102, 106, 142, 157, 159, 163

.zed/settings.json

@@ -0,0 +1,3 @@
+{
+  "tab_size": 2
+}

102-choose_num.dfy

@@ -0,0 +1,29 @@
+method choose_num(x : int, y : int) returns (num : int)
+  requires 0 <= x && 0 <= y
+  ensures num == -1 || (num >= x && num <= y)
+  ensures num == -1 || num % 2 == 0
+  ensures num == -1 || (forall i : int :: x <= i <= y && i % 2 == 0 ==> num >= i)
+  ensures num == -1 <==> x >= y
+{
+  num := -1;
+  if x >= y {
+    return;
+  }
+  if x % 2 == 0 {
+    num := x;
+  } else {
+    num := x + 1;
+  }
+  var i := x + 2;
+  while i <= y
+    invariant i >= x && i <= y + 1
+    invariant num == -1 || num % 2 == 0
+    invariant forall j : int :: x <= j < i && j % 2 == 0 ==> num >= j
+    invariant num == -1 || (num >= x && num < i)
+  {
+    if i % 2 == 0 {
+      num := i;
+    }
+    i := i + 1;
+  }
+}

106-f.dfy

@@ -0,0 +1,54 @@
+function factorial_spec(n : int) : int
+  requires n >= 0
+  decreases n
+{
+  if n == 0 then 1 else n * factorial_spec(n - 1)
+}
+
+function sum_spec(n : int) : int
+  requires n >= 0
+  decreases n
+{
+  if n == 0 then 1 else n + sum_spec(n - 1)
+}
+
+method f(n : int) returns (result : seq<int>)
+  requires n >= 1
+  ensures |result| == n
+  ensures forall i : int :: i >= 0 && i < |result| && i % 2 == 0 ==> result[i] == factorial_spec(i)
+  ensures forall i : int :: i >= 0 && i < |result| && i % 2 != 0 ==> result[i] == sum_spec(i)
+{
+  result := [];
+  var i := 0;
+  while i < n
+    invariant i >= 0 && i <= n
+    invariant |result| == i
+    invariant forall i : int :: i >= 0 && i < |result| && i % 2 == 0 ==> result[i] == factorial_spec(i)
+    invariant forall i : int :: i >= 0 && i < |result| && i % 2 != 0 ==> result[i] == sum_spec(i)
+  {
+    if i % 2 == 0 {
+      var x := 1;
+      var j := 0;
+      while j < i
+        invariant j >= 0 && j <= i
+        invariant x == factorial_spec(j)
+      {
+        j := j + 1;
+        x := x * j;
+      }
+      result := result + [x];
+    } else {
+      var x := 1;
+      var j := 0;
+      while j < i
+        invariant j >= 0 && j <= i
+        invariant x == sum_spec(j)
+      {
+        j := j + 1;
+        x := x + j;
+      }
+      result := result + [x];
+    }
+    i := i + 1;
+  }
+}

142-sum_squares.dfy

@@ -0,0 +1,23 @@
+method sum_squares(a : seq<int>) returns (result : seq<int>)
+  ensures |result| == |a|
+  ensures forall i : int :: i >= 0 && i < |result| && i % 3 == 0 ==> result[i] == a[i] * a[i]
+  ensures forall i : int :: i >= 0 && i < |result| && i % 4 == 0 && i % 3 != 0 ==> result[i] == a[i] * a[i] * a[i]
+{
+  result := [];
+  var i := 0;
+  while i < |a|
+    invariant i >= 0 && i <= |a|
+    invariant |result| == i
+    invariant forall j : int :: j >= 0 && j < |result| && j % 3 == 0 ==> result[j] == a[j] * a[j]
+    invariant forall j : int :: j >= 0 && j < |result| && j % 4 == 0 && j % 3 != 0 ==> result[j] == a[j] * a[j] * a[j]
+  {
+    if i % 3 == 0 {
+      result := result + [a[i] * a[i]];
+    } else if i % 4 == 0 && i % 3 != 0 {
+      result := result + [a[i] * a[i] * a[i]];
+    } else {
+      result := result + [a[i]];
+    }
+    i := i + 1;
+  }
+}

157-right_angle_triangle.dfy

@@ -0,0 +1,5 @@
+method right_angle_triangle(a : int, b : int, c : int) returns (result : bool)
+  ensures result == (a * a + b * b == c * c || a * a + c * c == b * b || b * b + c * c == a * a)
+{
+  result := a * a + b * b == c * c || a * a + c * c == b * b || b * b + c * c == a * a;
+}

159-eat.dfy

@@ -0,0 +1,12 @@
+method eat(number : int, need : int, remaining : int) returns (result: seq<int>)
+  requires number >= 0 && need >= 0 && remaining >= 0
+  ensures |result| == 2
+  ensures remaining >= need ==> result[0] == number + need && result[1] == remaining - need
+  ensures remaining < need ==> result[0] == number + remaining && result[1] == 0
+{
+  if remaining < need {
+    result := [number + remaining, 0];
+  } else {
+    result := [number + need, remaining - need];
+  }
+}

163-generate_integers.dfy

@@ -0,0 +1,36 @@
+method min(a : int, b : int) returns (m : int)
+  ensures m == a || m == b
+  ensures m <= a && m <= b
+{
+  if a < b { m := a; } else { m := b; }
+}
+
+method max(a : int, b : int) returns (m : int)
+  ensures m == a || m == b
+  ensures m >= a && m >= b
+{
+  if a > b { m := a; } else { m := b; }
+}
+
+method generate_integers(a : int, b : int) returns (result: seq<int>)
+  ensures forall i : int :: i >= 0 && i < |result| ==> result[i] % 2 == 0
+  ensures forall i : int :: i >= 0 && i < |result| ==> result[i] in [2, 4, 6, 8]
+{
+  var left := min(a, b);
+  var right := max(a, b);
+
+  var lower := max(2, left);
+  var upper := min(8, right);
+
+  result := [];
+  var i := lower;
+  while i <= upper
+    invariant forall i : int :: i >= 0 && i < |result| ==> result[i] % 2 == 0
+    invariant forall j : int :: j >= 0 && j < |result| ==> result[j] in [2, 4, 6, 8]
+  {
+    if i % 2 == 0 {
+      result := result + [i];
+    }
+    i := i + 1;
+  }
+}

README.md

@@ -104,11 +104,11 @@ Current status:
 - [ ] 99. closest_integer
 - [ ] 100. make_a_pile
 - [ ] 101. words_string
-- [ ] 102. choose_num
+- [x] 102. choose_num
 - [ ] 103. rounded_avg
 - [ ] 104. unique_digits
 - [ ] 105. by_length
-- [ ] 106. f
+- [x] 106. f
 - [ ] 107. even_odd_palindrome
 - [ ] 108. count_nums
 - [ ] 109. move_one_ball
@@ -159,10 +159,10 @@ Current status:
 - [ ] 154. cycpattern_check
 - [ ] 155. even_odd_count
 - [ ] 156. int_to_mini_roman
-- [ ] 157. right_angle_triangle
+- [x] 157. right_angle_triangle
 - [ ] 158. find_max
-- [ ] 159. eat
+- [x] 159. eat
 - [ ] 160. do_algebra
 - [ ] 161. solve
 - [ ] 162. string_to_md5
-- [ ] 163. generate_integers
+- [x] 163. generate_integers