11,710
-the arguments, namely, the
-environment and those
-
-1037
-00:57:11,710 --> 00:57:14,790
-arguments, those unevaluated
-arguments, so there they are
-
-1038
-00:57:14,790 --> 00:57:15,620
-sitting on the stack.
-
-1039
-00:57:15,620 --> 00:57:18,370
-And we're about to go off to
-evaluate the operator.
-
-1040
-00:57:18,370 --> 00:57:23,130
-
-
-1041
-00:57:23,130 --> 00:57:26,920
-Well, when we return from
-this particular call--
-
-1042
-00:57:26,920 --> 00:57:29,380
-so we're about to call
-eval-dispatch here--
-
-1043
-00:57:29,380 --> 00:57:32,730
-when we return from this call,
-the value of that operator,
-
-1044
-00:57:32,730 --> 00:57:34,890
-which, in this case, is going to
-be the primitive multiplier
-
-1045
-00:57:34,890 --> 00:57:43,080
-procedure, will end up in the
-FUN register, all right?
-
-1046
-00:57:43,080 --> 00:57:44,530
-We're going to evaluate
-some arguments.
-
-1047
-00:57:44,530 --> 00:57:47,730
-They will evaluate in here.
-
-1048
-00:57:47,730 --> 00:57:50,250
-That'll give us 5,
-in this case.
-
-1049
-00:57:50,250 --> 00:57:53,480
-We're going to put that in the
-argl register, and then we'll
-
-1050
-00:57:53,480 --> 00:57:57,460
-go off to evaluate the
-second operand.
-
-1051
-00:57:57,460 --> 00:58:00,050
-So, at the point where we go
-off to evaluate the second
-
-1052
-00:58:00,050 --> 00:58:02,390
-operand-- and I'll skip details
-like computing, and
-
-1053
-00:58:02,390 --> 00:58:04,510
-minus 1, and all of that--
-but, when we go off to
-
-1054
-00:58:04,510 --> 00:58:08,210
-evaluate the second operand,
-that will eventually reduce to
-
-1055
-00:58:08,210 --> 00:58:09,460
-another call to fact-recursive.
-
-1056
-00:58:09,460 --> 00:58:12,060
-
-
-1057
-00:58:12,060 --> 00:58:17,520
-And, what we've got on the stack
-here is the operator
-
-1058
-00:58:17,520 --> 00:58:20,290
-from that combination that we're
-going to use it in and
-
-1059
-00:58:20,290 --> 00:58:23,790
-the other argument, OK?
-
-1060
-00:58:23,790 --> 00:58:28,490
-So, now, we're set up
-for another call
-
-1061
-00:58:28,490 --> 00:58:30,200
-to recursive factorial.
-
-1062
-00:58:30,200 --> 00:58:32,300
-And, when we're done with this
-one, we're going to go to
-
-1063
-00:58:32,300 --> 00:58:33,935
-accumulate the last arg.
-
-1064
-00:58:33,935 --> 00:58:35,200
-And remember what that'll do?
-
-1065
-00:58:35,200 --> 00:58:38,290
-That'll say oh, whatever the
-result of this has to get
-
-1066
-00:58:38,290 --> 00:58:41,690
-combined with that, and we're
-going to multiply them.
-
-1067
-00:58:41,690 --> 00:58:45,720
-But, notice now, we're at
-another recursive factorial.
-
-1068
-00:58:45,720 --> 00:58:49,710
-We're about to call
-eval-dispatch again, except we
-
-1069
-00:58:49,710 --> 00:58:51,250
-haven't really reduced it
-because there's stuff
-
-1070
-00:58:51,250 --> 00:58:53,700
-on the stack now.
-
-1071
-00:58:53,700 --> 00:58:55,490
-The stuff on the stack says oh,
-when you get back, you'd
-
-1072
-00:58:55,490 --> 00:58:58,430
-better multiply it by the
-5 you had hanging there.
-
-1073
-00:58:58,430 --> 00:59:07,430
-So, when we go off to make
-another call, we
-
-1074
-00:59:07,430 --> 00:59:09,300
-evaluate the n minus 1.
-
-1075
-00:59:09,300 --> 00:59:12,050
-That gives us another
-environment in which the new
-
-1076
-00:59:12,050 --> 00:59:14,600
-n's going to be down to 4.
-
-1077
-00:59:14,600 --> 00:59:18,930
-And we're about to call
-eval-dispatch again, right?
-
-1078
-00:59:18,930 --> 00:59:21,350
-We get another call.
-
-1079
-00:59:21,350 --> 00:59:26,040
-That 4 is going to end up
-in the same situation.
-
-1080
-00:59:26,040 --> 00:59:30,020
-We'll end up with another call
-to fact-recursive n.
-
-1081
-00:59:30,020 --> 00:59:32,330
-And sitting on the stack will be
-the stuff from the original
-
-1082
-00:59:32,330 --> 00:59:35,360
-one and, now, the subsidiary
-one we're doing.
-
-1083
-00:59:35,360 --> 00:59:36,910
-And both of them are waiting
-for the same thing.
-
-1084
-00:59:36,910 --> 00:59:40,600
-They're going to go to
-accumulate a last argument.
-
-1085
-00:59:40,600 --> 00:59:43,480
-And then, of course, when we
-go to the fourth call, the
-
-1086
-00:59:43,480 --> 00:59:45,640
-same thing happens, right?
-
-1087
-00:59:45,640 --> 00:59:47,300
-And this goes on,
-and on, and on.
-
-1088
-00:59:47,300 --> 00:59:51,430
-And what you see here on the
-stack, exactly what's sitting
-
-1089
-00:59:51,430 --> 00:59:54,960
-here on the stack, the thing
-that says times and 5.
-
-1090
-00:59:54,960 --> 00:59:57,490
-And what you're going to do with
-that is accumulate that
-
-1091
-00:59:57,490 --> 01:00:00,470
-into a last argument.
-
-1092
-01:00:00,470 --> 01:00:02,760
-That's exactly this, right?
-
-1093
-01:00:02,760 --> 01:00:05,650
-This is exactly where that
-stuff is hanging.
-
-1094
-01:00:05,650 --> 01:00:12,650
-Effectively, the operator you're
-going to apply, the
-
-1095
-01:00:12,650 --> 01:00:15,300
-other argument that it's got to
-be multiplied by when you
-
-1096
-01:00:15,300 --> 01:00:17,620
-get back and the parentheses,
-which says yeah, what you
-
-1097
-01:00:17,620 --> 01:00:19,620
-wanted to do was accumulate
-them.
-
-1098
-01:00:19,620 --> 01:00:22,560
-So, you see, the substitution
-model is not such a lie.
-
-1099
-01:00:22,560 --> 01:00:24,460
-That really is, in some
-sense, what's sitting
-
-1100
-01:00:24,460 --> 01:00:27,198
-right on the stack.
-
-1101
-01:00:27,198 --> 01:00:29,046
-OK.
-
-1102
-01:00:29,046 --> 01:00:33,260
-All right, so that, in some
-sense, should explain for you,
-
-1103
-01:00:33,260 --> 01:00:37,850
-or at least convince you, that,
-somehow, this evaluator
-
-1104
-01:00:37,850 --> 01:00:41,870
-is managing to take these
-procedures and execute some of
-
-1105
-01:00:41,870 --> 01:00:46,410
-them iteratively and some of
-them recursively, even though,
-
-1106
-01:00:46,410 --> 01:00:49,430
-as syntactically, they look
-like recursive procedures.
-
-1107
-01:00:49,430 --> 01:00:50,660
-How's it managing to do that?
-
-1108
-01:00:50,660 --> 01:00:54,090
-Well, the basic reason it's
-managing to do that is the
-
-1109
-01:00:54,090 --> 01:01:01,090
-evaluator is set up to save
-only what it needs later.
-
-1110
-01:01:01,090 --> 01:01:04,670
-So, for example, at the point
-where you've reduced
-
-1111
-01:01:04,670 --> 01:01:08,580
-evaluating an expression and an
-environment to applying a
-
-1112
-01:01:08,580 --> 01:01:11,700
-procedure to some arguments, it
-doesn't need that original
-
-1113
-01:01:11,700 --> 01:01:15,110
-environment anymore because any
-environment stuff will be
-
-1114
-01:01:15,110 --> 01:01:18,160
-packaged inside the procedures
-where the
-
-1115
-01:01:18,160 --> 01:01:20,160
-application's going to happen.
-
-1116
-01:01:20,160 --> 01:01:23,120
-All right, similarly, when
-you're going along evaluating
-
-1117
-01:01:23,120 --> 01:01:25,910
-an argument list, when you've
-finished evaluating the list,
-
-1118
-01:01:25,910 --> 01:01:28,200
-when you're finished evaluating
-the last argument,
-
-1119
-01:01:28,200 --> 01:01:31,500
-you don't need that argument
-list any more, right?
-
-1120
-01:01:31,500 --> 01:01:33,330
-And you don't need the
-environment where those
-
-1121
-01:01:33,330 --> 01:01:36,690
-arguments would be
-evaluated, OK?
-
-1122
-01:01:36,690 --> 01:01:40,890
-So the basic reason that this
-interpreter is being so smart
-
-1123
-01:01:40,890 --> 01:01:43,050
-is that it's not being smart
-at all, it's being stupid.
-
-1124
-01:01:43,050 --> 01:01:44,760
-It's just saying I'm
-only going to save
-
-1125
-01:01:44,760 --> 01:01:46,010
-what I really need.
-
-1126
-01:01:46,010 --> 01:01:48,700
-
-
-1127
-01:01:48,700 --> 01:01:51,000
-Well, let me show you here.
-
-1128
-01:01:51,000 --> 01:01:54,880
-
-
-1129
-01:01:54,880 --> 01:01:58,310
-Here's the actual thing that's
-making a tail recursive.
-
-1130
-01:01:58,310 --> 01:02:00,135
-Remember, it's the restore
-of continue.
-
-1131
-01:02:00,135 --> 01:02:09,090
-It's saying when I go off to
-evaluate the procedure body, I
-
-1132
-01:02:09,090 --> 01:02:12,090
-should tell eval to come back
-to the place where that
-
-1133
-01:02:12,090 --> 01:02:15,170
-original evaluation was supposed
-to come back to.
-
-1134
-01:02:15,170 --> 01:02:17,700
-So, in some sense, you want to
-say what's the actual line
-
-1135
-01:02:17,700 --> 01:02:18,770
-that makes a tail recursive?
-
-1136
-01:02:18,770 --> 01:02:19,920
-It's that one.
-
-1137
-01:02:19,920 --> 01:02:23,680
-If I wanted to build a non-tail
-recursive evaluator,
-
-1138
-01:02:23,680 --> 01:02:27,650
-for some strange reason, all I
-would need to do is, instead
-
-1139
-01:02:27,650 --> 01:02:31,300
-of restoring continue at this
-point, I'd set up a label down
-
-1140
-01:02:31,300 --> 01:02:35,340
-here called, "Where to come
-back after you've finished
-
-1141
-01:02:35,340 --> 01:02:38,560
-applying the procedure."
-Instead, I'd
-
-1142
-01:02:38,560 --> 01:02:39,920
-set continue to that.
-
-1143
-01:02:39,920 --> 01:02:42,240
-I'd go to eval-dispatch,
-and then eval-dispatch
-
-1144
-01:02:42,240 --> 01:02:43,790
-would come back here.
-
-1145
-01:02:43,790 --> 01:02:45,920
-At that point, I would restore
-continue and go to the
-
-1146
-01:02:45,920 --> 01:02:47,920
-original one.
-
-1147
-01:02:47,920 --> 01:02:51,790
-So here, the only consequence
-of that would be to make it
-
-1148
-01:02:51,790 --> 01:02:52,840
-non-tail recursive.
-
-1149
-01:02:52,840 --> 01:02:55,340
-It would give you exactly the
-same answers, except, if you
-
-1150
-01:02:55,340 --> 01:02:57,800
-did that iterative factorial
-and all those iterative
-
-1151
-01:02:57,800 --> 01:02:59,500
-procedures, it would execute
-recursively.
-
-1152
-01:02:59,500 --> 01:03:03,080
-
-
-1153
-01:03:03,080 --> 01:03:05,760
-Well, I lied to you a little
-bit, but just a little bit,
-
-1154
-01:03:05,760 --> 01:03:07,670
-because I showed you a slightly
-over-simplified
-
-1155
-01:03:07,670 --> 01:03:12,510
-evaluator where it assumes that
-each procedure body has
-
-1156
-01:03:12,510 --> 01:03:13,890
-only one expression.
-
-1157
-01:03:13,890 --> 01:03:15,790
-Remember, in general, a
-procedure has a sequence of
-
-1158
-01:03:15,790 --> 01:03:17,870
-expressions in it.
-
-1159
-01:03:17,870 --> 01:03:20,490
-So there's nothing really
-conceptually new.
-
-1160
-01:03:20,490 --> 01:03:23,480
-Let me just show you the actual
-evaluator that handles
-
-1161
-01:03:23,480 --> 01:03:24,730
-sequences of expressions.
-
-1162
-01:03:24,730 --> 01:03:28,470
-
-
-1163
-01:03:28,470 --> 01:03:30,650
-This is compound-apply now, and
-the only difference from
-
-1164
-01:03:30,650 --> 01:03:35,980
-the old one is that, instead of
-going off to eval directly,
-
-1165
-01:03:35,980 --> 01:03:38,510
-it takes the whole body of the
-procedure, which, in this
-
-1166
-01:03:38,510 --> 01:03:40,920
-case, is a sequence of
-expressions, and goes off to
-
-1167
-01:03:40,920 --> 01:03:42,670
-eval-sequence.
-
-1168
-01:03:42,670 --> 01:03:48,380
-And eval-sequence is a little
-loop that, basically, does
-
-1169
-01:03:48,380 --> 01:03:49,980
-these evaluations
-one at a time.
-
-1170
-01:03:49,980 --> 01:03:52,630
-
-
-1171
-01:03:52,630 --> 01:03:53,900
-So it does an evaluation.
-
-1172
-01:03:53,900 --> 01:03:56,110
-Says oh, when I come back, I'd
-better come back here to do
-
-1173
-01:03:56,110 --> 01:03:58,440
-the next one.
-
-1174
-01:03:58,440 --> 01:04:00,410
-And, when I'm all done, when
-I want to get the last
-
-1175
-01:04:00,410 --> 01:04:04,800
-expression, I just restore
-my continue and go off to
-
-1176
-01:04:04,800 --> 01:04:06,410
-eval-dispatch.
-
-1177
-01:04:06,410 --> 01:04:08,880
-And, again, if you wanted for
-some reason to break tail
-
-1178
-01:04:08,880 --> 01:04:11,690
-recursion in this evaluator,
-all you need to do is not
-
-1179
-01:04:11,690 --> 01:04:14,900
-handle the last expression,
-especially.
-
-1180
-01:04:14,900 --> 01:04:17,820
-Just say, after you've done the
-last expression, come back
-
-1181
-01:04:17,820 --> 01:04:21,900
-to some other place after which
-you restore continue.
-
-1182
-01:04:21,900 --> 01:04:24,920
-And, for some reason, a lot
-of LISP evaluators tended
-
-1183
-01:04:24,920 --> 01:04:26,550
-to work that way.
-
-1184
-01:04:26,550 --> 01:04:29,300
-And the only consequence of
-that is that iterative
-
-1185
-01:04:29,300 --> 01:04:31,614
-procedures built up stack.
-
-1186
-01:04:31,614 --> 01:04:35,670
-And it's not clear why
-that happened.
-
-1187
-01:04:35,670 --> 01:04:36,210
-All right.
-
-1188
-01:04:36,210 --> 01:04:38,990
-Well, let me just sort of
-summarize, since this is a lot
-
-1189
-01:04:38,990 --> 01:04:41,120
-of details in a big program.
-
-1190
-01:04:41,120 --> 01:04:44,040
-But the main point is that
-it's no different,
-
-1191
-01:04:44,040 --> 01:04:47,060
-conceptually, from translating
-any other program.
-
-1192
-01:04:47,060 --> 01:04:49,760
-And the main idea is that we
-have this universal evaluator
-
-1193
-01:04:49,760 --> 01:04:51,870
-program, the meta-circular
-evaluator.
-
-1194
-01:04:51,870 --> 01:04:53,250
-If we translate that
-into LISP, then
-
-1195
-01:04:53,250 --> 01:04:54,560
-we have all of LISP.
-
-1196
-01:04:54,560 --> 01:04:57,980
-And that's all we did, OK?
-
-1197
-01:04:57,980 --> 01:04:59,680
-The second point is that
-the magic's gone away.
-
-1198
-01:04:59,680 --> 01:05:01,970
-There should be no more magic
-in this whole system, right?
-
-1199
-01:05:01,970 --> 01:05:04,820
-
-
-1200
-01:05:04,820 --> 01:05:08,720
-In principle, it should all be
-very clear except, maybe, for
-
-1201
-01:05:08,720 --> 01:05:10,940
-how list structured
-memory works, and
-
-1202
-01:05:10,940 --> 01:05:12,640
-we'll see that later.
-
-1203
-01:05:12,640 --> 01:05:15,450
-But that's not very hard.
-
-1204
-01:05:15,450 --> 01:05:18,720
-The third point is that all this
-tail recursion came from
-
-1205
-01:05:18,720 --> 01:05:23,580
-the discipline of eval being
-very careful to save only what
-
-1206
-01:05:23,580 --> 01:05:25,870
-it needs next time.
-
-1207
-01:05:25,870 --> 01:05:28,180
-It's not some arbitrary thing
-where we're saying well,
-
-1208
-01:05:28,180 --> 01:05:30,440
-whenever we call a sub-routine,
-we'll save all
-
-1209
-01:05:30,440 --> 01:05:33,940
-the registers in the world
-and come back, right?
-
-1210
-01:05:33,940 --> 01:05:37,150
-See, sometimes it pays to really
-worry about efficiency.
-
-1211
-01:05:37,150 --> 01:05:39,400
-And, when you're down in the
-guts of your evaluator
-
-1212
-01:05:39,400 --> 01:05:42,560
-machine, it really pays to think
-about things like that
-
-1213
-01:05:42,560 --> 01:05:45,230
-because it makes big
-consequences.
-
-1214
-01:05:45,230 --> 01:05:49,680
-Well, I hope what this has
-done is really made the
-
-1215
-01:05:49,680 --> 01:05:52,560
-evaluator seem concrete,
-right?
-
-1216
-01:05:52,560 --> 01:05:57,120
-I hope you really believe that
-somebody could hold a LISP
-
-1217
-01:05:57,120 --> 01:05:59,390
-evaluator in the palm
-of their hand.
-
-1218
-01:05:59,390 --> 01:06:02,540
-Maybe to help you believe that,
-here's a LISP evaluator
-
-1219
-01:06:02,540 --> 01:06:06,160
-that I'm holding the palm
-of my hand, right?
-
-1220
-01:06:06,160 --> 01:06:11,750
-And this is a chip which is
-actually quite a bit more
-
-1221
-01:06:11,750 --> 01:06:13,700
-complicated than the evaluator
-I showed you.
-
-1222
-01:06:13,700 --> 01:06:17,815
-
-
-1223
-01:06:17,815 --> 01:06:19,200
-Maybe, here's a better
-picture of it.
-
-1224
-01:06:19,200 --> 01:06:22,070
-
-
-1225
-01:06:22,070 --> 01:06:24,730
-What there is, is you can see
-the same overall structure.
-
-1226
-01:06:24,730 --> 01:06:26,940
-This is a register array.
-
-1227
-01:06:26,940 --> 01:06:27,910
-These are the data paths.
-
-1228
-01:06:27,910 --> 01:06:29,800
-Here's a finite state
-controller.
-
-1229
-01:06:29,800 --> 01:06:32,810
-And again, finite state,
-that's all there is.
-
-1230
-01:06:32,810 --> 01:06:34,160
-And somewhere there's
-external memory
-
-1231
-01:06:34,160 --> 01:06:35,750
-that'll worry about things.
-
-1232
-01:06:35,750 --> 01:06:38,090
-And this particular one is very
-complicated because it's
-
-1233
-01:06:38,090 --> 01:06:41,450
-trying to run LISP fast. And
-it has some very, very fast
-
-1234
-01:06:41,450 --> 01:06:45,570
-parallel operations in there
-like, if you want to index
-
-1235
-01:06:45,570 --> 01:06:50,040
-into an array, simultaneously
-check that the index is an
-
-1236
-01:06:50,040 --> 01:06:53,750
-integer, check that it doesn't
-exceed the array bands, and go
-
-1237
-01:06:53,750 --> 01:06:55,810
-off and do the memory access,
-and do all those things
-
-1238
-01:06:55,810 --> 01:06:57,120
-simultaneously.
-
-1239
-01:06:57,120 --> 01:06:58,970
-And then, later, if they're
-all OK, actually
-
-1240
-01:06:58,970 --> 01:07:00,420
-get the value there.
-
-1241
-01:07:00,420 --> 01:07:02,520
-So there are a lot of
-complicated operations in
-
-1242
-01:07:02,520 --> 01:07:06,550
-these data paths for making
-LISP run in parallel.
-
-1243
-01:07:06,550 --> 01:07:10,640
-It's a completely non-risk
-philosophy of evaluating LISP.
-
-1244
-01:07:10,640 --> 01:07:13,740
-And then, this microcode
-is pretty complicated.
-
-1245
-01:07:13,740 --> 01:07:17,740
-Let's see, there's what?
-
-1246
-01:07:17,740 --> 01:07:23,600
-There's about 389 instructions
-of 220-bit microcode sitting
-
-1247
-01:07:23,600 --> 01:07:27,940
-here because these are very
-complicated data paths.
-
-1248
-01:07:27,940 --> 01:07:33,580
-And the whole thing has about
-89,000 transistors, OK?
-
-1249
-01:07:33,580 --> 01:07:33,840
-OK.
-
-1250
-01:07:33,840 --> 01:07:37,970
-Well, I hope that that takes
-away a lot of the mystery.
-
-1251
-01:07:37,970 --> 01:07:39,240
-Maybe somebody wants
-to look at this.
-
-1252
-01:07:39,240 --> 01:07:42,048
-
-
-1253
-01:07:42,048 --> 01:07:43,298
-Yeah.
-
-1254
-01:07:43,298 --> 01:07:46,260
-
-
-1255
-01:07:46,260 --> 01:07:46,480
-OK.
-
-1256
-01:07:46,480 --> 01:07:47,730
-Let's stop.
-
-1257
-01:07:47,730 --> 01:07:55,890
-
-
-1258
-01:07:55,890 --> 01:07:57,815
-Questions?
-
-1259
-01:07:57,815 --> 01:08:00,130
-AUDIENCE: OK, now, it sounds
-like what you're saying is
-
-1260
-01:08:00,130 --> 01:08:03,070
-that, with the restore continue
-put in the proper
-
-1261
-01:08:03,070 --> 01:08:08,830
-place, that procedures that
-would invoke a recursive
-
-1262
-01:08:08,830 --> 01:08:13,385
-process now invoke an integer
-process just by the way that
-
-1263
-01:08:13,385 --> 01:08:15,165
-the eval signature is?
-
-1264
-01:08:15,165 --> 01:08:17,850
-PROFESSOR: I think the way I'd
-prefer to put it is that, with
-
-1265
-01:08:17,850 --> 01:08:22,540
-restore continue put in the
-wrong place, you can cause any
-
-1266
-01:08:22,540 --> 01:08:25,880
-syntactically-looking recursive
-procedure, in fact,
-
-1267
-01:08:25,880 --> 01:08:28,029
-to build up stack as it runs.
-
-1268
-01:08:28,029 --> 01:08:34,350
-But there's no reason for that,
-so you might want to
-
-1269
-01:08:34,350 --> 01:08:35,660
-play around with it.
-
-1270
-01:08:35,660 --> 01:08:38,640
-You can just switch around two
-or three instructions in the
-
-1271
-01:08:38,640 --> 01:08:42,260
-way compound-apply comes back,
-and you'll get something which
-
-1272
-01:08:42,260 --> 01:08:45,060
-isn't tail recursive.
-
-1273
-01:08:45,060 --> 01:08:47,670
-But the thing I wanted to
-emphasize is there's no magic.
-
-1274
-01:08:47,670 --> 01:08:51,689
-It's not as if there's some
-very clever pre-processing
-
-1275
-01:08:51,689 --> 01:08:55,540
-program that's looking at this
-procedure, factorial iter, and
-
-1276
-01:08:55,540 --> 01:08:59,920
-say oh, gee, I really notice
-that I don't have to push
-
-1277
-01:08:59,920 --> 01:09:01,060
-stack in order to do this.
-
-1278
-01:09:01,060 --> 01:09:03,760
-Some people think that that's
-what's going on.
-
-1279
-01:09:03,760 --> 01:09:05,840
-It's something much, much more
-dumb than that, it's this one
-
-1280
-01:09:05,840 --> 01:09:08,880
-place you're putting the
-restore instruction.
-
-1281
-01:09:08,880 --> 01:09:10,353
-It's just automatic.
-
-1282
-01:09:10,353 --> 01:09:11,603
-AUDIENCE: OK.
-
-1283
-01:09:11,603 --> 01:09:14,217
-
-
-1284
-01:09:14,217 --> 01:09:16,109
-AUDIENCE: But that's not
-affecting the time
-
-1285
-01:09:16,109 --> 01:09:17,850
-complexity is it?
-
-1286
-01:09:17,850 --> 01:09:18,275
-PROFESSOR: No.
-
-1287
-01:09:18,275 --> 01:09:21,810
-AUDIENCE: It's just that it's
-handling it recursively
-
-1288
-01:09:21,810 --> 01:09:23,020
-instead of iteratively.
-
-1289
-01:09:23,020 --> 01:09:26,960
-But, in terms of the order of
-time it takes to finish the
-
-1290
-01:09:26,960 --> 01:09:29,220
-operation, it's the same one
-way or the other, right?
-
-1291
-01:09:29,220 --> 01:09:29,920
-PROFESSOR: Yes.
-
-1292
-01:09:29,920 --> 01:09:32,609
-Tail recursion is not going to
-change the time complexity of
-
-1293
-01:09:32,609 --> 01:09:34,420
-anything because, in some sense,
-it's the same algorithm
-
-1294
-01:09:34,420 --> 01:09:36,029
-that's going on.
-
-1295
-01:09:36,029 --> 01:09:38,790
-What it's doing is really making
-this thing run as an
-
-1296
-01:09:38,790 --> 01:09:41,210
-iteration, right?
-
-1297
-01:09:41,210 --> 01:09:44,750
-Not going to run out of memory
-counting up to a giant number
-
-1298
-01:09:44,750 --> 01:09:47,683
-simply because the stack
-would get pushed.
-
-1299
-01:09:47,683 --> 01:09:49,970
-See, the thing you really
-have to believe is
-
-1300
-01:09:49,970 --> 01:09:51,640
-that, when we write--
-
-1301
-01:09:51,640 --> 01:09:53,040
-see, we've been writing all
-these things called
-
-1302
-01:09:53,040 --> 01:09:57,990
-iterations, infinite loops,
-define loop to be called loop.
-
-1303
-01:09:57,990 --> 01:10:01,660
-
-
-1304
-01:10:01,660 --> 01:10:05,390
-That's is as much an iteration
-as if we wrote do forever
-
-1305
-01:10:05,390 --> 01:10:07,630
-loop, right?
-
-1306
-01:10:07,630 --> 01:10:09,280
-It's just syntactic sugar
-as the difference.
-
-1307
-01:10:09,280 --> 01:10:14,730
-These things are real, honest
-to god, iterations, right?
-
-1308
-01:10:14,730 --> 01:10:17,285
-They don't change the time
-complexity, but they turn them
-
-1309
-01:10:17,285 --> 01:10:18,535
-into real iterations.
-
-1310
-01:10:18,535 --> 01:10:21,686
-
-
-1311
-01:10:21,686 --> 01:10:23,800
-All right, thank you.
-
-1312
-01:10:23,800 --> 01:10:42,633
-
+1
+00:00:15,840 --> 00:00:20,260
+PROFESSOR: Well, I hope you appreciate that we have
+
+2
+00:00:20,260 --> 00:00:24,562
+inducted you into some real magic,
+
+3
+00:00:24,562 --> 00:00:29,500
+the magic of building languages, really building new languages.
+
+4
+00:00:29,500 --> 00:00:31,275
+What have we looked at? We've looked at 
+
+5
+00:00:31,275 --> 00:00:38,925
+an Escher picture language:
+
+6
+00:00:38,925 --> 00:00:42,141
+this language invented by Peter Henderson.
+
+7
+00:00:42,141 --> 00:00:47,600
+We looked at digital logic language.
+
+8
+00:00:53,000 --> 00:00:56,944
+Let's see.We've looked at the query language.
+
+9
+00:00:59,700 --> 00:01:04,700
+And the thing you should realize is, even though these were toy examples,  
+
+10
+00:01:04,700 --> 00:01:08,250
+they really are the kernels of really useful things.
+
+11
+00:01:08,250 --> 00:01:12,375
+So, for instance, the Escher picture language was taken by
+
+12
+00:01:12,375 --> 00:01:14,450
+Henry Wu, who's a student at MIT, 
+
+13
+00:01:14,450 --> 00:01:20,350
+and developed into a real language for laying out PC boards, 
+
+14
+00:01:20,350 --> 00:01:23,244
+based just on extending those structures.
+
+15
+00:01:23,244 --> 00:01:26,350
+And the digital logic language, Jerry mentioned when he showed it to you,
+
+16
+00:01:26,350 --> 00:01:30,850
+was really extended to be used as the basis for a simulator 
+
+17
+00:01:30,850 --> 00:01:33,460
+that was used to design a real computer.
+
+18
+00:01:33,460 --> 00:01:37,510
+And the query language, of course, is kind of the germ of prologue.
+
+19
+00:01:37,510 --> 00:01:39,425
+So we built all of these languages, 
+
+20
+00:01:39,425 --> 00:01:42,300
+they're all based on LISP.
+
+21
+00:01:43,630 --> 00:01:45,275
+A lot of people ask 
+
+22
+00:01:45,275 --> 00:01:48,606
+what particular problems is LISP good for solving for?
+
+23
+00:01:48,606 --> 00:01:53,450
+The answer is LISP is not good for solving any particular problems.
+
+24
+00:01:53,450 --> 00:01:56,213
+What LISP is good for is constructing within it
+
+25
+00:01:56,213 --> 00:01:59,175
+the right language to solve the problems you want to solve,
+
+26
+00:01:59,175 --> 00:02:01,470
+and that's how you should think about it.
+
+27
+00:02:01,470 --> 00:02:04,326
+So all of these languages were based on LISP.
+
+28
+00:02:04,326 --> 00:02:06,925
+Now, what's LISP based on?
+
+29
+00:02:06,925 --> 00:02:09,400
+Where's that come from? Well, we looked at that too.
+
+30
+00:02:09,400 --> 00:02:22,935
+We looked at the meta-circular evaluator 
+
+31
+00:02:22,935 --> 00:02:25,810
+and said well, LISP is based on LISP.
+
+32
+00:02:25,810 --> 00:02:28,275
+And when we start looking at that, 
+
+33
+00:02:28,275 --> 00:02:29,950
+we've got to do some real magic, right?
+
+34
+00:02:29,950 --> 00:02:31,660
+So what does that mean, right?
+
+35
+00:02:31,660 --> 00:02:37,350
+Why operators, and fixed points, and the idea that
+
+36
+00:02:37,350 --> 00:02:41,000
+what this means is that LISP is somehow the fixed-point equation
+
+37
+00:02:41,000 --> 00:02:47,400
+for this funny set of things which are defined in terms of themselves.
+
+38
+00:02:47,400 --> 00:02:49,070
+Now, it's real magic.
+
+39
+00:02:49,070 --> 00:02:52,625
+Well, today, for a final piece of magic, 
+
+40
+00:02:52,625 --> 00:03:01,852
+we're going to make all the magic go away.
+
+41
+00:03:06,430 --> 00:03:09,770
+We already know how to do that.
+
+42
+00:03:09,770 --> 00:03:13,135
+The idea is, we're going to take the register machine architecture
+
+43
+00:03:13,135 --> 00:03:15,500
+and show how to implement LISP on terms of that.
+
+44
+00:03:15,500 --> 00:03:21,325
+And, remember, the idea of the register machine is that
+
+45
+00:03:21,325 --> 00:03:24,800
+there's a fixed and finite part of the machine.
+
+46
+00:03:24,800 --> 00:03:27,050
+There's a finite-state controller, which does some
+
+47
+00:03:27,050 --> 00:03:30,510
+particular thing with a particular amount of hardware.
+
+48
+00:03:30,510 --> 00:03:33,550
+There are particular data paths, the operation the machine does 
+
+49
+00:03:33,550 --> 00:03:37,725
+And then, in order to implement recursion and sustain the illusion of infinity, 
+
+50
+00:03:37,725 --> 00:03:42,060
+there's some large amount of memory, which is the stack.
+
+51
+00:03:42,060 --> 00:03:47,025
+So, if we implement LISP in terms of a register machine,
+
+52
+00:03:47,025 --> 00:03:49,850
+then everything ought to become, at this point,completely concrete.
+
+53
+00:03:49,850 --> 00:03:51,650
+All the magic should go away.
+
+54
+00:03:51,650 --> 00:03:55,140
+And, by the end of this talk, I want you get the feeling
+
+55
+00:03:55,140 --> 00:03:59,675
+that, as opposed to this very mysterious meta-circular evaluator
+
+56
+00:03:59,675 --> 00:04:02,850
+that a LISP evaluator really is something that's concrete enough
+
+57
+00:04:02,850 --> 00:04:04,720
+that you can hold in the palm of your hand.
+
+58
+00:04:04,720 --> 00:04:06,450
+You should be able to imagine holding
+
+59
+00:04:06,450 --> 00:04:09,546
+holding a LISP interpreter there.
+
+60
+00:04:09,546 --> 00:04:10,950
+All right, how are we going to do this?
+
+61
+00:04:10,950 --> 00:04:13,960
+We already have all the ingredients.
+
+62
+00:04:13,960 --> 00:04:17,450
+See, what you learned last time from Jerry 
+
+63
+00:04:17,450 --> 00:04:22,600
+is how to take any particular couple of LISP procedures
+
+64
+00:04:22,600 --> 00:04:28,210
+and hand-translate them into something that runs on a register machine.
+
+65
+00:04:28,210 --> 00:04:30,525
+So, to implement all of LISP on a register machine,
+
+66
+00:04:30,525 --> 00:04:33,600
+all we have to do is take the particular procedures 
+
+67
+00:04:33,600 --> 00:04:36,050
+that are the meta-circular evaluator 
+
+68
+00:04:36,050 --> 00:04:38,825
+and hand-translate them for a register machine.
+
+69
+00:04:38,825 --> 00:04:42,320
+And that does all of LISP, right?
+
+70
+00:04:42,320 --> 00:04:45,380
+So, in principle, we already know how to do this.
+
+71
+00:04:45,380 --> 00:04:51,275
+And, indeed, it's going to be no different, in kind, from
+
+72
+00:04:51,275 --> 00:04:54,670
+from translating, say, recursive factorial or recursive Fibonacci. 
+
+73
+00:04:54,670 --> 00:04:56,840
+It's just bigger and there's more of it.
+
+74
+00:04:56,840 --> 00:05:01,375
+So it'd just be more details,  but nothing really conceptually new. 
+
+75
+00:05:01,375 --> 00:05:04,876
+And also, when we've done that, and the thing is completely explicit,
+
+76
+00:05:04,876 --> 00:05:06,990
+and we see how to implement LISP in terms of
+
+77
+00:05:06,990 --> 00:05:10,085
+the actual sequential register operations, 
+
+78
+00:05:10,085 --> 00:05:14,810
+that's going to be our final most explicit model of LISP in this course. 
+
+79
+00:05:14,810 --> 00:05:16,950
+And, remember, that's a progression through this course. 
+
+80
+00:05:16,950 --> 00:05:20,100
+We started out with substitution,  which is sort of like algebra. 
+
+81
+00:05:20,100 --> 00:05:21,838
+And then we went to the environment model,
+
+82
+00:05:21,838 --> 00:05:26,125
+which talked about the actual frames and how they got linked together. 
+
+83
+00:05:26,125 --> 00:05:31,080
+And then we made that more concrete in the meta-circular evaluator. 
+
+84
+00:05:31,080 --> 00:05:34,360
+There are things the meta-circular evaluator doesn't tell us. 
+
+85
+00:05:34,360 --> 00:05:36,090
+You should realize that.
+
+86
+00:05:36,090 --> 00:05:40,420
+For instance, it left unanswered the question of how
+
+87
+00:05:40,420 --> 00:05:45,175
+a procedure, like recursive factorial here,
+
+88
+00:05:45,175 --> 00:05:47,210
+somehow takes space that grows.
+
+89
+00:05:47,210 --> 00:05:51,948
+On the other hand, a procedure which also looks syntactically recursive,
+
+90
+00:05:51,948 --> 00:05:56,760
+called fact-iter, somehow doesn't take space.We justify ,
+
+91
+00:05:56,760 --> 00:06:00,500
+We justify that it doesn't need to take space
+
+92
+00:06:00,500 --> 00:06:01,960
+by showing the substitution model.
+
+93
+00:06:01,960 --> 00:06:07,275
+But we didn't really say how it happens that the machine manages to do that, 
+
+94
+00:06:07,275 --> 00:06:09,161
+that that has to do with the details 
+
+95
+00:06:09,161 --> 00:06:12,250
+of how arguments are passed to procedures.
+
+96
+00:06:12,250 --> 00:06:15,846
+And that's the thing we didn't see in the meta-circular evaluator precisely
+
+97
+00:06:15,846 --> 00:06:19,700
+because the way arguments got passed to procedures in this LISP 
+
+98
+00:06:19,700 --> 00:06:25,050
+depended on the way arguments got passed to procedures in this LISP. 
+
+99
+00:06:26,070 --> 00:06:30,740
+But, now, that's going to become extremely explicit.
+
+100
+00:06:30,740 --> 00:06:31,230
+OK.
+
+101
+00:06:31,230 --> 00:06:34,426
+Well, before going on to the evaluator, 
+
+102
+00:06:34,426 --> 00:06:37,600
+let me just give you a sense of what a whole LISP system looks like 
+
+103
+00:06:37,600 --> 00:06:39,086
+so you can see the parts we're going to talk about 
+
+104
+00:06:39,086 --> 00:06:43,250
+and the parts we're not going to talk about.
+
+105
+00:06:43,250 --> 00:06:48,675
+Let's see, over here is a happy LISP user,
+
+106
+00:06:48,675 --> 00:06:53,245
+and the LISP user is talking to something called the reader.
+
+107
+00:07:00,360 --> 00:07:14,170
+The reader's job in life is to take characters from the user
+
+108
+00:07:14,170 --> 00:07:17,960
+and turn them into data structures in something called
+
+109
+00:07:17,960 --> 00:07:21,405
+a list structure memory.
+
+110
+00:07:29,783 --> 00:07:32,653
+All right, so the reader is going to take 
+
+111
+00:07:32,653 --> 00:07:36,953
+symbols, parentheses, and A's and B's, and 1s and 3s that you type in, 
+
+112
+00:07:36,953 --> 00:07:39,150
+and turn these into actual list structure:
+
+113
+00:07:39,150 --> 00:07:39,156
+pairs, and pointers, and things. 
+
+114
+00:07:39,156 --> 00:07:42,340
+pairs, and pointers, and things. 
+
+115
+00:07:42,340 --> 00:07:45,850
+And so, by the time evaluator is going, there are no characters in the world. 
+
+116
+00:07:45,850 --> 00:07:49,480
+And, of course, in more modern list systems, there's sort of
+
+117
+00:07:49,480 --> 00:07:52,325
+a big morass here that might sit between the user and the reader:
+
+118
+00:07:52,325 --> 00:07:54,775
+Windows systems, and top levels, 
+
+119
+00:07:54,775 --> 00:07:56,280
+and mice, and all kinds of things.
+
+120
+00:07:56,280 --> 00:07:59,590
+But conceptually, characters are coming in.
+
+121
+00:07:59,590 --> 00:08:05,525
+All right, the reader transforms these into pointers
+
+122
+00:08:05,525 --> 00:08:08,275
+pointers to stuff in this memory, 
+
+123
+00:08:08,275 --> 00:08:12,445
+and that's what the evaluator sees
+
+124
+00:08:15,300 --> 00:08:17,090
+OK? 
+
+125
+00:08:17,090 --> 00:08:17,300
+The evaluator has a bunch of helpers.
+
+126
+00:08:17,300 --> 00:08:19,780
+The evaluator has a bunch of helpers.
+
+127
+00:08:19,780 --> 00:08:23,080
+It has all possible primitive operators you might want.
+
+128
+00:08:23,080 --> 00:08:28,400
+So there's a completely separate box,
+
+129
+00:08:28,400 --> 00:08:32,225
+a floating point unit, 
+
+130
+00:08:32,225 --> 00:08:35,960
+or all sorts of things, which do the primitive operators.
+
+131
+00:08:35,960 --> 00:08:37,548
+And, if you want more special primitives, 
+
+132
+00:08:37,548 --> 00:08:42,080
+you build more primitive operators, but they're separate from the evaluator.
+
+133
+00:08:42,080 --> 00:08:45,025
+The evaluator finally gets an answer
+
+134
+00:08:45,025 --> 00:08:50,450
+and communicates that to the printer.
+
+135
+00:08:50,780 --> 00:08:52,265
+And now, the printer's job in life is to take
+
+136
+00:08:52,265 --> 00:08:55,318
+this list structure coming from the evaluator, 
+
+137
+00:08:55,318 --> 00:08:57,614
+and turn it back into characters,
+
+138
+00:09:01,700 --> 00:09:04,075
+and communicate them to the user through 
+
+139
+00:09:04,075 --> 00:09:05,750
+whatever interface there is.
+
+140
+00:09:08,050 --> 00:09:12,670
+OK. Well, today, what we're going to talk about is this evaluator.  
+
+141
+00:09:12,670 --> 00:09:15,200
+The primitive operators have nothing particular to do with LISP,
+
+142
+00:09:15,200 --> 00:09:19,175
+they're however you like to implement primitive operations. 
+
+143
+00:09:19,175 --> 00:09:22,187
+The reader and printer are actually complicated, 
+
+144
+00:09:22,187 --> 00:09:24,420
+but we're not going to talk about them.
+
+145
+00:09:24,420 --> 00:09:27,100
+They sort of have to do with details of how you might build
+
+146
+00:09:27,100 --> 00:09:29,900
+build up list structure from characters.
+
+147
+00:09:29,900 --> 00:09:32,490
+So that is a long story, but we're not going to talk about it,
+
+148
+00:09:32,490 --> 00:09:36,930
+the list structure memory, we'll talk about next time.
+
+149
+00:09:36,930 --> 00:09:40,125
+So, pretty much, except for the details of reading and printing,
+
+150
+00:09:40,125 --> 00:09:43,250
+the only mystery that's going to be left after you see the evaluator
+
+151
+00:09:43,250 --> 00:09:46,295
+is how you build list structure on conventional memories. 
+
+152
+00:09:46,295 --> 00:09:50,580
+But we'll worry about that next time too.
+
+153
+00:09:50,580 --> 00:09:51,830
+OK.
+
+154
+00:09:53,350 --> 00:09:56,110
+Well, let's start talking about the evaluator.
+
+155
+00:09:56,110 --> 00:09:59,775
+The one that we're going to show you, of course, is not,
+
+156
+00:09:59,775 --> 00:10:01,120
+I think, nothing special about it.
+
+157
+00:10:01,120 --> 00:10:04,810
+It's just a particular register machine that runs LISP. 
+
+158
+00:10:04,810 --> 00:10:09,890
+And it has seven registers, and here are the seven registers. 
+
+159
+00:10:09,890 --> 00:10:14,925
+There's a register, called EXP, and its job is to 
+
+160
+00:10:14,925 --> 00:10:18,370
+hold the expression to be evaluated.
+
+161
+00:10:18,370 --> 00:10:21,750
+And by that, I mean it's going to hold a pointer
+
+162
+00:10:21,750 --> 00:10:23,764
+to someplace in list structure memory that holds
+
+163
+00:10:23,764 --> 00:10:26,550
+the expression to be evaluated.
+
+164
+00:10:26,550 --> 00:10:31,000
+There's a register, called ENV, which holds the environment
+
+165
+00:10:31,000 --> 00:10:34,070
+in which this expression is to be evaluated.
+
+166
+00:10:34,070 --> 00:10:38,240
+And, again, I made a pointer. The environment is some data structure. 
+
+167
+00:10:38,240 --> 00:10:40,425
+There's a register, called FUN, which will 
+
+168
+00:10:40,425 --> 00:10:44,350
+which will hold the procedure to be applied when you go to apply a procedure.
+
+169
+00:10:44,350 --> 00:10:47,325
+A register, called ARGL, 
+
+170
+00:10:47,325 --> 00:10:50,200
+which wants the list of evaluated arguments.
+
+171
+00:10:50,200 --> 00:10:53,140
+What you can start seeing here is the basic structure of the evaluator. 
+
+172
+00:10:53,140 --> 00:10:54,490
+Remember how evaluators work.
+
+173
+00:10:54,490 --> 00:10:57,670
+There's a piece that takes expressions and environments,
+
+174
+00:10:57,670 --> 00:10:59,100
+and there's a piece that takes
+
+175
+00:10:59,100 --> 00:11:03,480
+functions, or procedures and arguments.
+
+176
+00:11:03,480 --> 00:11:07,294
+And going back and forth around here is the eval/apply loop. 
+
+177
+00:11:07,294 --> 00:11:10,000
+So those are the basic pieces of the eval and apply.
+
+178
+00:11:10,000 --> 00:11:11,610
+Then there's some other things, there's continue.
+
+179
+00:11:11,610 --> 00:11:15,340
+You just saw before how the continue register is used to
+
+180
+00:11:15,340 --> 00:11:18,750
+implement recursion and stack discipline.
+
+181
+00:11:18,750 --> 00:11:23,925
+There's a register that's going to hold the result of some evaluation. 
+
+182
+00:11:23,925 --> 00:11:26,555
+And then, besides that, there's one temporary register, 
+
+183
+00:11:26,555 --> 00:11:29,280
+called UNEV, which typically, in the evaluator,
+
+184
+00:11:29,280 --> 00:11:30,625
+is going to be used to hold 
+
+185
+00:11:30,625 --> 00:11:33,950
+temporary pieces of the expression you're working on, 
+
+186
+00:11:33,950 --> 00:11:37,150
+which you haven't gotten around to evaluate yet, right? 
+
+187
+00:11:37,150 --> 00:11:40,646
+So there's my machine: a seven-register machine.
+
+188
+00:11:40,646 --> 00:11:42,981
+And, of course, you might want to make a machine with
+
+189
+00:11:42,981 --> 00:11:44,846
+a lot more registers to get better performance, 
+
+190
+00:11:44,846 --> 00:11:48,480
+but this is just a tiny, minimal one.
+
+191
+00:11:48,480 --> 00:11:49,780
+Well, how about the data paths?
+
+192
+00:11:49,780 --> 00:11:55,100
+This machine has a lot of special operations for LISP.
+
+193
+00:11:55,100 --> 00:12:00,120
+So, here are some typical data paths.
+
+194
+00:12:00,120 --> 00:12:03,320
+A typical one might be, oh, assign to the VAL register
+
+195
+00:12:03,320 --> 00:12:06,710
+the contents of the EXP register.
+
+196
+00:12:06,710 --> 00:12:11,900
+In terms of those diagrams you saw, that's a little button on some arrow. 
+
+197
+00:12:11,900 --> 00:12:13,699
+Here's a more complicated one.
+
+198
+00:12:13,699 --> 00:12:18,810
+It says branch, if the thing in the expression register is
+
+199
+00:12:18,810 --> 00:12:23,550
+a conditional to some label here, called the ev-conditional. 
+
+200
+00:12:23,550 --> 00:12:26,230
+And you can imagine this implemented in a lot of different ways. 
+
+201
+00:12:26,230 --> 00:12:30,600
+You might imagine this conditional test as a special purpose sub-routine,  
+
+202
+00:12:30,600 --> 00:12:33,845
+and conditional might be represented as some data abstraction
+
+203
+00:12:33,845 --> 00:12:36,610
+that you don't care about at this level of detail.
+
+204
+00:12:36,610 --> 00:12:37,980
+So that might be done as a sub-routine.
+
+205
+00:12:37,980 --> 00:12:40,900
+This might be a machine with hardware-types, 
+
+206
+00:12:40,900 --> 00:12:45,350
+and conditional might be testing some bits for a particular code.
+
+207
+00:12:45,350 --> 00:12:46,417
+There are all sorts of ways that's 
+
+208
+00:12:46,417 --> 00:12:50,190
+beneath the level of abstraction we're looking at. 
+
+209
+00:12:50,190 --> 00:12:53,247
+Another kind of operation, and there are a lot of different operations
+
+210
+00:12:53,247 --> 00:12:56,840
+assigned to EXP, the first clause of what's in EXP. 
+
+211
+00:12:56,840 --> 00:12:59,260
+This might be part of processing a conditional.
+
+212
+00:12:59,260 --> 00:13:04,258
+And, again, first clause is some selector whose details we don't care about. 
+
+213
+00:13:04,258 --> 00:13:06,300
+And you can, again, imagine that as a sub-routine
+
+214
+00:13:06,300 --> 00:13:09,180
+which'll do some list operations, or you can imagine that as
+
+215
+00:13:09,180 --> 00:13:12,170
+something that's built directly into hardware.
+
+216
+00:13:12,170 --> 00:13:15,222
+The reason I keep saying you can imagine it built directly into hardware
+
+217
+00:13:15,222 --> 00:13:18,360
+is even though there are a lot of operations,
+
+218
+00:13:18,360 --> 00:13:19,740
+there are still a fixed number of them.
+
+219
+00:13:19,740 --> 00:13:22,370
+I forget how many, maybe 150.
+
+220
+00:13:22,370 --> 00:13:26,167
+So, it's plausible to think of building these directly into hardware. 
+
+221
+00:13:26,167 --> 00:13:28,275
+Here's a more complicated one.
+
+222
+00:13:28,275 --> 00:13:31,500
+You can see this has to do with looking up the values of variables. 
+
+223
+00:13:31,500 --> 00:13:35,550
+It says assign to the VAL register the result of looking up
+
+224
+00:13:35,550 --> 00:13:39,025
+the variable value of some particular expression, 
+
+225
+00:13:39,025 --> 00:13:42,600
+which,in this case, is supposed to be a variable in some environment. 
+
+226
+00:13:42,600 --> 00:13:46,280
+And this'll be some operation that searches through 
+
+227
+00:13:46,280 --> 00:13:49,325
+the environment structure, however it is represented, 
+
+228
+00:13:49,325 --> 00:13:52,019
+and goes and looks up that variable.
+
+229
+00:13:52,019 --> 00:13:55,790
+And, again, that's below the level of detail that we're thinking about. 
+
+230
+00:13:55,790 --> 00:13:57,300
+This has to do with the details of 
+
+231
+00:13:57,300 --> 00:14:00,075
+the data structures for representing environments. 
+
+232
+00:14:00,075 --> 00:14:03,679
+But, anyway, there is this fixed and finite number 
+
+233
+00:14:03,679 --> 00:14:06,325
+of operations in the register machine.
+
+234
+00:14:08,500 --> 00:14:11,720
+Well, what's its overall structure?
+
+235
+00:14:11,720 --> 00:14:14,675
+Those are some typical operations.
+
+236
+00:14:14,675 --> 00:14:16,442
+Remember what we have to do, 
+
+237
+00:14:16,442 --> 00:14:20,172
+we have to take the meta-circular evaluator--
+
+238
+00:14:20,172 --> 00:14:22,767
+and here's a piece of the meta-circular evaluator.
+
+239
+00:14:22,767 --> 00:14:28,050
+This is the one using abstract syntax that's in the book.
+
+240
+00:14:28,050 --> 00:14:33,500
+It's a little bit different from the one that Jerry shows you. 
+
+241
+00:14:33,500 --> 00:14:37,874
+And the main thing to remember about the evaluator is that
+
+242
+00:14:37,874 --> 00:14:43,425
+it's doing some sort of case analysis on the kinds of expressions: 
+
+243
+00:14:43,425 --> 00:14:48,560
+so if it's either self-evaluated, or quoted, or whatever else. 
+
+244
+00:14:48,560 --> 00:14:50,864
+And then, in the general case where
+
+245
+00:14:50,864 --> 00:14:53,550
+the expression it's looking at is an application, 
+
+246
+00:14:53,550 --> 00:14:55,750
+there's some tricky recursions going on.
+
+247
+00:14:55,750 --> 00:15:00,730
+First of all, eval has to call itself both to evaluate the
+
+248
+00:15:00,730 --> 00:15:05,880
+operator and to evaluate all the operands.
+
+249
+00:15:05,880 --> 00:15:10,850
+So there's this sort of red recursion of values walking down the tree
+
+250
+00:15:10,850 --> 00:15:12,270
+that's really the easy recursion.
+
+251
+00:15:12,270 --> 00:15:14,750
+That's just a val walking down this tree of expressions.
+
+252
+00:15:14,750 --> 00:15:16,305
+Then, in the evaluator, there's a hard recursion.
+
+253
+00:15:16,305 --> 00:15:21,650
+There's the red to green. Eval calls apply. 
+
+254
+00:15:22,470 --> 00:15:26,450
+That's the case where evaluating a procedure or argument 
+
+255
+00:15:26,450 --> 00:15:30,370
+reduces to applying the procedure to the list of arguments. 
+
+256
+00:15:30,370 --> 00:15:33,875
+And then, apply comes over here.
+
+257
+00:15:34,770 --> 00:15:37,650
+Apply takes a procedure and arguments
+
+258
+00:15:37,650 --> 00:15:41,051
+and, in the general case where there's a compound procedure, 
+
+259
+00:15:41,051 --> 00:15:44,560
+apply goes around and green calls red. Eval --
+
+260
+00:15:44,560 --> 00:15:48,170
+Apply comes around and calls eval again.
+
+261
+00:15:48,170 --> 00:15:51,330
+Eval's the body of the procedure in the result of
+
+262
+00:15:51,330 --> 00:15:55,485
+extending the environment with the parameters of the procedure
+
+263
+00:15:55,485 --> 00:15:57,379
+by binding the arguments.
+
+264
+00:15:59,620 --> 00:16:01,626
+Except in the primitive case, where it just calls something else
+
+265
+00:16:01,626 --> 00:16:05,980
+primitive-apply, which is not really the business of the evaluator. 
+
+266
+00:16:05,980 --> 00:16:11,249
+So this sort of red to green, to red to green, that's the
+
+267
+00:16:11,249 --> 00:16:13,975
+that's the eval/apply loop, 
+
+268
+00:16:13,975 --> 00:16:19,475
+and that's the thing that we're going to want to see in the evaluator.
+
+269
+00:16:19,475 --> 00:16:21,079
+Well, it won't surprise you at all that 
+
+270
+00:16:21,079 --> 00:16:27,470
+the two big pieces of this evaluator correspond to eval and apply.
+
+271
+00:16:27,470 --> 00:16:29,548
+There's a piece called eval-dispatch, 
+
+272
+00:16:29,548 --> 00:16:31,913
+and a piece called apply-dispatch.
+
+273
+00:16:31,913 --> 00:16:34,095
+And, before we get into the details of the code, 
+
+274
+00:16:34,095 --> 00:16:37,760
+the way to understand this is to think, again, in terms of
+
+275
+00:16:37,760 --> 00:16:41,870
+these pieces of the evaluator having contracts with the rest of the world. 
+
+276
+00:16:41,870 --> 00:16:45,780
+What do they do from the outside before getting into the grungy details? 
+
+277
+00:16:45,780 --> 00:16:51,300
+Well, the contract for eval-dispatch-- remember, it corresponds to eval. 
+
+278
+00:16:51,300 --> 00:16:54,100
+It's got to evaluate an expression in an environment.
+
+279
+00:16:54,100 --> 00:16:56,525
+So, in particular, what this one is going to do,
+
+280
+00:16:56,525 --> 00:16:59,920
+eval-dispatch will assume that, when you call it, that
+
+281
+00:16:59,920 --> 00:17:03,640
+the expression you want to evaluate is in the EXP register. 
+
+282
+00:17:03,640 --> 00:17:07,750
+The environment in which you want the evaluation to take place
+
+283
+00:17:07,750 --> 00:17:09,569
+is in the ENV register. 
+
+284
+00:17:09,569 --> 00:17:11,899
+And continue tells you the place where the machine should
+
+285
+00:17:11,899 --> 00:17:14,575
+go next when the evaluation is done.
+
+286
+00:17:17,440 --> 00:17:21,070
+Eval-dispatch's contract is that it'll actually perform that evaluation, 
+
+287
+00:17:21,070 --> 00:17:26,619
+and, at the end of which, it'll end up at the place specified by continue. 
+
+288
+00:17:26,619 --> 00:17:29,825
+The result of the evaluation will be in the VAL register.
+
+289
+00:17:29,825 --> 00:17:32,964
+And it just warns you, it makes no promises about
+
+290
+00:17:32,964 --> 00:17:35,230
+what happens to the registers.
+
+291
+00:17:35,230 --> 00:17:37,490
+All other registers might be destroyed.
+
+292
+00:17:37,490 --> 00:17:41,412
+So, there's one piece, OK?
+
+293
+00:17:41,412 --> 00:17:45,925
+Together, the pieces, apply-dispatch that corresponds to apply,
+
+294
+00:17:45,925 --> 00:17:48,731
+it's got to apply a procedure to some arguments, 
+
+295
+00:17:48,731 --> 00:17:51,434
+so it assumes that this register, ARGL,
+
+296
+00:17:51,434 --> 00:17:54,540
+contains a list of the evaluated arguments.
+
+297
+00:17:54,540 --> 00:17:57,220
+FUN contains the procedure.
+
+298
+00:17:57,220 --> 00:17:59,500
+Those correspond to the arguments to the apply
+
+299
+00:17:59,500 --> 00:18:02,300
+procedure in the meta-circular evaluator.
+
+300
+00:18:03,970 --> 00:18:07,676
+And apply, in this particular evaluator, we're going to use a discipline which says
+
+301
+00:18:07,676 --> 00:18:12,556
+the place the machine should go to next when apply is done 
+
+302
+00:18:12,556 --> 00:18:17,070
+is, at the moment apply-dispatch is called at the top of the stack
+
+303
+00:18:17,070 --> 00:18:21,840
+that's just discipline for the way this particular machine's organized. 
+
+304
+00:18:21,840 --> 00:18:23,700
+And now apply's contract is given all that.
+
+305
+00:18:23,700 --> 00:18:25,540
+It'll perform the application.
+
+306
+00:18:25,540 --> 00:18:28,890
+The result of that application will end up in VAL.
+
+307
+00:18:28,890 --> 00:18:31,120
+The stack will be popped.
+
+308
+00:18:31,120 --> 00:18:34,841
+And, again, the contents of all the other registers may be destroyed.
+
+309
+00:18:34,841 --> 00:18:39,760
+All right? So that's the basic organization of this machine.
+
+310
+00:18:39,760 --> 00:18:41,110
+Let's break for a little bit and see if there are any
+
+311
+00:18:41,110 --> 00:18:42,700
+questions, and then we'll do a real example.
+
+312
+00:19:47,850 --> 00:19:50,175
+Well, let's take the register machine now, 
+
+313
+00:19:50,175 --> 00:19:52,175
+and actually step through,
+
+314
+00:19:52,200 --> 00:19:58,708
+and really, in real detail, so you see completely concrete
+
+315
+00:19:58,708 --> 00:20:03,400
+how some expressions are evaluated, all right?
+
+316
+00:20:03,400 --> 00:20:09,300
+So, let's start with a very simple expression.
+
+317
+00:20:09,620 --> 00:20:14,150
+Let's evaluate the expression 1.
+
+318
+00:20:18,775 --> 00:20:21,279
+And we need an environment, so let's imagine that 
+
+319
+00:20:21,279 --> 00:20:24,025
+somewhere there's an environment, we'll call it E,0.
+
+320
+00:20:30,260 --> 00:20:35,620
+And just, since we'll use these later, 
+
+321
+00:20:35,620 --> 00:20:38,360
+we obviously don't really need anything to evaluate 1.
+
+322
+00:20:38,360 --> 00:20:41,202
+But, just for reference later, let's assume that E,0 has in it
+
+323
+00:20:41,202 --> 00:20:49,140
+an X that's bound to 3 and a Y that's bound to 4, OK?
+
+324
+00:20:49,140 --> 00:20:53,700
+And now what we're going to do is we're going to evaluate 1
+
+325
+00:20:53,700 --> 00:20:59,650
+in this environment, and so the ENV register has a pointer
+
+326
+00:20:59,650 --> 00:21:03,560
+to this environment, E,0, all right?
+
+327
+00:21:03,560 --> 00:21:05,650
+So let's watch that thing go.
+
+328
+00:21:05,650 --> 00:21:08,260
+What I'm going to do is step through the code.
+
+329
+00:21:08,260 --> 00:21:09,782
+And, let's see, I'll be the controller.
+
+330
+00:21:09,782 --> 00:21:12,980
+And now what I need, since this gets rather complicated,
+
+331
+00:21:12,980 --> 00:21:16,830
+is a very little execution unit.
+
+332
+00:21:16,830 --> 00:21:21,310
+So here's the execution unit, OK?
+
+333
+00:21:22,624 --> 00:21:23,874
+OK.
+
+334
+00:21:27,088 --> 00:21:28,590
+OK.
+
+335
+00:21:28,590 --> 00:21:30,533
+All right, now we're going to start.
+
+336
+00:21:30,533 --> 00:21:33,700
+We're going to start the machine at eval-dispatch, right? 
+
+337
+00:21:33,700 --> 00:21:35,875
+That's the beginning of this.
+
+338
+00:21:35,875 --> 00:21:39,320
+Eval-dispatch is going to look at the expression in dispatch,
+
+339
+00:21:39,320 --> 00:21:40,875
+just like eval 
+
+340
+00:21:40,875 --> 00:21:41,760
+where we look at the very first thing.
+
+341
+00:21:41,760 --> 00:21:47,950
+We branch on whether or not this expression is self-evaluating. 
+
+342
+00:21:47,950 --> 00:21:52,171
+Self-evaluating is some abstraction we put into the machine-- 
+
+343
+00:21:52,171 --> 00:21:53,515
+it's going to be true for numbers--
+
+344
+00:21:53,515 --> 00:21:56,775
+to a place called ev-self-eval, right?
+
+345
+00:21:56,775 --> 00:22:00,010
+So me, being the controller, looks at ev-self-eval, 
+
+346
+00:22:00,010 --> 00:22:02,607
+so we'll go over to there.
+
+347
+00:22:02,607 --> 00:22:08,128
+Ev-self-eval says fine, assign to val 
+
+348
+00:22:08,128 --> 00:22:15,220
+whatever is in the expression unit, OK?
+
+349
+00:22:15,220 --> 00:22:17,600
+And I have a bug 
+
+350
+00:22:17,600 --> 00:22:17,650
+because what I didn't do when I initialized this machine
+
+351
+00:22:17,650 --> 00:22:21,625
+because what I didn't do when I initialized this machine
+
+352
+00:22:21,625 --> 00:22:24,650
+is also say what's supposed to happen when it's done, 
+
+353
+00:22:24,650 --> 00:22:27,640
+so I should have started out the machine with
+
+354
+00:22:27,640 --> 00:22:32,050
+done being in the continue register, OK?
+
+355
+00:22:32,050 --> 00:22:33,079
+So we assign to VAL.
+
+356
+00:22:33,079 --> 00:22:38,000
+And now go to fetch of continue, and now change-- 
+
+357
+00:22:38,000 --> 00:22:40,000
+OK.
+
+358
+00:22:40,000 --> 00:22:42,160
+OK, let's try something harder.
+
+359
+00:22:42,160 --> 00:22:44,787
+Let's reset the machine here, 
+
+360
+00:22:44,787 --> 00:22:51,562
+and we'll put in the expression register, X, OK?
+
+361
+00:22:56,710 --> 00:22:59,610
+Start again at eval-dispatch.
+
+362
+00:22:59,610 --> 00:23:01,690
+Check, is it self-evaluating?
+
+363
+00:23:01,690 --> 00:23:02,650
+No.
+
+364
+00:23:02,650 --> 00:23:04,630
+Is it a variable?
+
+365
+00:23:04,630 --> 00:23:05,560
+Yes.
+
+366
+00:23:05,560 --> 00:23:08,380
+We go off to ev-variable.
+
+367
+00:23:08,380 --> 00:23:12,131
+It says assign to VAL,
+
+368
+00:23:12,131 --> 00:23:16,150
+look up the variable value in the expression register, OK?
+
+369
+00:23:21,075 --> 00:23:23,625
+Go to fetch of continue.
+
+370
+00:23:23,625 --> 00:23:24,875
+PROFESSOR: Done.
+
+371
+00:23:27,252 --> 00:23:28,950
+PROFESSOR: OK.
+
+372
+00:23:28,950 --> 00:23:29,430
+All right.
+
+373
+00:23:29,430 --> 00:23:31,330
+Well, that's the basic idea.
+
+374
+00:23:31,330 --> 00:23:32,688
+That's a simple operation of the machine.
+
+375
+00:23:32,688 --> 00:23:36,070
+Now, let's actually do something a little bit more interesting. 
+
+376
+00:23:36,070 --> 00:23:49,678
+Let's look at the expression the sum of x and y.
+
+377
+00:23:49,678 --> 00:23:50,130
+OK.
+
+378
+00:23:50,130 --> 00:23:54,350
+And now we'll see how you start unrolling these expression trees.
+
+379
+00:23:56,625 --> 00:23:59,434
+Well, start again at eval-dispatch.
+
+380
+00:24:04,610 --> 00:24:05,935
+Self-evaluating?
+
+381
+00:24:05,935 --> 00:24:06,850
+No.
+
+382
+00:24:06,850 --> 00:24:07,850
+Variable? No. 
+
+383
+00:24:07,850 --> 00:24:10,270
+All the other special forms which I didn't write down,
+
+384
+00:24:10,270 --> 00:24:12,480
+like quote, and lambda, and set, and whatever,
+
+385
+00:24:12,480 --> 00:24:13,260
+it's none of those.
+
+386
+00:24:13,260 --> 00:24:15,889
+It turns out to be an application,
+
+387
+00:24:15,889 --> 00:24:19,970
+so we go off to ev-application, OK?
+
+388
+00:24:19,970 --> 00:24:25,580
+Ev-application, remember what it's going to do overall.
+
+389
+00:24:25,580 --> 00:24:28,310
+It is going to evaluate the operator.
+
+390
+00:24:28,310 --> 00:24:32,225
+It's going to evaluate the arguments,
+
+391
+00:24:32,225 --> 00:24:35,060
+and then it's going to go apply them.
+
+392
+00:24:35,060 --> 00:24:37,887
+So, before we start, since we're being very literal, 
+
+393
+00:24:37,887 --> 00:24:40,435
+we'd better remember that, somewhere in this environment,
+
+394
+00:24:40,435 --> 00:24:44,475
+it's linked to another environment in which
+
+395
+00:24:44,475 --> 00:24:51,475
+plus is bound to the primitive procedure plus 
+
+396
+00:24:51,475 --> 00:24:55,340
+before we get an unknown variable in our machine.
+
+397
+00:24:55,340 --> 00:24:58,625
+OK, so we're at ev-application.
+
+398
+00:24:59,700 --> 00:25:04,405
+OK, assign to UNEV the operands 
+
+399
+00:25:04,405 --> 00:25:07,920
+of what's in the expression register, OK?
+
+400
+00:25:07,920 --> 00:25:09,230
+Those are the operands.
+
+401
+00:25:09,230 --> 00:25:13,225
+UNEV's a temporary register where we're going to save them. 
+
+402
+00:25:13,225 --> 00:25:13,860
+PROFESSOR: I'm assigning.
+
+403
+00:25:13,860 --> 00:25:18,070
+PROFESSOR: Assign to x the operator.
+
+404
+00:25:18,070 --> 00:25:21,849
+Now, notice we've destroyed that expression in x, 
+
+405
+00:25:21,849 --> 00:25:25,820
+but the piece that we need is now in UNEV. OK.
+
+406
+00:25:25,820 --> 00:25:28,750
+Now, we're going to get set up to recursively evaluate the operator. 
+
+407
+00:25:28,750 --> 00:25:32,825
+Save the continue register on the stack.
+
+408
+00:25:34,870 --> 00:25:37,600
+Save the environment.
+
+409
+00:25:40,520 --> 00:25:43,594
+Save UNEV. 
+
+410
+00:25:49,409 --> 00:25:56,234
+OK, assign to continue a label called eval-args.
+
+411
+00:26:01,400 --> 00:26:01,950
+Now, what have we done?
+
+412
+00:26:01,950 --> 00:26:04,380
+We've set up for a recursive call. 
+
+413
+00:26:04,380 --> 00:26:06,280
+We're about to go to eval-dispatch.
+
+414
+00:26:06,280 --> 00:26:10,230
+We've set up for a recursive call to eval-dispatch.
+
+415
+00:26:10,230 --> 00:26:11,020
+What did we do?
+
+416
+00:26:11,020 --> 00:26:14,425
+We took the things we're going to need later,
+
+417
+00:26:14,425 --> 00:26:16,363
+those operands that were in UNEV;
+
+418
+00:26:16,363 --> 00:26:19,073
+the environment in which we're going to eventually have to, 
+
+419
+00:26:19,073 --> 00:26:22,129
+maybe, evaluate those operands;
+
+420
+00:26:22,129 --> 00:26:25,265
+the place we eventually want to go to, which, in this case, was done;
+
+421
+00:26:25,265 --> 00:26:27,275
+we've saved them on the stack.
+
+422
+00:26:27,275 --> 00:26:28,724
+The reason we saved them on the stack is because
+
+423
+00:26:28,724 --> 00:26:33,550
+eval-dispatch makes no promises about what registers it may destroy. 
+
+424
+00:26:33,550 --> 00:26:35,020
+So all that stuff is saved on the stack.
+
+425
+00:26:35,020 --> 00:26:37,380
+Now, we've set up eval-dispatch's contract.
+
+426
+00:26:37,380 --> 00:26:40,964
+There's a new expression, which is the operator plus;
+
+427
+00:26:40,964 --> 00:26:44,250
+a new environment, although, in this case, it's the same one;
+
+428
+00:26:44,250 --> 00:26:47,600
+and a new place to go to when you're done, which is eval-args. 
+
+429
+00:26:47,600 --> 00:26:48,130
+So that's set up.
+
+430
+00:26:48,130 --> 00:26:50,890
+Now, we're going to go off to eval-dispatch.
+
+431
+00:26:50,890 --> 00:26:53,090
+Here we are back at eval-dispatch.
+
+432
+00:26:53,090 --> 00:26:54,490
+It's not self-evaluating.
+
+433
+00:26:54,490 --> 00:27:00,147
+Oh, it's a variable, so we'd better go off to ev-variable, right? 
+
+434
+00:27:00,147 --> 00:27:02,880
+Ev-variable is assigned to VAL.
+
+435
+00:27:02,880 --> 00:27:08,770
+Look up the variable value of the expression, OK?
+
+436
+00:27:08,770 --> 00:27:13,000
+So VAL is the primitive procedure plus, OK?
+
+437
+00:27:13,000 --> 00:27:15,020
+And go to fetch of continue.
+
+438
+00:27:15,020 --> 00:27:16,050
+PROFESSOR: Eval-args.
+
+439
+00:27:16,050 --> 00:27:19,340
+PROFESSOR: Right, which is now eval-args not done.
+
+440
+00:27:19,340 --> 00:27:23,071
+So we come back here at eval-args, and what do we do?
+
+441
+00:27:23,071 --> 00:27:29,050
+We're going to restore the stuff that we saved, so we restore UNEV.
+
+442
+00:27:29,050 --> 00:27:32,900
+And notice, there, it wasn't necessary, although, in general, it would be. 
+
+443
+00:27:32,900 --> 00:27:35,430
+It might be some arbitrary evaluation that happened.
+
+444
+00:27:35,430 --> 00:27:54,900
+We restore ENV. OK, we assign to FUN fetch of VAL.
+
+445
+00:27:58,620 --> 00:28:04,340
+OK, now, we're going to go off and start evaluating some arguments. 
+
+446
+00:28:04,340 --> 00:28:08,330
+Well, first thing we'd better do is save FUN because some
+
+447
+00:28:08,330 --> 00:28:13,675
+arbitrary stuff might happen in that evaluation.
+
+448
+00:28:15,330 --> 00:28:20,750
+We initialize the argument list. Assign to argl an empty argument list, 
+
+449
+00:28:20,750 --> 00:28:25,460
+and go to eval-arg-loop, OK?
+
+450
+00:28:25,460 --> 00:28:29,580
+At eval-arg-loop, the idea of this is we're going to
+
+451
+00:28:29,580 --> 00:28:33,540
+evaluate the pieces of the expressions that are in UNEV, one by one, 
+
+452
+00:28:33,540 --> 00:28:35,688
+and move them from unevaluated in UNEV 
+
+453
+00:28:35,688 --> 00:28:38,090
+to evaluated in the arg list, OK?
+
+454
+00:28:38,090 --> 00:28:42,400
+So we save argl.
+
+455
+00:28:43,950 --> 00:28:49,145
+We assign to x the first operand of the stuff in UNEV.
+
+456
+00:28:53,772 --> 00:28:55,890
+Now, we check and see if that was the last operand.
+
+457
+00:28:55,890 --> 00:28:59,190
+In this case, it is not, all right?
+
+458
+00:28:59,190 --> 00:29:02,975
+So we save the environment.
+
+459
+00:29:07,850 --> 00:29:13,500
+We save UNEV because those are all things we might need later. 
+
+460
+00:29:13,500 --> 00:29:15,800
+We're going to need the environment to do some more evaluations. 
+
+461
+00:29:15,800 --> 00:29:20,340
+We're going to need UNEV to look at what the rest of those arguments were. 
+
+462
+00:29:20,340 --> 00:29:26,053
+We're going to assign continue a place called accumulate-args, or accumulate-arg. 
+
+463
+00:29:30,898 --> 00:29:36,810
+OK, now, we've set up for another call to eval-dispatch, OK? 
+
+464
+00:29:36,810 --> 00:29:39,125
+All right, now, let me short-circuit this
+
+465
+00:29:39,125 --> 00:29:41,090
+so we don't go through the details of eval-dispatch.
+
+466
+00:29:41,090 --> 00:29:45,103
+Eval-dispatch's contract says I'm going to end up,
+
+467
+00:29:45,103 --> 00:29:48,240
+the world will end up, with the value of evaluating this expression
+
+468
+00:29:48,240 --> 00:29:50,270
+in this environment in the VAL register,
+
+469
+00:29:50,270 --> 00:29:51,320
+and I'll end up there.
+
+470
+00:29:51,320 --> 00:29:58,010
+So we short-circuit all of this, and a 3 ends up in VAL.
+
+471
+00:29:58,010 --> 00:29:59,768
+And, when we return from eval-dispatch,
+
+472
+00:29:59,768 --> 00:30:02,110
+we're going to return to accumulate-arg.
+
+473
+00:30:02,110 --> 00:30:03,555
+PROFESSOR: Accumulate-arg.
+
+474
+00:30:06,185 --> 00:30:08,720
+PROFESSOR: With 3 in the VAL register, OK?
+
+475
+00:30:08,720 --> 00:30:10,650
+So that short-circuited that evaluation.
+
+476
+00:30:10,650 --> 00:30:11,320
+Now, what do we do?
+
+477
+00:30:11,320 --> 00:30:13,689
+We're going to go back and look at the rest of the arguments,
+
+478
+00:30:13,689 --> 00:30:15,609
+so we restore UNEV. 
+
+479
+00:30:17,513 --> 00:30:28,650
+We restore ENV. We restore argl.
+
+480
+00:30:28,650 --> 00:30:29,170
+One thing.
+
+481
+00:30:29,170 --> 00:30:30,536
+PROFESSOR: Oops!
+
+482
+00:30:30,536 --> 00:30:31,290
+Parity error.
+
+483
+00:30:31,290 --> 00:30:33,465
+[LAUGHTER]
+
+484
+00:30:33,465 --> 00:30:34,905
+PROFESSOR: Restore argl.
+
+485
+00:30:41,650 --> 00:30:42,900
+PROFESSOR: OK.
+
+486
+00:30:45,570 --> 00:30:50,400
+OK, we assign to argl consing on 
+
+487
+00:30:50,400 --> 00:30:53,130
+fetch of the value register to what's in argl.
+
+488
+00:30:58,985 --> 00:31:05,025
+OK, we assign to UNEV the rest of the operands in fetch of UNEV, 
+
+489
+00:31:08,700 --> 00:31:11,516
+and we go back to eval-arg-loop.
+
+490
+00:31:11,516 --> 00:31:12,280
+PROFESSOR: Eval-arg-loop.
+
+491
+00:31:12,280 --> 00:31:13,530
+PROFESSOR: OK.
+
+492
+00:31:15,880 --> 00:31:17,375
+Now, we're about to do the next argument, 
+
+493
+00:31:17,375 --> 00:31:19,800
+so the first thing we do is save argl.
+
+494
+00:31:25,400 --> 00:31:31,803
+OK, we assign to x the first operand of fetch of UNEV. 
+
+495
+00:31:34,650 --> 00:31:38,925
+OK,we test and see if that's the last operand.In this case, it is
+
+496
+00:31:38,925 --> 00:31:43,173
+so we're going to go to a special place that says evaluate the last argument  
+
+497
+00:31:43,173 --> 00:31:44,965
+because, notice,after evaluating the argument, 
+
+498
+00:31:44,965 --> 00:31:47,446
+we don't need the environment any more.
+
+499
+00:31:47,446 --> 00:31:50,250
+That's going to be the difference.
+
+500
+00:31:50,250 --> 00:31:52,054
+So here, at eval-last-arg, 
+
+501
+00:31:52,054 --> 00:31:55,382
+which is assigned to continue accumulate-last-arg, 
+
+502
+00:32:04,275 --> 00:32:06,900
+now, we're set up again for eval-dispatch.
+
+503
+00:32:06,900 --> 00:32:08,620
+We've got a place to go to when we're done.
+
+504
+00:32:08,620 --> 00:32:09,840
+We've got an expression.
+
+505
+00:32:09,840 --> 00:32:11,330
+We've got an environment.
+
+506
+00:32:11,330 --> 00:32:14,370
+OK, so we'll short-circuit the call to eval-dispatch.
+
+507
+00:32:14,370 --> 00:32:16,700
+And what'll happen is there's a y there,
+
+508
+00:32:16,700 --> 00:32:21,060
+it's 4 in that environment, so VAL will end up with 4 in it.
+
+509
+00:32:21,060 --> 00:32:25,450
+And, then, we're going to end up at accumulate-last-arg, OK?
+
+510
+00:32:25,450 --> 00:32:30,525
+So, at accumulate-last-arg, we restore argl.
+
+511
+00:32:41,490 --> 00:32:45,835
+We assign to argl cons of fetch of the new value onto it, 
+
+512
+00:32:45,835 --> 00:32:49,850
+so we cons a 4 onto that.
+
+513
+00:32:49,850 --> 00:32:53,446
+We restore what was saved in the function register.
+
+514
+00:32:53,446 --> 00:32:56,277
+And notice, in this case, it had not been destroyed, 
+
+515
+00:32:56,277 --> 00:32:59,132
+but in general, it will be.
+
+516
+00:32:59,132 --> 00:33:02,850
+And now, we're ready to go off to apply-dispatch, all right?
+
+517
+00:33:02,850 --> 00:33:04,510
+So we've just gone through the eval.
+
+518
+00:33:04,510 --> 00:33:07,980
+We evaluated the argument, the operator, and the arguments,
+
+519
+00:33:07,980 --> 00:33:09,580
+and now, we're about to apply them.
+
+520
+00:33:09,580 --> 00:33:17,481
+So we come off to apply-dispatch here, OK?
+
+521
+00:33:17,481 --> 00:33:20,575
+We come off to apply-dispatch, 
+
+522
+00:33:20,575 --> 00:33:23,450
+and we're going to check whether it's a primitive or a compound procedure.
+
+523
+00:33:23,450 --> 00:33:24,116
+PROFESSOR: Yes.
+
+524
+00:33:24,116 --> 00:33:24,830
+PROFESSOR: All right.
+
+525
+00:33:24,830 --> 00:33:27,375
+So, in this case, it's a primitive procedure, 
+
+526
+00:33:27,375 --> 00:33:29,790
+and we go off to primitive-apply.
+
+527
+00:33:29,790 --> 00:33:34,130
+So we go off to primitive-apply, and it says
+
+528
+00:33:34,130 --> 00:33:38,360
+assign to VAL the result of applying primitive procedure
+
+529
+00:33:38,360 --> 00:33:40,940
+of the function to the argument list.
+
+530
+00:33:40,940 --> 00:33:42,540
+PROFESSOR: I don't know how to add.
+
+531
+00:33:42,540 --> 00:33:43,995
+I'm just an execution unit.
+
+532
+00:33:43,995 --> 00:33:45,350
+PROFESSOR: Well, I don't know how to add either.
+
+533
+00:33:45,350 --> 00:33:48,360
+I'm just the evaluator, so we need a primitive operator.
+
+534
+00:33:48,360 --> 00:33:50,925
+Let's see, so the primitive operator, what's the
+
+535
+00:33:50,925 --> 00:33:52,605
+What's the sum of 3 and 4?
+
+536
+00:33:52,605 --> 00:33:53,205
+AUDIENCE: 7.
+
+537
+00:33:53,205 --> 00:33:55,050
+PROFESSOR: OK, 7.
+
+538
+00:33:55,050 --> 00:33:55,999
+PROFESSOR: Thank you.
+
+539
+00:33:58,837 --> 00:34:00,850
+PROFESSOR: Now, we restore continue, 
+
+540
+00:34:11,275 --> 00:34:12,900
+and we go to fetch of continue.
+
+541
+00:34:12,900 --> 00:34:13,880
+PROFESSOR: Done.
+
+542
+00:34:13,880 --> 00:34:14,929
+PROFESSOR: OK.
+
+543
+00:34:14,929 --> 00:34:18,413
+Well, that was in as much detail as you will ever see.
+
+544
+00:34:18,413 --> 00:34:21,590
+We'll never do it in as much detail again.
+
+545
+00:34:21,590 --> 00:34:25,233
+One very important thing to notice is that 
+
+546
+00:34:25,233 --> 00:34:29,780
+we just executed a recursive procedure, right?
+
+547
+00:34:29,780 --> 00:34:31,172
+This whole thing, we used a stack 
+
+548
+00:34:31,172 --> 00:34:33,070
+and the evaluator was recursive.
+
+549
+00:34:33,070 --> 00:34:36,480
+A lot of people think the reason that you need a stack
+
+550
+00:34:36,480 --> 00:34:39,090
+and recursion in an evaluator is because you might be
+
+551
+00:34:39,090 --> 00:34:42,150
+evaluating recursive procedures like factorial or Fibonacci. 
+
+552
+00:34:42,150 --> 00:34:43,670
+It's not true.
+
+553
+00:34:43,670 --> 00:34:46,110
+So you notice we did recursion here, and all we evaluated was
+
+554
+00:34:46,110 --> 00:34:48,010
+plus X, Y, all right?
+
+555
+00:34:48,010 --> 00:34:51,219
+The reason that you need recursion in the evaluator is
+
+556
+00:34:51,219 --> 00:34:54,450
+because the evaluation process, itself, is recursive, all right? 
+
+557
+00:34:54,450 --> 00:34:57,760
+It's not because the procedure that you might be evaluating in LISP 
+
+558
+00:34:57,760 --> 00:34:59,270
+is a recursive procedure.
+
+559
+00:34:59,270 --> 00:35:00,411
+So that's an important thing 
+
+560
+00:35:00,411 --> 00:35:03,010
+that people get confused about a lot.
+
+561
+00:35:03,010 --> 00:35:06,280
+The other thing to notice is that, when we're done here,
+
+562
+00:35:06,280 --> 00:35:07,120
+we're really done.
+
+563
+00:35:07,120 --> 00:35:10,878
+Not only are we at done, but 
+
+564
+00:35:10,878 --> 00:35:13,810
+there's no accumulated stuff on the stack, right?
+
+565
+00:35:13,810 --> 00:35:17,170
+The machine is back to its initial state, all right?
+
+566
+00:35:17,170 --> 00:35:19,715
+So that's part of what it means to be done.
+
+567
+00:35:19,715 --> 00:35:26,410
+Another way to say that is the evaluation process has reduced
+
+568
+00:35:26,410 --> 00:35:33,245
+the expression, plus X, Y, to the value here, 7.
+
+569
+00:35:33,245 --> 00:35:36,010
+And by reduced, I mean a very particular thing.
+
+570
+00:35:36,010 --> 00:35:38,180
+It means that there's nothing left on the stack.
+
+571
+00:35:38,180 --> 00:35:40,743
+The machine is now in the same state, 
+
+572
+00:35:40,743 --> 00:35:42,723
+except there's something in the value register.
+
+573
+00:35:42,723 --> 00:35:44,520
+It's not part of a sub-problem of anything.
+
+574
+00:35:44,520 --> 00:35:46,210
+There's nothing to go back to.
+
+575
+00:35:46,210 --> 00:35:46,440
+OK.
+
+576
+00:35:46,440 --> 00:35:47,690
+Let's break.
+
+577
+00:35:49,712 --> 00:35:50,159
+Question?
+
+578
+00:35:50,159 --> 00:35:54,027
+AUDIENCE: The question here, in the stack,
+
+579
+00:35:54,027 --> 00:35:55,820
+is because the data may be recursive.
+
+580
+00:35:55,820 --> 00:35:59,312
+You may have embedded expressions, for instance.
+
+581
+00:35:59,312 --> 00:36:02,080
+PROFESSOR: Yes, because you might have embedded expressions. 
+
+582
+00:36:02,080 --> 00:36:04,774
+But, again, don't confuse that 
+
+583
+00:36:04,774 --> 00:36:07,718
+with what people sometimes mean by the data may be recursive, 
+
+584
+00:36:07,718 --> 00:36:12,930
+which is to say you have these list-structured, recursive data list operations. 
+
+585
+00:36:12,930 --> 00:36:13,804
+That has nothing to do with it.
+
+586
+00:36:13,804 --> 00:36:17,363
+It's simply that the expressions contain sub-expressions. 
+
+587
+00:36:17,363 --> 00:36:19,618
+Yeah?
+
+588
+00:36:19,618 --> 00:36:23,457
+AUDIENCE: Why is it that the order of the arguments in the arg list got reversed? 
+
+589
+00:36:23,457 --> 00:36:27,260
+PROFESSOR: Ah! Yes, I should've mentioned that. 
+
+590
+00:36:27,260 --> 00:36:29,075
+Here, the reason the order is reversed--
+
+591
+00:36:32,507 --> 00:36:36,050
+it's a question of what you mean by reversed.
+
+592
+00:36:36,050 --> 00:36:40,624
+I believe it was Newton.
+
+593
+00:36:40,624 --> 00:36:43,800
+In the very early part of optics, people realized that,
+
+594
+00:36:43,800 --> 00:36:45,500
+when you look through the lens of your eye, 
+
+595
+00:36:45,500 --> 00:36:46,730
+the image was up-side down.
+
+596
+00:36:46,730 --> 00:36:48,044
+And there was a lot of argument about
+
+597
+00:36:48,044 --> 00:36:51,280
+why that didn't mean you saw things up-side down.
+
+598
+00:36:51,280 --> 00:36:52,860
+So it's sort of the same issue.
+
+599
+00:36:52,860 --> 00:36:54,810
+Reversed from what?
+
+600
+00:36:54,810 --> 00:36:57,940
+So we just need some convention.
+
+601
+00:36:57,940 --> 00:37:01,730
+The reason that they're coming at 4, 3 is because we're
+
+602
+00:37:01,730 --> 00:37:04,520
+taking UNEV and consing the result onto argl.
+
+603
+00:37:04,520 --> 00:37:06,771
+So you have to realize you've made that convention.
+
+604
+00:37:06,771 --> 00:37:09,987
+The place that you have to realize that--
+
+605
+00:37:09,987 --> 00:37:11,230
+well, there's actually two places.
+
+606
+00:37:11,230 --> 00:37:12,910
+One is in apply-primitive-operator,
+
+607
+00:37:12,910 --> 00:37:16,610
+which has to realize that the arguments to primitives go in,
+
+608
+00:37:16,610 --> 00:37:19,490
+in the opposite order from the way you're writing them down.
+
+609
+00:37:19,490 --> 00:37:21,008
+And the other one is, we'll see later 
+
+610
+00:37:21,008 --> 00:37:24,016
+when you actually go to bind a function's parameters, 
+
+611
+00:37:24,016 --> 00:37:25,745
+you should realize the arguments are going to come in 
+
+612
+00:37:25,745 --> 00:37:28,870
+from the opposite order of the variables to which you're binding them.
+
+613
+00:37:28,870 --> 00:37:31,830
+So, if you just keep track of that, there's no problem.
+
+614
+00:37:31,830 --> 00:37:33,900
+Also, this is completely arbitrary 
+
+615
+00:37:33,900 --> 00:37:37,420
+because, if we'd done, say, an iteration through a vector assigning them, 
+
+616
+00:37:37,420 --> 00:37:40,730
+they might come out in the other order, OK?
+
+617
+00:37:40,730 --> 00:37:45,085
+So it's just a convention of the way this particular evaluator works. 
+
+618
+00:37:45,085 --> 00:37:46,335
+All right, let's take a break.
+
+619
+00:38:41,840 --> 00:38:45,609
+We just saw evaluating an expression and, 
+
+620
+00:38:45,609 --> 00:38:46,950
+of course, that was very simple one.
+
+621
+00:38:46,950 --> 00:38:50,247
+But, in essence, it would be no different
+
+622
+00:38:50,247 --> 00:38:52,039
+if it was some big nested expression, 
+
+623
+00:38:52,039 --> 00:38:55,130
+so there would just be deeper recursion on the stack.
+
+624
+00:38:55,130 --> 00:38:56,470
+But what I want to do now is show you the last piece.
+
+625
+00:38:56,470 --> 00:39:01,013
+I want to walk you around this eval and apply loop, right?
+
+626
+00:39:01,013 --> 00:39:03,000
+That's the thing we haven't seen, really.
+
+627
+00:39:03,000 --> 00:39:05,200
+We haven't seen any compound procedures
+
+628
+00:39:05,200 --> 00:39:07,925
+where evalutation of procedure reduces to 
+
+629
+00:39:07,925 --> 00:39:12,250
+where applying of procedure reduces to evaluating the body of the procedure, 
+
+630
+00:39:12,250 --> 00:39:15,810
+so let's just suppose we had this.
+
+631
+00:39:15,810 --> 00:39:18,075
+Suppose we were looking at the procedure 
+
+632
+00:39:18,075 --> 00:39:33,995
+define F of A and B to be the sum of A and B. 
+
+633
+00:39:33,995 --> 00:39:37,325
+So, as we typed in that procedure previously,
+
+634
+00:39:37,325 --> 00:39:42,275
+and now we're going to evaluate F of X and Y
+
+635
+00:39:42,275 --> 00:39:44,209
+again, in this environment, E,0,
+
+636
+00:39:44,209 --> 00:39:47,280
+where X is bound to 3 and Y is bound to 4.
+
+637
+00:39:50,650 --> 00:39:53,825
+When the defined is executed, remember, there's a lambda here,
+
+638
+00:39:53,825 --> 00:39:55,950
+and lambdas create procedures.
+
+639
+00:39:55,950 --> 00:40:00,815
+And, basically, what will happen is, in E,0, 
+
+640
+00:40:00,815 --> 00:40:03,563
+we'll end up with a binding for F,
+
+641
+00:40:03,563 --> 00:40:07,151
+which will say F is a procedure,
+
+642
+00:40:07,151 --> 00:40:16,495
+and its args are A and B, and its body is plus a,b.
+
+643
+00:40:17,843 --> 00:40:21,053
+So that's what the environment would have looked like 
+
+644
+00:40:21,053 --> 00:40:22,675
+had we made that definition.
+
+645
+00:40:24,225 --> 00:40:28,600
+Then, when we go to evaluate F of X and Y, 
+
+646
+00:40:28,600 --> 00:40:31,615
+we'll go through exactly the same process that we did before.
+
+647
+00:40:31,615 --> 00:40:33,096
+It's even the same expression.
+
+648
+00:40:33,096 --> 00:40:36,030
+The only difference is that F, instead of having primitive
+
+649
+00:40:36,030 --> 00:40:39,250
+"plus" in it, will have this thing.
+
+650
+00:40:41,040 --> 00:40:43,600
+And so we'll go through exactly the same process,
+
+651
+00:40:43,600 --> 00:40:47,864
+except this time, when we end up at apply-dispatch, 
+
+652
+00:40:47,864 --> 00:40:50,285
+the function register, instead of having primitive plus, 
+
+653
+00:40:50,285 --> 00:40:54,300
+will have a thing that will represent it saying procedure,
+
+654
+00:40:54,300 --> 00:41:06,275
+where the args are A and B, and the body is plus A, B.
+
+655
+00:41:07,875 --> 00:41:11,092
+And, again, what I mean, by its ENV, I mean there's a pointer to it,
+
+656
+00:41:11,092 --> 00:41:13,280
+so don't worry that I'm writing a lot of stuff there. 
+
+657
+00:41:13,280 --> 00:41:15,636
+There's a pointer to this procedure data structure.
+
+658
+00:41:17,170 --> 00:41:20,960
+OK, so, we're in exactly the same situation.
+
+659
+00:41:20,960 --> 00:41:26,480
+We get to apply-dispatch, so, here, we come to apply-dispatch. 
+
+660
+00:41:26,480 --> 00:41:30,010
+Last time, we branched off to a primitive procedure.
+
+661
+00:41:30,010 --> 00:41:34,550
+Here, it says oh, we now have a compound procedure, 
+
+662
+00:41:34,550 --> 00:41:36,911
+so we're going to go off to compound-apply.
+
+663
+00:41:38,475 --> 00:41:40,075
+Now, what's compound-apply?
+
+664
+00:41:41,925 --> 00:41:45,090
+Well, remember what the meta-circular evaluator did?
+
+665
+00:41:45,090 --> 00:41:49,903
+Compound-apply said we're going to evaluate
+
+666
+00:41:49,903 --> 00:41:54,120
+the body of the procedure in some new environment.
+
+667
+00:41:54,120 --> 00:41:56,730
+Where does that new environment come from?
+
+668
+00:41:56,730 --> 00:42:01,362
+We take the environment that was packaged with the procedure, 
+
+669
+00:42:03,029 --> 00:42:05,791
+we bind the parameters of the procedure 
+
+670
+00:42:05,791 --> 00:42:09,759
+to the arguments that we're passing in,
+
+671
+00:42:09,759 --> 00:42:14,990
+and use that as a new frame to extend the procedure environment.
+
+672
+00:42:14,990 --> 00:42:21,630
+And that's the environment in which we evaluate the procedure body, right? 
+
+673
+00:42:21,630 --> 00:42:24,470
+That's going around the apply/eval loop.
+
+674
+00:42:24,470 --> 00:42:27,988
+That's apply coming back to call eval, all right?
+
+675
+00:42:30,910 --> 00:42:32,860
+OK.
+
+676
+00:42:32,860 --> 00:42:36,787
+So, now, that's all we have to do in compound-apply.
+
+677
+00:42:36,787 --> 00:42:37,720
+What are we going to do?
+
+678
+00:42:37,720 --> 00:42:40,975
+We're going to manufacture a new environment.
+
+679
+00:42:43,550 --> 00:42:46,768
+And we're going to manufacture a new environment that,
+
+680
+00:42:46,768 --> 00:42:48,310
+let's see, that we'll call E,1.
+
+681
+00:42:52,900 --> 00:42:57,310
+E,1 is going to be some environment where the
+
+682
+00:42:57,310 --> 00:43:01,765
+where the parameters of the procedure, where A is bound to 3
+
+683
+00:43:01,765 --> 00:43:05,768
+and B is bound to 4, and it's linked to E,0 
+
+684
+00:43:05,768 --> 00:43:09,270
+because that's where f is defined.
+
+685
+00:43:09,270 --> 00:43:12,050
+And, in this environment, we're going to evaluate the body of the procedure. 
+
+686
+00:43:12,050 --> 00:43:13,870
+So let's look at that, all right?
+
+687
+00:43:16,525 --> 00:43:20,690
+All right, here we are at compound-apply, which says
+
+688
+00:43:20,690 --> 00:43:24,500
+assign to the expression register
+
+689
+00:43:24,500 --> 00:43:28,163
+the body of the procedure that's in the function register.
+
+690
+00:43:28,163 --> 00:43:42,450
+So I assign to the expression register the procedure body, OK? 
+
+691
+00:43:42,450 --> 00:43:45,825
+That's going to be evaluated in an environment
+
+692
+00:43:45,825 --> 00:43:51,300
+which is formed by making some bindings
+
+693
+00:43:51,300 --> 00:43:53,673
+using information determined by the procedure--
+
+694
+00:43:53,673 --> 00:43:55,320
+that's what's in FUN--
+
+695
+00:43:55,320 --> 00:43:57,800
+and the argument list.
+
+696
+00:43:57,800 --> 00:44:00,230
+And let's not worry about exactly what that does, 
+
+697
+00:44:00,230 --> 00:44:01,930
+but you can see the information's there.
+
+698
+00:44:01,930 --> 00:44:05,948
+So make bindings will say oh, the procedure, itself,
+
+699
+00:44:05,948 --> 00:44:07,950
+had an environment attached to it.
+
+700
+00:44:07,950 --> 00:44:09,320
+I didn't write that quite here.
+
+701
+00:44:09,320 --> 00:44:11,300
+I should've said in environment
+
+702
+00:44:11,300 --> 00:44:13,660
+because every procedure gets built with an environment.
+
+703
+00:44:13,660 --> 00:44:16,600
+So, from that environment, it knows 
+
+704
+00:44:16,600 --> 00:44:19,290
+what the procedure's definition environment is.
+
+705
+00:44:19,290 --> 00:44:21,830
+It knows what the arguments are.
+
+706
+00:44:21,830 --> 00:44:24,280
+It looks at argl, and then you see a reversal convention here. 
+
+707
+00:44:24,280 --> 00:44:27,062
+It just has to know that argl is reversed,
+
+708
+00:44:27,062 --> 00:44:29,990
+and it builds this frame, E,1.
+
+709
+00:44:29,990 --> 00:44:33,364
+All right, so, let's assume that that's what make bindings returns,
+
+710
+00:44:33,364 --> 00:44:36,225
+so it assigns to ENV this thing, E,1.
+
+711
+00:44:41,490 --> 00:44:46,890
+All right, the next thing it says is restore continue.
+
+712
+00:44:46,890 --> 00:44:48,760
+Remember what continue was here?
+
+713
+00:44:48,760 --> 00:44:52,240
+It got put up in the last segment.
+
+714
+00:44:52,240 --> 00:44:54,020
+Continue got stored.
+
+715
+00:44:54,020 --> 00:44:56,565
+That was the original done, which said what are you going to do 
+
+716
+00:44:56,565 --> 00:44:59,920
+after you're done with this particular application?
+
+717
+00:44:59,920 --> 00:45:01,560
+It was one of the very first things that happened
+
+718
+00:45:01,560 --> 00:45:03,920
+when we evaluated the application.
+
+719
+00:45:03,920 --> 00:45:06,860
+And now, finally, we're going to restore continue.
+
+720
+00:45:06,860 --> 00:45:09,290
+Remember apply-dispatch's contract.
+
+721
+00:45:09,290 --> 00:45:12,035
+It assumes that where it should go to next was on the stack,
+
+722
+00:45:12,035 --> 00:45:13,590
+and there it was on the stack.
+
+723
+00:45:13,590 --> 00:45:19,940
+Continue has done, and now we're going to go back to eval-dispatch. 
+
+724
+00:45:19,940 --> 00:45:20,970
+We're set up again.
+
+725
+00:45:20,970 --> 00:45:25,511
+We have an expression, an environment, and a place to go to. 
+
+726
+00:45:25,511 --> 00:45:29,940
+We're not going to go through that because it's sort of the same expression. 
+
+727
+00:45:35,167 --> 00:45:39,342
+OK, but the thing, again, to notice is, at this point, 
+
+728
+00:45:39,342 --> 00:45:44,830
+we have reduced the original expression, F,X,Y, right?
+
+729
+00:45:44,830 --> 00:45:48,755
+We've reduced evaluating F,X,Y in environment E,0 
+
+730
+00:45:48,755 --> 00:45:52,670
+to evaluate plus A, B in E,1.
+
+731
+00:45:52,670 --> 00:45:55,720
+And notice, nothing's on the stack, right?
+
+732
+00:45:55,720 --> 00:45:56,830
+It's a reduction.
+
+733
+00:45:56,830 --> 00:46:01,769
+At this point, the machine does not contain, as part of its state, 
+
+734
+00:46:01,769 --> 00:46:05,493
+the fact that it's in the middle of evaluating some procedure called f,
+
+735
+00:46:05,493 --> 00:46:07,669
+that's gone, right?
+
+736
+00:46:07,669 --> 00:46:13,072
+There's no accumulated state, OK?
+
+737
+00:46:13,072 --> 00:46:14,370
+Again, that's a very important idea.
+
+738
+00:46:14,370 --> 00:46:18,396
+That's the meaning of, when we used to write in the substitution model,
+
+739
+00:46:18,396 --> 00:46:21,350
+this expression reduces to that expression. 
+
+740
+00:46:21,350 --> 00:46:22,660
+And you don't have to remember anything.
+
+741
+00:46:22,660 --> 00:46:24,500
+And here, you see the meaning of reduction.
+
+742
+00:46:24,500 --> 00:46:26,160
+At this point, there is nothing on the stack.
+
+743
+00:46:31,590 --> 00:46:35,240
+See, that has very important consequences.
+
+744
+00:46:35,240 --> 00:46:38,325
+Let's go back and look at iterative factorial,
+
+745
+00:46:40,425 --> 00:46:45,130
+all right? Remember, this was some sort of loop and doing iter.
+
+746
+00:46:45,130 --> 00:46:49,430
+And we kept saying that's an iterative procedure, right?
+
+747
+00:46:49,430 --> 00:47:04,660
+And what we wrote, remember, are things like, we said,
+
+748
+00:47:04,660 --> 00:47:12,360
+fact-iter of 5.
+
+749
+00:47:12,360 --> 00:47:19,030
+We wrote things like reduces to iter of 1, and 1, and 5,
+
+750
+00:47:19,030 --> 00:47:25,324
+which reduces to iter of 1, and 2, and 5, 
+
+751
+00:47:25,324 --> 00:47:27,079
+and so on, and so on, and so on.
+
+752
+00:47:27,079 --> 00:47:28,175
+And we kept saying well, look,
+
+753
+00:47:28,175 --> 00:47:31,720
+you don't have to build up any storage to do that.
+
+754
+00:47:31,720 --> 00:47:35,040
+And we waved our hands, and said in principle, there's no storage needed. 
+
+755
+00:47:35,040 --> 00:47:36,170
+Now, you see no storage needed.
+
+756
+00:47:36,170 --> 00:47:39,090
+Each of these is a real reduction, right?
+
+757
+00:47:39,090 --> 00:47:42,825
+As you walk through these expressions,
+
+758
+00:47:47,300 --> 00:47:51,370
+As you walk through these expressions, what you'll see
+
+759
+00:47:51,370 --> 00:47:53,751
+are these expressions on the stack 
+
+760
+00:47:53,751 --> 00:47:56,425
+in some particular environment, 
+
+761
+00:47:56,425 --> 00:48:00,023
+and then these expressions in the EXP register 
+
+762
+00:48:00,023 --> 00:48:01,575
+in some particular environment. 
+
+763
+00:48:01,575 --> 00:48:04,365
+And, at each point, there'll be no accumulated stuff on the stack 
+
+764
+00:48:04,365 --> 00:48:06,100
+because each one's a real reduction, OK?
+
+765
+00:48:09,135 --> 00:48:10,581
+All right, so, for example, 
+
+766
+00:48:10,581 --> 00:48:13,460
+just to go through it in a little bit more care,
+
+767
+00:48:13,460 --> 00:48:17,108
+if I start out with an expression that says something like, 
+
+768
+00:48:17,825 --> 00:48:34,400
+oh, say, fact-iter of 5 in some environment
+
+769
+00:48:41,900 --> 00:48:46,810
+that will, at some point, create an environment
+
+770
+00:48:46,810 --> 00:48:48,549
+in which n is down to 5.
+
+771
+00:48:51,340 --> 00:48:52,590
+Let's call that--
+
+772
+00:48:55,750 --> 00:49:02,757
+And, at some point, the machine will reduce this whole thing 
+
+773
+00:49:02,757 --> 00:49:07,673
+to a thing that says that's really iter 
+
+774
+00:49:07,673 --> 00:49:15,875
+of 1, and 1, and n, evaluated in this environment, E,1
+
+775
+00:49:15,875 --> 00:49:17,160
+with nothing on the stack.
+
+776
+00:49:17,160 --> 00:49:20,710
+See, at this moment, the machine is not remembering
+
+777
+00:49:20,710 --> 00:49:22,500
+that evaluating this expression, iter--
+
+778
+00:49:25,000 --> 00:49:29,366
+which is the loop-- is part of this thing called iterative factorial. 
+
+779
+00:49:29,366 --> 00:49:30,590
+It's not remembering that.
+
+780
+00:49:30,590 --> 00:49:33,170
+It's just reducing the expression to that, right?
+
+781
+00:49:33,170 --> 00:49:38,050
+If we look again at the body of iterative factorial,
+
+782
+00:49:38,050 --> 00:49:42,810
+this expression has reduced to that expression.
+
+783
+00:49:42,810 --> 00:49:44,060
+Oh, I shouldn't have the n there.
+
+784
+00:49:46,590 --> 00:49:53,340
+It's a slightly different convention from the slide to the program, OK? 
+
+785
+00:49:53,340 --> 00:49:56,124
+And, then, what's the body of iter?
+
+786
+00:49:56,124 --> 00:49:58,625
+Well, iter's going to be an if, 
+
+787
+00:49:58,625 --> 00:50:00,060
+and I won't go through the details of if. 
+
+788
+00:50:00,060 --> 00:50:02,225
+It'll evaluate the predicate.
+
+789
+00:50:02,225 --> 00:50:03,810
+In this case, it'll be false.
+
+790
+00:50:03,810 --> 00:50:09,850
+And this iter will now reduce to the expression
+
+791
+00:50:09,850 --> 00:50:21,620
+iter of whatever it says, star, counter product, and--
+
+792
+00:50:21,620 --> 00:50:22,650
+what does it say--
+
+793
+00:50:22,650 --> 00:50:32,975
+plus counter 1 in some other environment, by this time, E,2, 
+
+794
+00:50:32,975 --> 00:50:43,200
+where E,2 will be set up having bindings for product and counter, right? 
+
+795
+00:50:43,200 --> 00:50:45,140
+And it'll reduce to that, right?
+
+796
+00:50:45,140 --> 00:50:47,156
+It won't be remembering that it's part of 
+
+797
+00:50:47,156 --> 00:50:49,340
+something that it has to return to.
+
+798
+00:50:49,340 --> 00:50:53,053
+And when iter calls iter again, it'll reduce to another thing that looks like this
+
+799
+00:50:53,053 --> 00:50:59,160
+in some environment, E,3, which has new bindings for product and counter. 
+
+800
+00:50:59,160 --> 00:51:08,450
+So, if you're wondering, see, if you've always been queasy
+
+801
+00:51:08,450 --> 00:51:10,678
+about how it is we've been saying those procedures
+
+802
+00:51:10,678 --> 00:51:12,458
+that look syntactically recursive, 
+
+803
+00:51:12,458 --> 00:51:18,100
+are, in fact, iterative, run in constant space,
+
+804
+00:51:18,100 --> 00:51:19,750
+well, I don't know if this makes you less queasy, 
+
+805
+00:51:19,750 --> 00:51:21,230
+but at least it shows you what's happening.
+
+806
+00:51:21,230 --> 00:51:22,830
+There really isn't any buildup there.
+
+807
+00:51:25,910 --> 00:51:27,984
+Now, you might ask well, is there buildup
+
+808
+00:51:27,984 --> 00:51:31,710
+in principle in these environment frames?
+
+809
+00:51:31,710 --> 00:51:32,375
+And the answer is yeah,
+
+810
+00:51:32,375 --> 00:51:32,443
+you have to make these new environment frames, 
+
+811
+00:51:32,443 --> 00:51:33,848
+you have to make these new environment frames, 
+
+812
+00:51:33,848 --> 00:51:36,440
+but you don't have to hang onto them when you're done. 
+
+813
+00:51:36,440 --> 00:51:40,720
+They can be garbage collected, or the space can be reused automatically. 
+
+814
+00:51:40,720 --> 00:51:43,250
+But you see the control structure of the evaluator
+
+815
+00:51:43,250 --> 00:51:47,020
+is really using this idea that you actually have a reduction,
+
+816
+00:51:47,020 --> 00:51:50,132
+so these procedures really are iterative procedures.
+
+817
+00:51:50,132 --> 00:51:51,382
+All right, let's stop for questions.
+
+818
+00:52:02,288 --> 00:52:03,538
+All right, let's break.
+
+819
+00:52:48,770 --> 00:52:52,775
+Let me contrast the iterative procedure
+
+820
+00:52:52,775 --> 00:52:56,000
+just so you'll see where space does build up with a recursive procedure, 
+
+821
+00:52:56,000 --> 00:52:58,030
+so you can see the difference.
+
+822
+00:52:58,030 --> 00:53:02,880
+Let's look at the evaluation of recursive factorial, all right? 
+
+823
+00:53:02,880 --> 00:53:07,220
+So, here's fact-recursive, or standard factorial definition.
+
+824
+00:53:07,220 --> 00:53:09,910
+We said this one is still a recursive procedure, 
+
+825
+00:53:09,910 --> 00:53:13,750
+but this is actually a recursive process.
+
+826
+00:53:13,750 --> 00:53:16,566
+And then, just to link it back to the way we started, 
+
+827
+00:53:16,566 --> 00:53:20,530
+we said oh, you can see that it's going to be recursive process
+
+828
+00:53:20,530 --> 00:53:22,122
+by the substitution model 
+
+829
+00:53:22,122 --> 00:53:30,450
+because, if I say recursive factorial of 5, 
+
+830
+00:53:30,450 --> 00:53:36,000
+that turns into 5 times--
+
+831
+00:53:36,000 --> 00:53:37,989
+what is it, fact-rec, or record fact--
+
+832
+00:53:42,620 --> 00:53:54,230
+5 times recursive factorial of 4, which turns into 5 times 4
+
+833
+00:53:54,230 --> 00:54:08,090
+times fact-rec of 3, which returns into 5 times 4 times 3
+
+834
+00:54:08,090 --> 00:54:15,240
+times, and so on, right?
+
+835
+00:54:15,240 --> 00:54:18,100
+The idea is there was this chain of stuff building up,
+
+836
+00:54:18,100 --> 00:54:21,520
+which justified, in the substitution model, the fact that it's recursive. 
+
+837
+00:54:21,520 --> 00:54:24,180
+And now, let's actually see that chain of stuff build up
+
+838
+00:54:24,180 --> 00:54:27,465
+and where it is in the machine, OK?
+
+839
+00:54:27,465 --> 00:54:30,230
+All right, well, let's imagine we're going to start out again. 
+
+840
+00:54:30,230 --> 00:54:41,451
+We'll tell it to evaluate recursive factorial of 5
+
+841
+00:54:41,451 --> 00:54:45,000
+in some environment, again, E,0 
+
+842
+00:54:45,000 --> 00:54:49,275
+where recursive factorial is defined, OK?
+
+843
+00:54:49,275 --> 00:54:52,490
+Well, now we know what's eventually going to happen.
+
+844
+00:54:52,490 --> 00:54:53,925
+This is going to come along,
+
+845
+00:54:53,925 --> 00:54:57,071
+it'll evaluate those things, figure out it's a procedure, 
+
+846
+00:54:57,071 --> 00:55:00,255
+build somewhere over here an environment, E,1,
+
+847
+00:55:00,255 --> 00:55:06,725
+which has n bound to 5, which hangs off of E,0, 
+
+848
+00:55:07,800 --> 00:55:10,847
+which would be, presumably, the definition environment 
+
+849
+00:55:10,847 --> 00:55:12,847
+of recursive factorial, OK? 
+
+850
+00:55:14,610 --> 00:55:19,670
+And, in this environment, it's going to go off and evaluate the body. 
+
+851
+00:55:19,670 --> 00:55:27,000
+So, again, the evaluation here will reduce to 
+
+852
+00:55:27,000 --> 00:55:29,950
+evaluating the body in E,1.
+
+853
+00:55:29,950 --> 00:55:33,530
+That's going to look at an if, and I won't go through the details of if. 
+
+854
+00:55:33,530 --> 00:55:34,880
+It'll look at the predicate.
+
+855
+00:55:34,880 --> 00:55:37,840
+It'll decide it eventually has to evaluate the alternative.
+
+856
+00:55:37,840 --> 00:55:41,300
+So this whole thing, again, will reduce to
+
+857
+00:55:41,300 --> 00:55:47,139
+the alternative of recursive factorial, the alternative clause, 
+
+858
+00:55:47,139 --> 00:55:53,075
+which says that this whole thing reduces to times n 
+
+859
+00:55:53,075 --> 00:56:08,720
+of recursive factorial of n minus 1 in the environment E,1, OK?
+
+860
+00:56:08,720 --> 00:56:11,200
+So the original expression, now, is going to reduce to
+
+861
+00:56:11,200 --> 00:56:13,754
+evaluating that expression, all right?
+
+862
+00:56:13,754 --> 00:56:16,280
+Now we have an application.
+
+863
+00:56:16,280 --> 00:56:18,225
+We did an application before.
+
+864
+00:56:18,225 --> 00:56:20,390
+Remember what happens in an application?
+
+865
+00:56:20,390 --> 00:56:21,975
+The first thing you do is you go off and you 
+
+866
+00:56:21,975 --> 00:56:25,350
+save the value of the continue register on the stack.
+
+867
+00:56:25,350 --> 00:56:27,365
+So the stack here is going to have done in it.
+
+868
+00:56:29,980 --> 00:56:35,130
+And then you're going to set up to evaluate the sub-parts, OK? 
+
+869
+00:56:35,130 --> 00:56:37,200
+So here we go off to evaluate the sub-parts.
+
+870
+00:56:39,375 --> 00:56:41,450
+First thing we're going to do is evaluate the operator.
+
+871
+00:56:44,490 --> 00:56:47,250
+What happens when we evaluate an operator?
+
+872
+00:56:47,250 --> 00:56:51,480
+Well, we arrange things so that the operator ends up in the expression register. 
+
+873
+00:56:51,480 --> 00:56:54,630
+The environments in the ENV register continue someplace
+
+874
+00:56:54,630 --> 00:56:56,590
+where we're going to go evaluate the arguments.
+
+875
+00:56:56,590 --> 00:56:59,520
+And, on the stack, we've saved the original continue, 
+
+876
+00:56:59,520 --> 00:57:01,720
+which is where we wanted to be when we're all done.
+
+877
+00:57:01,720 --> 00:57:03,400
+And then the things we needed
+
+878
+00:57:03,400 --> 00:57:05,807
+when we're going to get done evaluating the operator,
+
+879
+00:57:05,807 --> 00:57:08,333
+the things we'll need to evaluate the arguments, namely, 
+
+880
+00:57:08,333 --> 00:57:14,000
+the environment and those arguments, those unevaluated arguments, 
+
+881
+00:57:14,000 --> 00:57:15,620
+so there they are sitting on the stack.
+
+882
+00:57:15,620 --> 00:57:18,370
+And we're about to go off to evaluate the operator.
+
+883
+00:57:23,130 --> 00:57:26,920
+Well, when we return from this particular call--
+
+884
+00:57:26,920 --> 00:57:29,380
+so we're about to call eval-dispatch here--
+
+885
+00:57:29,380 --> 00:57:32,730
+when we return from this call, the value of that operator,
+
+886
+00:57:32,730 --> 00:57:36,275
+which, in this case, is going to be the primitive multiplier procedure, 
+
+887
+00:57:36,275 --> 00:57:42,800
+will end up in the FUN register, all right?
+
+888
+00:57:42,800 --> 00:57:44,530
+We're going to evaluate some arguments.
+
+889
+00:57:44,530 --> 00:57:47,730
+They will evaluate n here.
+
+890
+00:57:47,730 --> 00:57:50,250
+That'll give us 5, in this case.
+
+891
+00:57:50,250 --> 00:57:52,900
+We're going to put that in the argl register,
+
+892
+00:57:52,900 --> 00:57:57,460
+and then we'll go off to evaluate the second operand.
+
+893
+00:57:57,460 --> 00:58:00,365
+So, at the point where we go off to evaluate the second operand--
+
+894
+00:58:00,365 --> 00:58:03,633
+and I'll skip details like computing, and minus 1, and all of that--
+
+895
+00:58:03,633 --> 00:58:06,385
+but, when we go off to evaluate the second operand,
+
+896
+00:58:06,385 --> 00:58:10,737
+that will eventually reduce to another call to fact-recursive.
+
+897
+00:58:12,000 --> 00:58:16,525
+And, what we've got on the stack here is
+
+898
+00:58:16,525 --> 00:58:19,942
+the operator from that combination that we're going to use it in 
+
+899
+00:58:19,942 --> 00:58:23,790
+and the other argument, OK?
+
+900
+00:58:23,790 --> 00:58:30,200
+So, now, we're set up for another call to recursive factorial. 
+
+901
+00:58:30,200 --> 00:58:31,438
+And, when we're done with this one, 
+
+902
+00:58:31,438 --> 00:58:33,935
+we're going to go to accumulate the last arg.
+
+903
+00:58:33,935 --> 00:58:35,200
+And remember what that'll do?
+
+904
+00:58:35,200 --> 00:58:36,425
+That'll say oh, 
+
+905
+00:58:36,425 --> 00:58:36,450
+whatever the result of this has to get combined with that, 
+
+906
+00:58:36,450 --> 00:58:39,281
+whatever the result of this has to get combined with that, 
+
+907
+00:58:39,281 --> 00:58:41,690
+and we're going to multiply them.
+
+908
+00:58:41,690 --> 00:58:45,720
+But, notice now, we're at another recursive factorial.
+
+909
+00:58:45,720 --> 00:58:49,325
+We're about to call eval-dispatch again,
+
+910
+00:58:49,325 --> 00:58:53,700
+except we haven't really reduced it because there's stuff on the stack now. 
+
+911
+00:58:53,700 --> 00:58:55,244
+The stuff on the stack says oh, when you get back, 
+
+912
+00:58:55,244 --> 00:58:58,430
+you'd better multiply it by the 5 you had hanging there.
+
+913
+00:58:58,430 --> 00:59:07,125
+So, when we go off to make another call, 
+
+914
+00:59:07,125 --> 00:59:09,300
+we evaluate the n minus 1.
+
+915
+00:59:09,300 --> 00:59:11,256
+That gives us another environment 
+
+916
+00:59:11,256 --> 00:59:14,600
+in which the new n's going to be down to 4.
+
+917
+00:59:14,600 --> 00:59:18,930
+And we're about to call eval-dispatch again, right?
+
+918
+00:59:18,930 --> 00:59:21,350
+We get another call.
+
+919
+00:59:21,350 --> 00:59:26,040
+That 4 is going to end up in the same situation.
+
+920
+00:59:26,040 --> 00:59:30,020
+We'll end up with another call to fact-recursive n.
+
+921
+00:59:30,020 --> 00:59:32,684
+And sitting on the stack will be the stuff from the original one 
+
+922
+00:59:32,684 --> 00:59:35,360
+and, now, the subsidiary one we're doing.
+
+923
+00:59:35,360 --> 00:59:36,910
+And both of them are waiting for the same thing.
+
+924
+00:59:36,910 --> 00:59:40,600
+They're going to go to accumulate a last argument.
+
+925
+00:59:40,600 --> 00:59:43,258
+And then, of course, when we go to the fourth call, 
+
+926
+00:59:43,258 --> 00:59:45,640
+the same thing happens, right?
+
+927
+00:59:45,640 --> 00:59:47,300
+And this goes on, and on, and on.
+
+928
+00:59:47,300 --> 00:59:50,075
+And what you see here on the stack, 
+
+929
+00:59:50,107 --> 00:59:52,225
+exactly what's sitting here on the stack,
+
+930
+00:59:52,225 --> 00:59:54,960
+the thing that says times and 5.
+
+931
+00:59:54,960 --> 01:00:00,470
+And what you're going to do with that is accumulate that into a last argument. 
+
+932
+01:00:00,470 --> 01:00:02,760
+That's exactly this, right?
+
+933
+01:00:02,760 --> 01:00:05,650
+This is exactly where that stuff is hanging.
+
+934
+01:00:05,650 --> 01:00:11,659
+Effectively, the operator you're going to apply,
+
+935
+01:00:11,659 --> 01:00:13,625
+the other argument 
+
+936
+01:00:13,672 --> 01:00:15,300
+that it's got to be multiplied by when you get back
+
+937
+01:00:15,300 --> 01:00:16,879
+and the parentheses, 
+
+938
+01:00:16,879 --> 01:00:19,620
+which says yeah, what you wanted to do was accumulate them. 
+
+939
+01:00:19,620 --> 01:00:22,560
+So, you see, the substitution model is not such a lie.
+
+940
+01:00:22,560 --> 01:00:27,198
+That really is, in some sense, what's sitting right on the stack. 
+
+941
+01:00:27,198 --> 01:00:29,046
+OK.
+
+942
+01:00:29,046 --> 01:00:33,260
+All right, so that, in some sense, should explain for you,
+
+943
+01:00:33,260 --> 01:00:36,596
+or at least convince you, that, 
+
+944
+01:00:36,596 --> 01:00:39,870
+somehow, this evaluator is managing 
+
+945
+01:00:39,870 --> 01:00:42,959
+to take these procedures and execute some of them iteratively
+
+946
+01:00:42,959 --> 01:00:46,410
+and some of them recursively, even though,
+
+947
+01:00:46,410 --> 01:00:49,215
+as syntactically, they look like recursive procedures.
+
+948
+01:00:49,215 --> 01:00:50,660
+How's it managing to do that?
+
+949
+01:00:50,660 --> 01:00:53,725
+Well, the basic reason it's managing to do that
+
+950
+01:00:53,725 --> 01:01:01,090
+is the evaluator is set up to save only what it needs later.
+
+951
+01:01:01,090 --> 01:01:04,670
+So, for example, at the point where you've reduced
+
+952
+01:01:04,670 --> 01:01:07,683
+evaluating an expression and an environment 
+
+953
+01:01:07,683 --> 01:01:10,525
+to applying a procedure to some arguments, 
+
+954
+01:01:10,525 --> 01:01:13,375
+it doesn't need that original environment anymore 
+
+955
+01:01:13,375 --> 01:01:17,675
+because any environment stuff will be packaged inside the procedures 
+
+956
+01:01:17,675 --> 01:01:20,160
+where the application's going to happen.
+
+957
+01:01:20,160 --> 01:01:23,656
+All right, similarly, when you're going along evaluating an argument list, 
+
+958
+01:01:23,656 --> 01:01:25,910
+when you've finished evaluating the list,
+
+959
+01:01:25,910 --> 01:01:28,200
+when you're finished evaluating the last argument,
+
+960
+01:01:28,200 --> 01:01:31,500
+you don't need that argument list any more, right?
+
+961
+01:01:31,500 --> 01:01:32,941
+And you don't need the environment where 
+
+962
+01:01:32,941 --> 01:01:36,690
+those arguments would be evaluated, OK?
+
+963
+01:01:36,690 --> 01:01:40,890
+So the basic reason that this interpreter is being so smart
+
+964
+01:01:40,890 --> 01:01:43,050
+is that it's not being smart at all, it's being stupid.
+
+965
+01:01:43,050 --> 01:01:46,010
+It's just saying I'm only going to save what I really need. 
+
+966
+01:01:48,700 --> 01:01:51,000
+Well, let me show you here.
+
+967
+01:01:54,880 --> 01:01:58,310
+Here's the actual thing that's making a tail recursive.
+
+968
+01:01:58,310 --> 01:02:00,135
+Remember, it's the restore of continue.
+
+969
+01:02:00,135 --> 01:02:08,800
+It's saying when I go off to evaluate the procedure body,
+
+970
+01:02:08,800 --> 01:02:11,252
+I should tell eval to come back to 
+
+971
+01:02:11,252 --> 01:02:15,170
+the place where that original evaluation was supposed to come back to.
+
+972
+01:02:15,170 --> 01:02:17,700
+So, in some sense, you want to say what's the actual line
+
+973
+01:02:17,700 --> 01:02:18,770
+that makes a tail recursive?
+
+974
+01:02:18,770 --> 01:02:19,920
+It's that one.
+
+975
+01:02:19,920 --> 01:02:23,680
+If I wanted to build a non-tail recursive evaluator,
+
+976
+01:02:23,680 --> 01:02:27,124
+for some strange reason, all I would need to do is,
+
+977
+01:02:27,124 --> 01:02:32,750
+instead of restoring continue at this point, I'd set up a label down here
+
+978
+01:02:32,750 --> 01:02:37,455
+called, "Where to come back after you've finished applying the procedure."
+
+979
+01:02:37,455 --> 01:02:39,920
+Instead, I'd set continue to that. 
+
+980
+01:02:39,920 --> 01:02:41,299
+I'd go to eval-dispatch, 
+
+981
+01:02:41,299 --> 01:02:43,790
+and then eval-dispatch would come back here.
+
+982
+01:02:43,790 --> 01:02:47,920
+At that point, I would restore continue and go to the original one. 
+
+983
+01:02:47,920 --> 01:02:51,075
+So here, the only consequence of that 
+
+984
+01:02:51,075 --> 01:02:52,840
+would be to make it non-tail recursive.
+
+985
+01:02:52,840 --> 01:02:54,629
+It would give you exactly the same answers, 
+
+986
+01:02:54,629 --> 01:02:56,656
+except if you did that iterative factorial
+
+987
+01:02:56,656 --> 01:02:59,875
+and all those iterative procedures, it would execute recursively.
+
+988
+01:03:02,900 --> 01:03:05,760
+Well, I lied to you a little bit, but just a little bit,
+
+989
+01:03:05,760 --> 01:03:08,550
+because I showed you a slightly over-simplified evaluator
+
+990
+01:03:08,550 --> 01:03:11,225
+where it assumes that each procedure --
+
+991
+01:03:11,225 --> 01:03:13,890
+each procedure body has only one expression.
+
+992
+01:03:13,890 --> 01:03:17,870
+Remember, in general, a procedure has a sequence of expressions in it. 
+
+993
+01:03:17,870 --> 01:03:20,490
+So there's nothing really conceptually new.
+
+994
+01:03:20,490 --> 01:03:22,725
+Let me just show you the actual evaluator
+
+995
+01:03:22,725 --> 01:03:24,730
+that handles sequences of expressions.
+
+996
+01:03:28,470 --> 01:03:32,075
+This is compound-apply now, and the only difference from the old one
+
+997
+01:03:32,075 --> 01:03:35,980
+is that, instead of going off to eval directly,
+
+998
+01:03:35,980 --> 01:03:38,039
+it takes the whole body of the procedure, 
+
+999
+01:03:38,039 --> 01:03:40,151
+which, in this case, is a sequence of expressions, 
+
+1000
+01:03:40,151 --> 01:03:42,325
+and goes off to eval-sequence.
+
+1001
+01:03:42,325 --> 01:03:47,907
+And eval-sequence is a little loop that, basically, 
+
+1002
+01:03:47,907 --> 01:03:49,980
+does these evaluations one at a time.
+
+1003
+01:03:52,630 --> 01:03:53,900
+So it does an evaluation.
+
+1004
+01:03:53,900 --> 01:03:58,440
+Says oh, when I come back, I'd better come back here to do the next one. 
+
+1005
+01:03:58,440 --> 01:04:01,038
+And, when I'm all done, when I want to get the last expression,
+
+1006
+01:04:01,038 --> 01:04:06,410
+I just restore my continue and go off to eval-dispatch. 
+
+1007
+01:04:06,410 --> 01:04:08,200
+And, again, if you wanted for some reason to
+
+1008
+01:04:08,200 --> 01:04:10,492
+break tail recursion in this evaluator, 
+
+1009
+01:04:10,492 --> 01:04:14,900
+all you need to do is not handle the last expression, especially. 
+
+1010
+01:04:14,900 --> 01:04:17,247
+Just say, after you've done the last expression,
+
+1011
+01:04:17,247 --> 01:04:21,900
+come back to some other place after which you restore continue.
+
+1012
+01:04:21,900 --> 01:04:26,550
+And, for some reason, a lot of LISP evaluators tended to work that way. 
+
+1013
+01:04:26,550 --> 01:04:28,545
+And the only consequence of that is that 
+
+1014
+01:04:28,545 --> 01:04:31,614
+iterative procedures built up stack.
+
+1015
+01:04:31,614 --> 01:04:35,670
+And it's not clear why that happened.
+
+1016
+01:04:35,670 --> 01:04:36,210
+All right.
+
+1017
+01:04:36,210 --> 01:04:38,095
+Well, let me just sort of summarize, 
+
+1018
+01:04:38,095 --> 01:04:41,120
+since this is a lot of details in a big program.
+
+1019
+01:04:41,120 --> 01:04:44,040
+But the main point is that it's no different,
+
+1020
+01:04:44,040 --> 01:04:47,060
+conceptually, from translating any other program.
+
+1021
+01:04:47,060 --> 01:04:50,156
+And the main idea is that we have this universal evaluator program,
+
+1022
+01:04:50,156 --> 01:04:51,870
+the meta-circular evaluator.
+
+1023
+01:04:51,870 --> 01:04:54,560
+If we translate that into LISP, then we have all of LISP. 
+
+1024
+01:04:54,560 --> 01:04:57,980
+And that's all we did, OK?
+
+1025
+01:04:57,980 --> 01:04:59,680
+The second point is that the magic's gone away.
+
+1026
+01:04:59,680 --> 01:05:01,970
+There should be no more magic in this whole system, right?
+
+1027
+01:05:01,970 --> 01:05:08,720
+In principle, it should all be very clear except, maybe, for
+
+1028
+01:05:08,720 --> 01:05:10,940
+how list structured memory works, and
+
+1029
+01:05:10,940 --> 01:05:12,640
+we'll see that later.
+
+1030
+01:05:12,640 --> 01:05:15,450
+But that's not very hard.
+
+1031
+01:05:15,450 --> 01:05:18,720
+The third point is that all this tail recursion came from
+
+1032
+01:05:18,720 --> 01:05:22,550
+the discipline of eval being very careful 
+
+1033
+01:05:22,550 --> 01:05:25,870
+to save only what it needs next time.
+
+1034
+01:05:25,870 --> 01:05:28,180
+It's not some arbitrary thing where we're saying well,
+
+1035
+01:05:28,180 --> 01:05:29,864
+whenever we call a sub-routine, 
+
+1036
+01:05:29,864 --> 01:05:33,940
+we'll save all the registers in the world and come back, right?
+
+1037
+01:05:33,940 --> 01:05:37,150
+See, sometimes it pays to really worry about efficiency.
+
+1038
+01:05:37,150 --> 01:05:40,459
+And, when you're down in the guts of your evaluator machine, 
+
+1039
+01:05:40,459 --> 01:05:42,560
+it really pays to think about things like that
+
+1040
+01:05:42,560 --> 01:05:45,230
+because it makes big consequences.
+
+1041
+01:05:45,230 --> 01:05:47,842
+Well, I hope what this has done
+
+1042
+01:05:47,842 --> 01:05:52,560
+is really made the evaluator seem concrete, right?
+
+1043
+01:05:52,560 --> 01:05:56,631
+I hope you really believe that somebody could hold a LISP
+
+1044
+01:05:56,631 --> 01:05:59,075
+LISP evaluator in the palm of their hand.
+
+1045
+01:05:59,075 --> 01:06:02,540
+Maybe to help you believe that, here's a LISP evaluator
+
+1046
+01:06:02,540 --> 01:06:06,160
+that I'm holding the palm of my hand, right?
+
+1047
+01:06:06,160 --> 01:06:10,738
+And this is a chip which is actually
+
+1048
+01:06:10,738 --> 01:06:13,700
+quite a bit more complicated than the evaluator I showed you.
+
+1049
+01:06:17,815 --> 01:06:19,200
+Maybe, here's a better picture of it.
+
+1050
+01:06:22,070 --> 01:06:24,730
+What there is, is you can see the same overall structure.
+
+1051
+01:06:24,730 --> 01:06:26,940
+This is a register array.
+
+1052
+01:06:26,940 --> 01:06:27,910
+These are the data paths.
+
+1053
+01:06:27,910 --> 01:06:29,800
+Here's a finite state controller.
+
+1054
+01:06:29,800 --> 01:06:32,810
+And again, finite state, that's all there is.
+
+1055
+01:06:32,810 --> 01:06:34,160
+And somewhere there's external memory
+
+1056
+01:06:34,160 --> 01:06:35,750
+that'll worry about things.
+
+1057
+01:06:35,750 --> 01:06:37,552
+And this particular one is very complicated 
+
+1058
+01:06:37,552 --> 01:06:39,664
+because it's trying to run LISP fast. 
+
+1059
+01:06:39,664 --> 01:06:42,976
+And it has some very, very fast parallel operations in there 
+
+1060
+01:06:42,976 --> 01:06:46,650
+like, if you want to index into an array, 
+
+1061
+01:06:46,650 --> 01:06:50,362
+simultaneously check that the index is an integer, 
+
+1062
+01:06:50,362 --> 01:06:52,863
+check that it doesn't exceed the array bands, 
+
+1063
+01:06:52,863 --> 01:06:57,120
+and go off and do the memory access, and do all those things simultaneously. 
+
+1064
+01:06:57,120 --> 01:06:58,970
+And then, later, if they're all OK, actually
+
+1065
+01:06:58,970 --> 01:07:00,420
+get the value there.
+
+1066
+01:07:00,420 --> 01:07:02,327
+So there are a lot of complicated operations 
+
+1067
+01:07:02,327 --> 01:07:06,550
+in these data paths for making LISP run in parallel.
+
+1068
+01:07:06,550 --> 01:07:10,640
+It's a completely non-risk philosophy of evaluating LISP.
+
+1069
+01:07:10,640 --> 01:07:13,740
+And then, this microcode is pretty complicated.
+
+1070
+01:07:13,740 --> 01:07:17,740
+Let's see, there's what?
+
+1071
+01:07:17,740 --> 01:07:24,079
+There's about 389 instructions of 220-bit microcode sitting here 
+
+1072
+01:07:24,079 --> 01:07:27,940
+because these are very complicated data paths.
+
+1073
+01:07:27,940 --> 01:07:33,580
+And the whole thing has about 89,000 transistors, OK?
+
+1074
+01:07:33,580 --> 01:07:33,840
+OK.
+
+1075
+01:07:33,840 --> 01:07:37,970
+Well, I hope that that takes away a lot of the mystery.
+
+1076
+01:07:37,970 --> 01:07:39,240
+Maybe somebody wants to look at this.
+
+1077
+01:07:42,048 --> 01:07:43,298
+Yeah.
+
+1078
+01:07:46,260 --> 01:07:46,480
+OK.
+
+1079
+01:07:46,480 --> 01:07:47,730
+Let's stop.
+
+1080
+01:07:55,890 --> 01:07:57,815
+Questions?
+
+1081
+01:07:57,815 --> 01:08:00,420
+AUDIENCE: OK, now, it sounds like what you're saying is that, 
+
+1082
+01:08:00,420 --> 01:08:04,600
+with the restore continue put in the proper place, that
+
+1083
+01:08:04,600 --> 01:08:09,422
+procedures that would invoke a recursive process 
+
+1084
+01:08:09,422 --> 01:08:12,675
+now invoke an integer process 
+
+1085
+01:08:12,675 --> 01:08:15,165
+just by the way that the eval signature is?
+
+1086
+01:08:15,165 --> 01:08:17,549
+PROFESSOR: I think the way I'd prefer to put it is that,
+
+1087
+01:08:17,549 --> 01:08:20,557
+with restore continue put in the wrong place, 
+
+1088
+01:08:20,557 --> 01:08:25,880
+you can cause any syntactically-looking recursive procedure, in fact,
+
+1089
+01:08:25,880 --> 01:08:28,029
+to build up stack as it runs.
+
+1090
+01:08:28,029 --> 01:08:33,150
+But there's no reason for that, 
+
+1091
+01:08:33,150 --> 01:08:35,660
+so you might want to play around with it.
+
+1092
+01:08:35,660 --> 01:08:38,185
+You can just switch around two or three instructions 
+
+1093
+01:08:38,185 --> 01:08:41,129
+in the way compound-apply comes back, 
+
+1094
+01:08:41,129 --> 01:08:45,060
+and you'll get something which isn't tail recursive.
+
+1095
+01:08:45,060 --> 01:08:47,670
+But the thing I wanted to emphasize is there's no magic.
+
+1096
+01:08:47,670 --> 01:08:52,455
+It's not as if there's some very clever pre-processing program
+
+1097
+01:08:52,455 --> 01:08:57,425
+that's looking at this procedure, factorial iter, and say oh, gee, 
+
+1098
+01:08:57,425 --> 01:09:01,060
+I really notice that I don't have to push stack in order to do this. 
+
+1099
+01:09:01,060 --> 01:09:03,760
+Some people think that that's what's going on.
+
+1100
+01:09:03,760 --> 01:09:05,383
+It's something much, much more dumb than that, 
+
+1101
+01:09:05,383 --> 01:09:08,880
+it's this one place you're putting the restore instruction.
+
+1102
+01:09:08,880 --> 01:09:10,353
+It's just automatic.
+
+1103
+01:09:10,353 --> 01:09:11,603
+AUDIENCE: OK.
+
+1104
+01:09:14,217 --> 01:09:17,850
+AUDIENCE: But that's not affecting the time complexity is it? 
+
+1105
+01:09:17,850 --> 01:09:18,275
+PROFESSOR: No.
+
+1106
+01:09:18,275 --> 01:09:21,810
+AUDIENCE: It's just that it's handling it recursively
+
+1107
+01:09:21,810 --> 01:09:23,020
+instead of iteratively.
+
+1108
+01:09:23,020 --> 01:09:27,179
+But, in terms of the order of time it takes to finish the operation, 
+
+1109
+01:09:27,179 --> 01:09:29,220
+it's the same one way or the other, right?
+
+1110
+01:09:29,220 --> 01:09:29,920
+PROFESSOR: Yes.
+
+1111
+01:09:29,920 --> 01:09:32,609
+Tail recursion is not going to change the time complexity of anything 
+
+1112
+01:09:32,609 --> 01:09:36,029
+because, in some sense, it's the same algorithm that's going on. 
+
+1113
+01:09:36,029 --> 01:09:41,210
+What it's doing is really making this thing run as an iteration, right? 
+
+1114
+01:09:41,210 --> 01:09:44,750
+Not going to run out of memory counting up to a giant number
+
+1115
+01:09:44,750 --> 01:09:47,683
+simply because the stack would get pushed.
+
+1116
+01:09:47,683 --> 01:09:51,640
+See, the thing you really have to believe is that, when we write-- 
+
+1117
+01:09:51,640 --> 01:09:53,781
+see, we've been writing all these things called iterations,
+
+1118
+01:09:53,781 --> 01:09:57,990
+infinite loops, define loop to be called loop.
+
+1119
+01:10:00,325 --> 01:10:03,650
+That's is as much an iteration 
+
+1120
+01:10:03,650 --> 01:10:07,630
+as if we wrote do forever loop, right?
+
+1121
+01:10:07,630 --> 01:10:09,280
+It's just syntactic sugar as the difference.
+
+1122
+01:10:09,280 --> 01:10:14,730
+These things are real, honest to god, iterations, right?
+
+1123
+01:10:14,730 --> 01:10:16,681
+They don't change the time complexity, but they 
+
+1124
+01:10:16,681 --> 01:10:18,535
+turn them into real iterations.
+
+1125
+01:10:21,686 --> 01:10:23,800
+All right, thank you.
+