Remove predicates, ensure each file has at least one method

001-separate-paren-groups.dfy

@@ -12,12 +12,12 @@ function ParenthesesDepth(s: string, i: int, j: int): int
         ParenthesesDepth(s, i+1, j)
 }
 
-predicate InnerDepthsPositive(s: string)
+function InnerDepthsPositive(s: string) : bool
 {
     forall i :: 0 < i < |s| ==> ParenthesesDepth(s, 0, i) > 0
 }
 
-predicate InnerDepthsNonnegative(s: string)
+function InnerDepthsNonnegative(s: string) : bool
 {
     forall i :: 0 < i < |s| ==> ParenthesesDepth(s, 0, i) >= 0
 }

002-truncate.dfy

@@ -1,6 +1,6 @@
 
 
-function truncate(x : real) : (i : real)
+method truncate(x : real) returns (i : real)
     // pre-conditions-start
     requires x >= 0.0
     // pre-conditions-end
@@ -9,6 +9,6 @@ function truncate(x : real) : (i : real)
     // post-conditions-end
     {
       // impl-start
-        x.Floor as real
+      return x.Floor as real;
       // impl-end
     }

011-string_xor.dfy

@@ -1,4 +1,4 @@
-predicate represents_byte(a: char)
+function represents_byte(a: char) : bool
 {
     a in "01"
 }

021-rescale_to_unit.dfy

@@ -15,7 +15,7 @@ lemma affine_unit(x: real, shift: real, scale: real)
     ensures affine(x, shift, scale) == 1.0 {}
 
 
-predicate affine_seq(s: seq<real>, r: seq<real>, shift: real, scale: real)
+function affine_seq(s: seq<real>, r: seq<real>, shift: real, scale: real) : bool
   requires scale > 0.0
   requires |r| == |s|
 {

023-strlen.dfy

@@ -1,9 +1,9 @@
-function strlen(s: string) : (len: int)
+method strlen(s: string) returns (len: int)
   // post-conditions-start
   ensures len == |s|
   // post-conditions-end
 {
   // impl-start
-  |s|
+  return |s|;
   // impl-end
 }

027-flip_case.dfy

@@ -1,13 +1,13 @@
-predicate lower(c: char)
+function lower(c: char) : bool
     {
         'a' <= c <= 'z'
     }
 
-predicate upper(c: char)
+function upper(c: char) : bool
     {
         'A' <= c <= 'Z'
     }
-predicate alpha(c: char)
+function alpha(c: char) : bool
     {
         lower(c) || upper(c)
     }
@@ -20,14 +20,14 @@ function flip_char(c: char) : (C: char)
         if upper(c) then c + 'a' - 'A' else c
     }
 
-    function flip_case(s: string) : (S: string)
-        // post-conditions-start
-        ensures |S| == |s|
-        ensures forall i :: 0 <= i < |s| ==> (lower(s[i]) <==> upper(S[i]))
-        ensures forall i :: 0 <= i < |s| ==> (upper(s[i]) <==> lower(S[i]))
-        // post-conditions-end
-        {
+method flip_case(s: string) returns (S: string)
+    // post-conditions-start
+    ensures |S| == |s|
+    ensures forall i :: 0 <= i < |s| ==> (lower(s[i]) <==> upper(S[i]))
+    ensures forall i :: 0 <= i < |s| ==> (upper(s[i]) <==> lower(S[i]))
+    // post-conditions-end
+    {
         // impl-start
-            seq(|s|, i requires 0 <= i < |s| => flip_char(s[i]))
+        return seq(|s|, i requires 0 <= i < |s| => flip_char(s[i]));
         // impl-end
-        }
+    }

059-largest-prime-factor.dfy

@@ -25,7 +25,7 @@ method is_prime(k: int) returns (result: bool)
   // impl-end
 }
 
-predicate is_prime_pred(k: int)
+function is_prime_pred(k: int) : bool
 {
   forall i :: 2 <= i < k ==> k % i != 0
 }

072-will_it_fly.dfy

@@ -49,7 +49,7 @@ method will_it_fly(s: seq<int>, w: int) returns (result: bool)
     // impl-end
 }
 
-predicate is_palindrome_pred(s : seq<int>) {
+function is_palindrome_pred(s : seq<int>) : bool {
     forall k :: 0 <= k < |s| ==> s[k] == s[|s| - 1 - k]
 }
 

075-is_multiply_prime.dfy

@@ -1,4 +1,4 @@
-predicate Prime(p: nat)
+function Prime(p: nat) : bool
     {
         p > 1 &&
         forall k :: 1 < k < p ==> p % k != 0

079-decimal_to_binary.dfy

@@ -3,7 +3,7 @@ type stringBin = s: string |
   forall i | 0 <= i < |s| :: s[i] in "01"
   witness "1"
 
-function decimal_to_binary(n: nat): (s: string)
+method decimal_to_binary(n: nat) returns (s: string)
   // post-conditions-start
   ensures |s| == |decimal_to_binary_helper(n)| + 4
   ensures s[..2] == "db"
@@ -12,7 +12,7 @@ function decimal_to_binary(n: nat): (s: string)
   // post-conditions-end
 {
   // impl-start
-  "db" + decimal_to_binary_helper(n) + "db"
+  return "db" + decimal_to_binary_helper(n) + "db";
   // impl-end
 }
 

080-is_happy.dfy

@@ -4,7 +4,7 @@ function ThreeDistinct(s: string, i: int): bool
     (s[i - 1] != s[i]) && (s[i] != s[i + 1]) && (s[i - 1] != s[i + 1])
 }
 
-predicate Happy(s: string)
+function Happy(s: string) : bool
 {
     |s| >= 3 &&
     forall i :: 0 < i < |s| - 1 ==> ThreeDistinct(s, i)

082-prime_length.dfy

@@ -1,15 +1,15 @@
-predicate IsPrime(n: int)
+function IsPrime(n: int) : bool
 {
   n > 1 &&
   forall k :: 2 <= k < n ==> n % k != 0
 }
 
-function PrimeLength(s: string): bool
+method PrimeLength(s: string) returns (p : bool)
   // post-conditions-start
-  ensures PrimeLength(s) <==> IsPrime(|s|)
+  ensures p <==> IsPrime(|s|)
   // post-conditions-end
 {
   // impl-start
-  IsPrime(|s|)
+  return IsPrime(|s|);
   // impl-end
 }

093-encode.dfy

@@ -53,7 +53,7 @@ function rot2(c: char): char
     (c as int + 2) as char
 }
 
-predicate is_vowel(c: char) {
+function is_vowel(c: char) : bool {
     (c == 'a' || c == 'e' || c == 'i' || c == 'o' || c == 'u')
     || (c == 'A' || c == 'E' || c == 'I' || c == 'O' || c == 'U')
 }

094-skjkasdkd.dfy

@@ -118,6 +118,6 @@ function max(a: int, b: int): int
   if a > b then a else b
 }
 
-predicate is_prime(k: int) {
+function is_prime(k: int) : bool {
   k != 1 && forall i :: 2 <= i < k ==> k % i != 0
 }

095-check_dict_case.dfy

@@ -1,9 +1,9 @@
-predicate IsLowerCase(s: string)
+function IsLowerCase(s: string) : bool
 {
   forall i :: 0 <= i < |s| ==> 'a' <= s[i] <= 'z'
 }
 
-predicate IsUpperCase(s: string)
+function IsUpperCase(s: string) : bool
 {
   forall i :: 0 <= i < |s| ==> 'A' <= s[i] <= 'Z'
 }

096-count_up_to.dfy

@@ -1,4 +1,4 @@
-predicate IsPrime(n: int)
+function IsPrime(n: int) : bool
 {
   n > 1 && forall k :: 2 <= k < n ==> n % k != 0
 }

098-count_upper.dfy

@@ -23,6 +23,6 @@ method count_upper(s: string) returns (cnt: int)
   // impl-end
 }
 
-predicate is_upper_vowel(c: char) {
+function is_upper_vowel(c: char) : bool {
   c == 'A' || c == 'E' || c == 'U' || c == 'I' || c == 'O'
 }

104-unique_digits.dfy

@@ -1,4 +1,4 @@
-predicate HasNoEvenDigit(n: int)
+function HasNoEvenDigit(n: int) : bool
   decreases n
 {
   n >= 0 && ((n < 10 && n % 2 == 1) || (n % 2 == 1 && HasNoEvenDigit(n / 10)))

107-even_odd_palindrome.dfy

@@ -1,4 +1,4 @@
-predicate is_palindrome(n: nat) {
+function is_palindrome(n: nat) : bool {
   var s := natToString(n);
   forall i | 0 <= i < |s| :: s[i] == s[|s|-1-i]
 }

109-move_one_ball.dfy

@@ -1,4 +1,4 @@
-predicate is_sorted(a: seq<int>) {
+function is_sorted(a: seq<int>) : bool {
   forall i, j :: 0 <= i < j < |a| ==> a[i] <= a[j]
 }
 

110-exchange.dfy

@@ -1,4 +1,4 @@
-predicate IsEven(n: int)
+function IsEven(n: int) : bool
 {
   n % 2 == 0
 }

112-reverse_delete.dfy

@@ -57,6 +57,6 @@ method check_palindrome(s: string) returns (result: bool)
   // impl-end
 }
 
-predicate is_palindrome_pred(s : string) {
+function is_palindrome_pred(s : string) : bool {
   forall k :: 0 <= k < |s| ==> s[k] == s[|s| - 1 - k]
 }

118-get_closest_vowel.dfy

@@ -1,10 +1,10 @@
-predicate IsVowel(c: char)
+function IsVowel(c: char) : bool
 {
   c == 'a' || c == 'e' || c == 'i' || c == 'o' || c == 'u' ||
   c == 'A' || c == 'E' || c == 'I' || c == 'O' || c == 'U'
 }
 
-predicate IsConsonant(c: char)
+function IsConsonant(c: char) : bool
 {
   ('A' <= c <= 'Z' || 'a' <= c <= 'z') && !IsVowel(c)
 }

127-intersection.dfy

@@ -1,4 +1,4 @@
-predicate IsPrime(n: nat)
+function IsPrime(n: nat) : bool
 {
   n > 1 &&
   forall k :: 2 <= k < n ==> n % k != 0

134-check_if_last_char_is_a_letter.dfy

@@ -8,6 +8,6 @@ method check_if_last_char_is_a_letter(s: string) returns (b: bool)
   // impl-end
 }
 
-predicate is_alpha(c: char) {
+function is_alpha(c: char) : bool {
     'a' <= c <= 'z' || 'A' <= c <= 'Z'
 }

148-bf.dfy

@@ -75,3 +75,16 @@ function GetPlanetsBetweenIndices(start: int, end: int): seq<string>
     case 7 => ["Neptune"]
   // impl-end
 }
+
+method bf(start: int, end: int) returns (planets: seq<string>)
+    // pre-conditions-start
+    requires 0 <= start <= 7 && 0 <= end <= 7
+    // pre-conditions-end
+    // post-conditions-start
+    ensures |planets| <= (if start <= end then end - start + 1 else 0)
+    // post-conditions-end
+    {
+        // impl-start
+        return GetPlanetsBetweenIndices(start, end);
+        // impl-end
+    }

149-sorted_list_sum.dfy

@@ -118,6 +118,7 @@ method sorted_list_sum(list: seq<string>) returns (sorted: seq<string>)
     {
         if |init[i]| % 2 == 0 {
             sorted := sorted + [init[i]];
+            assert multiset(sorted) <= multiset(init[0..i]);
             assert multiset(sorted) <= multiset(init[0..i + 1]); // assert-line
         } else {
             assert init[0..i + 1] == init[0..i] + [init[i]]; // assert-line

150-x_or_y.dfy

@@ -1,4 +1,4 @@
-predicate IsPrime(n: nat)
+function IsPrime(n: nat) : bool
 {
   n > 1 &&
   forall k :: 2 <= k < n ==> n % k != 0

154-cycpattern_check.dfy

@@ -1,4 +1,4 @@
-predicate IsSubstring(s: string, sub: string)
+function IsSubstring(s: string, sub: string) : bool
 {
   |s| >= |sub| && exists i {:trigger s[i..i+|sub|]} :: 0 <= i <= |s| - |sub| && s[i..i+|sub|] == sub
 }

161-solve.dfy

@@ -56,7 +56,7 @@ method reverse(s: string) returns (rev: string)
   // impl-end
 }
 
-predicate is_alpha(c: char) {
+function is_alpha(c: char) : bool {
   'a' <= c <= 'z' || 'A' <= c <= 'Z'
 }