A partial example program for SeqDecProbs in Haskell

talks/2016-11_Oxford/.gitignore

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+.stack-work/

talks/2016-11_Oxford/Example.hs

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+module Example where
+import Control.Monad (forM_)
+
+noOfStates = 6
+
+newtype S = S Int deriving (Eq, Show) -- 0 .. noOfStates-1
+data C = L | A | R deriving (Eq, Enum, Show)
+left, ahead, right :: S -> S
+left  (S i) = S $ (i-1) `mod` noOfStates
+ahead = id
+right (S i) = S $ (i+1) `mod` noOfStates
+
+type V = Int
+
+next :: S -> C -> S
+next x L = left  x
+next x A = ahead x
+next x R = right x
+
+reward :: S -> C -> S -> V
+reward x c (S i') = (if i' == 0 then 2 else 0) -- reward for finding column zero
+                  - (if c  == A then 0 else 1) -- cost of moving
+
+val :: S -> [C] -> V
+val x []      = 0
+val x (c:cs)  = v + val x' cs
+  where  x'  = next x c
+         v   = reward x c x'
+
+opt :: [C] ->   [C] -> S -> Bool
+opt cs = \cs' x -> val x cs' <= val x cs
+
+optExt :: [C] -> S -> C  -- [C] -> C would not work - different states make different controls optimal
+optExt [] (S 0) = A
+optExt [] (S 1) = L
+optExt [] (S i) | i == noOfStates-1  = R
+                | otherwise          = A
+optExt cs x = argMax (\c->val x (c:cs))
+-- Not correct
+
+argMax :: (C -> V) -> C
+argMax rew = toEnum $ bestIndex $ map rew [L,A,R]
+
+bestIndex :: Ord v => [v] -> Int
+bestIndex (v:vs) = go 0 0 v vs
+  where  go i ibest best [] = ibest
+         go i ibest best (v:vs)
+           | v <= best  = go (i+1) ibest best vs
+           | otherwise  = go (i+1) i     v    vs
+
+showPolicy :: Show c => (S -> c) -> String
+showPolicy p = show $ map (p.S) [0..noOfStates-1]
+
+test1 = optExt []
+
+test2 = optExt [A]
+
+test3 css = mapM_ putStrLn $ map showPolicy $ map (\cs x -> (cs, val x cs)) css
+
+test31 = test3 allCtrls1
+test32 = test3 allCtrls2
+
+lar = [L,A,R]
+allCtrls1 = map (:[]) lar
+allCtrls2 = crossWith (:) lar allCtrls1
+
+crossWith :: (a->b->c) -> [a] -> [b] -> [c]
+crossWith op xs ys = [op x y | y <- ys, x <- xs]

talks/2016-11_Oxford/LICENSE

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+Copyright (c) 2016, Patrik Jansson
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Patrik Jansson nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

talks/2016-11_Oxford/SeqDecProbs.cabal

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+-- Initial SeqDecProbs.cabal generated by cabal init.  For further 
+-- documentation, see http://haskell.org/cabal/users-guide/
+
+name:                SeqDecProbs
+version:             0.1.0.0
+-- synopsis:            
+-- description:         
+license:             BSD3
+license-file:        LICENSE
+author:              Patrik Jansson
+maintainer:          [email protected]
+-- copyright:           
+-- category:            
+build-type:          Simple
+-- extra-source-files:  
+cabal-version:       >=1.10
+
+library
+  exposed-modules:     Example
+  -- other-modules:       
+  -- other-extensions:    
+  build-depends:       base >=4.9 && <4.10
+  -- hs-source-dirs:      
+  default-language:    Haskell2010

talks/2016-11_Oxford/Setup.hs

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+import Distribution.Simple
+main = defaultMain

talks/2016-11_Oxford/stack.yaml

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+# This file was automatically generated by 'stack init'
+#
+# Some commonly used options have been documented as comments in this file.
+# For advanced use and comprehensive documentation of the format, please see:
+# http://docs.haskellstack.org/en/stable/yaml_configuration/
+
+# Resolver to choose a 'specific' stackage snapshot or a compiler version.
+# A snapshot resolver dictates the compiler version and the set of packages
+# to be used for project dependencies. For example:
+#
+# resolver: lts-3.5
+# resolver: nightly-2015-09-21
+# resolver: ghc-7.10.2
+# resolver: ghcjs-0.1.0_ghc-7.10.2
+# resolver:
+#  name: custom-snapshot
+#  location: "./custom-snapshot.yaml"
+resolver: lts-7.12
+
+# User packages to be built.
+# Various formats can be used as shown in the example below.
+#
+# packages:
+# - some-directory
+# - https://example.com/foo/bar/baz-0.0.2.tar.gz
+# - location:
+#    git: https://github.com/commercialhaskell/stack.git
+#    commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+# - location: https://github.com/commercialhaskell/stack/commit/e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+#   extra-dep: true
+#  subdirs:
+#  - auto-update
+#  - wai
+#
+# A package marked 'extra-dep: true' will only be built if demanded by a
+# non-dependency (i.e. a user package), and its test suites and benchmarks
+# will not be run. This is useful for tweaking upstream packages.
+packages:
+- '.'
+# Dependency packages to be pulled from upstream that are not in the resolver
+# (e.g., acme-missiles-0.3)
+extra-deps: []
+
+# Override default flag values for local packages and extra-deps
+flags: {}
+
+# Extra package databases containing global packages
+extra-package-dbs: []
+
+# Control whether we use the GHC we find on the path
+# system-ghc: true
+#
+# Require a specific version of stack, using version ranges
+# require-stack-version: -any # Default
+# require-stack-version: ">=1.2"
+#
+# Override the architecture used by stack, especially useful on Windows
+# arch: i386
+# arch: x86_64
+#
+# Extra directories used by stack for building
+# extra-include-dirs: [/path/to/dir]
+# extra-lib-dirs: [/path/to/dir]
+#
+# Allow a newer minor version of GHC than the snapshot specifies
+# compiler-check: newer-minor