004, 016, 026, 029 (#28)

.github/workflows/test-dafny.yml → .github/workflows/test-dafny-all.yml

@@ -1,14 +1,17 @@
 name: Test All Dafny Files
 
-on: [push]
+on:
+  push:
+    branches:
+      - main
 jobs:
   test:
     runs-on: ubuntu-20.04
     steps:
       - uses: actions/checkout@v4
       - name: Install Nix
         uses: cachix/install-nix-action@v20
-      - name: Test if all dafny files are named correctly
+      - name: Test that all dafny files are named correctly
         run: nix run .#dafny-namecheck
       - name: Run Dafny on all files
         run: nix run .#dafny-check

.github/workflows/test-dafny-new.yml

@@ -0,0 +1,23 @@
+name: Test New Dafny Files
+
+on:
+  pull_request:
+    branches:
+      - main
+jobs:
+  test-changed:
+    runs-on: ubuntu-20.04
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install Nix
+        uses: cachix/install-nix-action@v20
+      - name: Get changed files
+        id: changed-files
+        uses: tj-actions/changed-files@v45
+      - name: Test that all dafny files are named correctly
+        run: nix run .#dafny-namecheck
+
+      - name: Run Dafny on new files
+        env:
+          ALL_CHANGED_FILES: ${{ steps.changed-files.outputs.all_changed_files }}
+        run: nix run .#dafny-check-new "${ALL_CHANGED_FILES}"

.zed/settings.json

@@ -1,3 +1,4 @@
 {
-  "tab_size": 2
+  "tab_size": 2,
+  "format_on_save": "off"
 }

004-mean_absolute_derivation.dfy

@@ -0,0 +1,75 @@
+function sum(s: seq<real>) : real {
+  if |s| == 0 then 0.0 else s[0] + sum(s[1..])
+}
+
+lemma sum_prop(s: seq<real>)
+  requires |s| > 0
+  ensures sum(s) == sum(s[..|s| - 1]) + s[ |s| - 1 ]
+{
+  if (|s| > 1) {
+    assert (s[1..][..|s[1..]| - 1]) == s[1..|s| - 1];
+  }
+}
+
+function abs(x: real) : real
+  ensures abs(x) >= 0.0
+{
+  if x >= 0.0 then x else -x
+}
+
+function mean(s: seq<real>) : real
+  requires |s| > 0
+{
+  sum(s) / |s| as real
+}
+
+method mean_absolute_derivation(numbers: seq<real>) returns (derivation: real)
+  requires |numbers| > 0
+  ensures var m := mean(numbers);
+    derivation == mean(seq(|numbers|, i requires 0 <= i < |numbers| => abs(numbers[i] - m)))
+{
+  var s: real := 0.0;
+  var i := 0;
+  while i < |numbers|
+    invariant 0 <= i <= |numbers|
+    invariant s == sum(numbers[..i])
+  {
+    s := s + numbers[i];
+    assert sum(numbers[..i + 1]) == sum(numbers[..i]) + numbers[i] by {
+      assert numbers[..i+1][..i] == numbers[..i];
+      sum_prop(numbers[..i + 1]);
+    }
+    i := i + 1;
+  }
+
+  var m := s / |numbers| as real;
+  assert numbers[..|numbers|] == numbers;
+  assert m == mean(numbers);
+
+  var t: real := 0.0;
+  i := 0;
+
+  ghost var pref_seq := [];
+  while i < |numbers|
+    invariant 0 <= i <= |numbers|
+    invariant |pref_seq| == i
+    invariant pref_seq == seq(i, j requires 0 <= j < i => abs(numbers[j] - m))
+    invariant t == sum(pref_seq[..i])
+  {
+    ghost var pre_seq := pref_seq;
+    assert pre_seq[..|pre_seq|] == pre_seq[..i] == pre_seq;
+
+    pref_seq := pref_seq + [abs(numbers[i] - m)];
+
+    assert sum(pref_seq[..i + 1]) == sum(pref_seq[..i]) + pref_seq[i] by {
+      assert pref_seq[..i+1][..i] == pref_seq[..i];
+      sum_prop(pref_seq[..i + 1]);
+    }
+
+    t := t + abs(numbers[i] - m);
+    i := i + 1;
+  }
+
+  assert pref_seq[..|pref_seq|] == pref_seq;
+  derivation := t / |numbers| as real;
+}

016-count_distinct_characters.dfy

@@ -0,0 +1,33 @@
+function contains_char(s: string, c: char): bool
+  decreases |s|
+  requires forall i :: 0 <= i < |s| ==> 'a' <= s[i] <= 'z' || 'A' <= s[i] <= 'Z'
+  requires 'a' <= c <= 'z'
+{
+  if |s| == 0 then false else s[0] == c || contains_char(s[1..], c)
+}
+
+function upper_char(c: char) : (C: char)
+  requires 'a' <= c <= 'z'
+  ensures 'A' <= C <= 'Z'
+{ c - 'a' + 'A' }
+
+method count_distinct_characters(s: string) returns (count: int)
+  requires forall i :: 0 <= i < |s| ==> 'a' <= s[i] <= 'z' || 'A' <= s[i] <= 'Z'
+  ensures count == |set c | 'a' <= c <= 'z' && contains_char(s, c)|
+{
+  count := 0;
+  ghost var contained: set<char> := {};
+  var i := 'a';
+  while i <= 'z'
+    invariant 'a' <= i <= ('z' as int + 1) as char
+    invariant count == |contained|
+    invariant contained == set c | 'a' <= c < i && contains_char(s, c)
+  {
+    if contains_char(s, i) {
+      count := count + 1;
+      contained := contained + {i};
+    }
+    i := (i as int + 1) as char;
+  }
+  assert contained == set c | 'a' <= c <= 'z' && contains_char(s, c);
+}

026-remove_duplicates.dfy

@@ -0,0 +1,61 @@
+method remove_duplicates(a: seq<int>) returns (result: seq<int>)
+  requires forall i :: 0 <= i < |a| ==> count_rec(a, a[i]) >= 1
+  ensures forall i :: 0 <= i < |result| ==> count_rec(a, result[i]) == 1
+  ensures forall i :: 0 <= i < |a| ==> (a[i] in result <==> count_rec(a, a[i]) == 1)
+{
+  var res: seq<int> := [];
+  var i := 0;
+  while i < |a|
+    invariant 0 <= i <= |a|
+    invariant forall j :: 0 <= j < |res| ==> count_rec(a, res[j]) == 1
+    invariant forall j :: 0 <= j < i ==> (a[j] in res <==> count_rec(a, a[j]) == 1)
+    invariant forall j :: 0 <= j < |res| ==> res[j] in a[..i]
+  {
+    var cnt := count(a, a[i]);
+    if cnt == 1 {
+      res := res + [a[i]];
+    }
+    i := i + 1;
+  }
+  result := res;
+}
+
+function count_rec(a: seq<int>, x: int): int {
+  if |a| == 0 then 0
+  else count_rec(a[1..], x) + (if a[0] == x then 1 else 0)
+}
+
+lemma count_prop(s: seq<int>, x: int)
+    requires |s| > 0
+    ensures count_rec(s, x) == count_rec(s[..|s| - 1], x) + if s[|s| - 1] == x then 1 else 0
+{
+    if (|s| > 1) {
+        assert (s[1..][..|s[1..]| - 1]) == s[1..|s| - 1];
+    }
+}
+
+method count(a: seq<int>, x: int) returns (cnt: int)
+  ensures cnt == |set i | 0 <= i < |a| && a[i] == x|
+  ensures cnt == count_rec(a, x)
+{
+  cnt := 0;
+  ghost var positions: set<int> := {};
+  var i := 0;
+  while i < |a|
+    invariant 0 <= i <= |a|
+    invariant cnt == |positions|
+    invariant positions == set k | 0 <= k < i && a[k] == x
+    invariant cnt == count_rec(a[..i], x)
+  {
+    if a[i] == x {
+      cnt := cnt + 1;
+      positions := positions + {i};
+    }
+    assert count_rec(a[..i + 1], x) == count_rec(a[..i], x) + (if a[i] == x then 1 else 0) by {
+        assert a[..i+1][..i] == a[..i];
+        count_prop(a[..i + 1], x);
+    }
+    i := i + 1;
+  }
+  assert a == a[..|a|];
+}

029-filter_by_prefix.dfy

@@ -0,0 +1,19 @@
+method filter_by_prefix(xs: seq<string>, p: string) returns (filtered: seq<string>)
+  ensures forall i :: 0 <= i < |filtered| ==> starts_with(filtered[i], p)
+{
+  filtered := [];
+  var i := 0;
+  while i < |xs|
+    invariant 0 <= i <= |xs|
+    invariant forall j :: 0 <= j < |filtered| ==> starts_with(filtered[j], p)
+  {
+    if starts_with(xs[i], p) {
+      filtered := filtered + [xs[i]];
+    }
+    i := i + 1;
+  }
+}
+
+function starts_with(s: string, p: string): bool {
+  |p| == 0 || (|s| != 0 && |s| >= |p| && s[0] == p[0] && starts_with(s[1..], p[1..]))
+}

README.md

@@ -6,7 +6,7 @@ Current status:
 - [x] 1. separate_paren_groups
 - [x] 2. truncate
 - [x] 3. below_zero
-- [ ] 4. mean_absolute_derivation
+- [x] 4. mean_absolute_derivation
 - [x] 5. intersperse
 - [x] 6. parse_nested_parens
 - [x] 7. filter_by_substring
@@ -18,7 +18,7 @@ Current status:
 - [x] 13. greatest_common_divisor
 - [x] 14. all_prefixes
 - [ ] 15. string_sequence - complex strings
-- [ ] 16. count_distinct_characters
+- [x] 16. count_distinct_characters
 - [ ] 17. parse_music - complex strings
 - [ ] 18. how_many_times - complex strings
 - [ ] 19. sort_numbers - complex strings
@@ -28,10 +28,10 @@ Current status:
 - [x] 23. strlen
 - [x] 24. largest_divisor
 - [ ] 25. factorize
-- [ ] 26. remove_duplicates
+- [x] 26. remove_duplicates
 - [x] 27. flip_case
 - [ ] 28. concatenate
-- [ ] 29. filter_by_prefix
+- [x] 29. filter_by_prefix
 - [x] 30. get_positive
 - [x] 31. is_prime
 - [ ] 32. poly
@@ -41,7 +41,7 @@ Current status:
 - [ ] 36. fizz_buzz
 - [ ] 37. sort_even - sorting
 - [ ] 38. encode_cyclic
-- [ ] 39. prime_fib
+- [ ] 39. ~prime_fib~ -- unbounded loop, probably impossible
 - [x] 40. triples_sum_to_zero
 - [ ] 41. car_race_collision
 - [x] 42. incr_list

flake.nix

@@ -13,6 +13,7 @@
         packages = {
           dafny-check = pkgs.writeShellScriptBin "dafny-check" ''
             DIR=''${1:-.}
+
             file_count=$(find "$DIR" -maxdepth 1 -name "*.dfy" -printf '.' | wc -m | sed 's/ //g')
             file_no=0
             for f in "$DIR"/*.dfy
@@ -23,6 +24,28 @@
             done
           '';
 
+          dafny-check-new = pkgs.writeShellScriptBin "dafny-check" ''
+            file_count=0
+
+            echo "New files found:"
+            for f in $1; do
+              if [[ $f == *.dfy ]]; then
+                echo $f
+                file_count=$((file_count+1))
+              fi
+            done
+
+            echo "Staring the check"
+            for f in $1
+            do
+              if [[ $f == *.dfy ]]; then
+                file_no=$((file_no+1))
+                echo "Running dafny on $(basename "$f") ($file_no/$file_count)"
+                ${pkgs.dafny}/bin/dafny verify --allow-warnings --verification-time-limit 2400 $f || exit 1
+              fi
+            done
+          '';
+
           dafny-namecheck = pkgs.writeShellScriptBin "dafny-namecheck" ''
             # Directory to check, use current directory if not specified
             DIR=''${1:-.}