130, 139, 148, 150, 153, 154 (#7)

130-tri.dfy

@@ -0,0 +1,34 @@
+function tri(n: nat): nat
+  decreases if n % 2 == 0 then 0 else n
+{
+  if n == 1 then 3
+  else if n % 2 == 0 then 1 + n / 2
+  else tri(n - 1) + tri(n - 2) + tri(n + 1)
+}
+
+method Tribonacci(n: nat) returns (result: seq<nat>)
+  ensures |result| == n + 1
+  ensures forall i :: 0 <= i <= n ==> result[i] == tri(i)
+{
+  if n == 0 {
+    result := [1];
+  } else {
+    result := [1, 3];
+    var i := 2;
+    while i <= n
+      invariant 0 <= i <= n + 1
+      invariant |result| == i
+      invariant forall j :: 0 <= j < i ==> result[j] == tri(j)
+    {
+      if i % 2 == 0 {
+        result := result + [1 + i / 2];
+      } else {
+        assert result[i - 2] == tri(i - 2);
+        assert result[i - 1] == tri(i - 1);
+        assert (i + 3) / 2 == tri(i + 1);
+        result := result + [result[i - 2] + result[i - 1] + (i + 3) / 2];
+      }
+      i := i + 1;
+    }
+  }
+}

139-special_factorial.dfy

@@ -0,0 +1,31 @@
+function factorial(n: nat): nat
+  decreases n
+{
+  if n == 0 then 1 else n * factorial(n - 1)
+}
+
+function special_factorial_rec(n: nat): nat
+  decreases n
+{
+  if n == 0 then 1 else factorial(n) * special_factorial_rec(n - 1)
+}
+
+method special_factorial(n: nat) returns (result: nat)
+  requires n > 0
+  ensures result == special_factorial_rec(n)
+{
+  result := 1;
+  var fact := 1;
+
+  var i := 0;
+  while i < n
+    invariant 0 <= i <= n
+    invariant result == special_factorial_rec(i)
+    invariant fact == factorial(i)
+    decreases n - i + 1
+  {
+    i := i + 1;
+    fact := fact * i;
+    result := result * fact;
+  }
+}

148-bf.dfy

@@ -0,0 +1,67 @@
+datatype Planet = Mercury | Venus | Earth | Mars | Jupiter | Saturn | Uranus | Neptune
+datatype Option<T> = Some(value: T) | None
+
+function PlanetFromString(name: string): Option<Planet>
+  ensures PlanetFromString(name).Some? ==> 0 <= PlanetIndex(PlanetFromString(name).value) <= 7
+{
+  match name
+  case "Mercury" => Some(Mercury)
+  case "Venus" => Some(Venus)
+  case "Earth" => Some(Earth)
+  case "Mars" => Some(Mars)
+  case "Jupiter" => Some(Jupiter)
+  case "Saturn" => Some(Saturn)
+  case "Uranus" => Some(Uranus)
+  case "Neptune" => Some(Neptune)
+  case _ => None
+}
+
+function PlanetIndex(p: Planet): int
+{
+  match p
+  case Mercury => 0
+  case Venus => 1
+  case Earth => 2
+  case Mars => 3
+  case Jupiter => 4
+  case Saturn => 5
+  case Uranus => 6
+  case Neptune => 7
+}
+
+function GetPlanetsBetween(planet1: string, planet2: string): seq<string>
+  ensures |GetPlanetsBetween(planet1, planet2)| <= 6
+{
+  var p1 := PlanetFromString(planet1);
+  var p2 := PlanetFromString(planet2);
+  if p1.None? || p2.None? then
+    []
+  else
+    var i1 := PlanetIndex(p1.value);
+    var i2 := PlanetIndex(p2.value);
+    if i1 < i2 then
+      GetPlanetsBetweenIndices(i1 + 1, i2 - 1)
+    else if i1 > i2 then
+      GetPlanetsBetweenIndices(i2 + 1, i1 - 1)
+    else
+      []
+}
+
+function GetPlanetsBetweenIndices(start: int, end: int): seq<string>
+  requires 0 <= start <= 7 && 0 <= end <= 7
+  ensures |GetPlanetsBetweenIndices(start, end)| <= (if start <= end then end - start + 1 else 0)
+  decreases if start <= end then end - start + 1 else 0
+{
+  if start > end then
+    []
+  else
+    match start
+    case 0 => ["Mercury"] + GetPlanetsBetweenIndices(1, end)
+    case 1 => ["Venus"] + GetPlanetsBetweenIndices(2, end)
+    case 2 => ["Earth"] + GetPlanetsBetweenIndices(3, end)
+    case 3 => ["Mars"] + GetPlanetsBetweenIndices(4, end)
+    case 4 => ["Jupiter"] + GetPlanetsBetweenIndices(5, end)
+    case 5 => ["Saturn"] + GetPlanetsBetweenIndices(6, end)
+    case 6 => ["Uranus"] + GetPlanetsBetweenIndices(7, end)
+    case 7 => ["Neptune"]
+}

150-x_or_y.dfy

@@ -0,0 +1,16 @@
+predicate IsPrime(n: nat)
+{
+  n > 1 &&
+  forall k :: 2 <= k < n ==> n % k != 0
+}
+
+method x_or_y(n: nat, x: int, y: int) returns (result: int)
+  ensures IsPrime(n) ==> result == x
+  ensures !IsPrime(n) ==> result == y
+{
+  if IsPrime(n) {
+    return x;
+  } else {
+    return y;
+  }
+}

152-compare.dfy

@@ -1,27 +1,22 @@
 method Compare(scores: array<int>, guesses: array<int>) returns (result: array<int>)
   requires scores.Length == guesses.Length
   ensures result.Length == scores.Length
-  ensures forall i :: 0 <= i < result.Length ==> 
-    result[i] == if scores[i] == guesses[i] then 0 else abs(scores[i] - guesses[i])
+  ensures forall i :: 0 <= i < result.Length ==> result[i] == abs(scores[i] - guesses[i])
 {
   result := new int[scores.Length];
   var i := 0;
   while i < scores.Length
     invariant 0 <= i <= scores.Length
     invariant result.Length == scores.Length
-    invariant forall k :: 0 <= k < i ==> 
-      result[k] == if scores[k] == guesses[k] then 0 else abs(scores[k] - guesses[k])
+    invariant forall k :: 0 <= k < i ==> result[k] == abs(scores[k] - guesses[k])
   {
-    if scores[i] == guesses[i] {
-      result[i] := 0;
-    } else {
-      result[i] := abs(scores[i] - guesses[i]);
-    }
+    result[i] := abs(scores[i] - guesses[i]);
     i := i + 1;
   }
 }
 
 function abs(x: int): int
+    ensures 0 <= abs(x)
 {
   if x < 0 then -x else x
-}
+}

153-Strongest_Extension.dfy

@@ -0,0 +1,59 @@
+class Extension {
+    var name: string
+    var strength: int
+
+    constructor(n: string)
+        ensures name == n
+        ensures strength == CalculateStrength(n)
+    {
+        name := n;
+        strength := CalculateStrength(n);
+    }
+
+    static function CalculateStrength(s: string): int
+    {
+        CountUpperCase(s) - CountLowerCase(s)
+    }
+
+    static function CountUpperCase(s: string): int
+    {
+        if |s| == 0 then 0
+        else (if 'A' <= s[0] <= 'Z' then 1 else 0) + CountUpperCase(s[1..])
+    }
+
+    static function CountLowerCase(s: string): int
+    {
+        if |s| == 0 then 0
+        else (if 'a' <= s[0] <= 'z' then 1 else 0) + CountLowerCase(s[1..])
+    }
+}
+
+method Strongest_Extension(className: string, extensions: seq<string>) returns (result: string)
+    requires |extensions| > 0
+    ensures |result| > |className|
+    ensures result[..|className|] == className
+    ensures result[|className|] == '.'
+    ensures var extName := result[|className| + 1..];
+               extName in extensions
+    ensures var extName := result[|className| + 1..];
+               forall i :: 0 <= i < |extensions| ==> Extension.CalculateStrength(extName) >= Extension.CalculateStrength(extensions[i])
+{
+    var strongestExt := new Extension(extensions[0]);
+    ghost var strongestIndex := 0;
+
+    for i := 1 to |extensions|
+        invariant 0 <= strongestIndex < |extensions|
+        invariant strongestExt.name == extensions[strongestIndex]
+        invariant strongestExt.strength == Extension.CalculateStrength(extensions[strongestIndex])
+        invariant forall j :: 0 <= j < i ==> strongestExt.strength >= Extension.CalculateStrength(extensions[j])
+        invariant forall j :: 0 <= j < i ==> Extension.CalculateStrength(extensions[strongestIndex]) >= Extension.CalculateStrength(extensions[j])
+    {
+        var currentExt := new Extension(extensions[i]);
+        if currentExt.strength > strongestExt.strength {
+            strongestExt := currentExt;
+            strongestIndex := i;
+        }
+    }
+
+    result := className + "." + strongestExt.name;
+}

154-cycpattern_check.dfy

@@ -0,0 +1,27 @@
+predicate IsSubstring(s: string, sub: string)
+{
+  |s| >= |sub| && exists i {:trigger s[i..i+|sub|]} :: 0 <= i <= |s| - |sub| && s[i..i+|sub|] == sub
+}
+
+function RotateString(s: string, n: nat): string
+  requires 0 <= n <= |s|
+{
+  s[n..] + s[..n]
+}
+
+method CycpatternCheck(word: string, pattern: string) returns (result: bool)
+  ensures result ==> exists i :: 0 <= i <= |pattern| && IsSubstring(word, RotateString(pattern, i))
+  ensures !result ==> forall i :: 0 <= i <= |pattern| ==> !IsSubstring(word, RotateString(pattern, i))
+{
+  var i := 0;
+  while i <= |pattern|
+    invariant 0 <= i <= |pattern| + 1
+    invariant forall j :: 0 <= j < i ==> !IsSubstring(word, RotateString(pattern, j))
+  {
+    if IsSubstring(word, RotateString(pattern, i)) {
+      return true;
+    }
+    i := i + 1;
+  }
+  return false;
+}

README.md

@@ -132,7 +132,7 @@ Current status:
 - [ ] 127. intersection
 - [ ] 128. prod_signs
 - [ ] 129. minPath
-- [ ] 130. tri
+- [x] 130. tri
 - [ ] 131. digits
 - [ ] 132. is_nested
 - [ ] 133. sum_squares
@@ -141,7 +141,7 @@ Current status:
 - [ ] 136. largest_smallest_integers
 - [ ] 137. compare_one
 - [ ] 138. is_equal_to_sum_even
-- [ ] 139. special_factorial
+- [x] 139. special_factorial
 - [ ] 140. fix_spaces
 - [ ] 141. file_name_check
 - [ ] 142. sum_squares
@@ -150,13 +150,13 @@ Current status:
 - [ ] 145. order_by_points
 - [ ] 146. specialFilter
 - [ ] 147. get_max_triples
-- [ ] 148. bf
+- [x] 148. bf
 - [ ] 149. sorted_list_sum
-- [ ] 150. x_or_y
+- [x] 150. x_or_y
 - [ ] 151. double_the_difference
 - [x] 152. compare
-- [ ] 153. Strongest_Extension
-- [ ] 154. cycpattern_check
+- [x] 153. Strongest_Extension
+- [x] 154. cycpattern_check
 - [ ] 155. even_odd_count
 - [ ] 156. int_to_mini_roman
 - [x] 157. right_angle_triangle

flake.nix

@@ -10,7 +10,7 @@
     flake-parts.lib.mkFlake { inherit inputs; } {
       systems = [ "x86_64-linux" "aarch64-linux" "aarch64-darwin" "x86_64-darwin" ];
       perSystem = { pkgs, ... }: {
-        packages = rec {
+        packages = {
           dafny-check = pkgs.writeShellScriptBin "dafny-check" ''
             DIR=''${1:-.}
             for f in "$DIR"/*.dfy