16, 36, 161

Bench/016-count_distinct_characters.py

@@ -0,0 +1,46 @@
+from typing import cast, List, Dict, Set, Optional, Union, Tuple
+from nagini_contracts.contracts import *
+
+@Pure
+def contains_char(s : List[int], c : int, i : int, j : int) -> bool:
+    Requires(Acc(list_pred(s)))
+    Requires(Forall(int, lambda d_0_i_:
+        not (((0) <= (d_0_i_)) and ((d_0_i_) < (len(s)))) or (((97) <= ((s)[d_0_i_])) and (((s)[d_0_i_]) <= (122)))))
+    Requires(0 <= i and i <= j and j <= len(s))
+    Requires(((97) <= (c)) and ((c) <= (122)))
+    if i == j:
+        return False
+    else:
+        return s[j - 1] == c or contains_char(s, c, i, j - 1)
+
+@Pure 
+def count_chars_inter(s : List[int], c : int) -> int:
+    Requires(Acc(list_pred(s)))
+    Requires(Forall(int, lambda d_0_i_:
+        not (((0) <= (d_0_i_)) and ((d_0_i_) < (len(s)))) or (((97) <= ((s)[d_0_i_])) and (((s)[d_0_i_]) <= (122)))))
+    Requires(((97) <= (c)) and ((c) <= (123)))
+    if c == 97:
+        return 0
+    else:
+        return count_chars_inter(s, c - 1) + (1 if contains_char(s, c - 1, 0, len(s)) else 0)
+
+def count_distinct_characters(s : List[int]) -> int:
+    Requires(Acc(list_pred(s)))
+    Requires(Forall(int, lambda d_1_i_:
+        not (((0) <= (d_1_i_)) and ((d_1_i_) < (len(s)))) or (((97) <= ((s)[d_1_i_])) and (((s)[d_1_i_]) <= (122)))))
+    Ensures(Acc(list_pred(s)))
+    Ensures(Forall(int, lambda d_1_i_:
+        not (((0) <= (d_1_i_)) and ((d_1_i_) < (len(s)))) or (((97) <= ((s)[d_1_i_])) and (((s)[d_1_i_]) <= (122)))))
+    Ensures((Result()) == count_chars_inter(s, 123))
+    c = int(0) # type : int
+    d_2_i_ = int(97) # type : int
+    while (d_2_i_) <= (122):
+        Invariant(Acc(list_pred(s)))
+        Invariant(((97) <= (d_2_i_)) and ((d_2_i_) <= (123)))
+        Invariant(Forall(int, lambda d_1_i_:
+            not (((0) <= (d_1_i_)) and ((d_1_i_) < (len(s)))) or (((97) <= ((s)[d_1_i_])) and (((s)[d_1_i_]) <= (122)))))
+        Invariant(c == count_chars_inter(s, d_2_i_))
+        if contains_char(s, d_2_i_, 0, len(s)):
+            c = c + 1
+        d_2_i_ = d_2_i_ + 1
+    return c

Bench/036-fizz_buzz.py

@@ -0,0 +1,57 @@
+from typing import cast, List, Dict, Set, Optional, Union
+from nagini_contracts.contracts import *
+
+def fizz__buzz(n : int) -> int:
+    Requires(n >= 0)
+    Ensures(Result() >= 0)
+    Ensures((Result()) == fizz_buzz_fun(n))
+    result = int(0) # type : int
+    result = 0
+    d_1_i_ = int(0) # type : int
+    d_1_i_ = 0
+    while (d_1_i_) < (n):
+        Invariant(((0) <= (d_1_i_)) and ((d_1_i_) <= (n)))
+        Invariant(Forall(int, lambda x : (Implies(x >= 0 and x < n, 
+            fizz_buzz_fun(x + 1) == (count7__r(x) if ((x % 11 == 0) or (x % 13 == 0)) else 0) + fizz_buzz_fun(x)), [[fizz_buzz_fun(x + 1)]])))
+        Invariant(result == fizz_buzz_fun(d_1_i_))
+        if (((d_1_i_ % 11)) == (0)) or (((d_1_i_ % 13)) == (0)):
+            d_4_cnt_ = int(0) # type : int
+            d_4_cnt_ = count7(d_1_i_)
+            result = (result) + (d_4_cnt_)
+        d_1_i_ = (d_1_i_) + (1)
+    return result
+
+@Pure 
+def fizz_buzz_fun(n : int) -> int:
+    Requires(n >= 0)
+    Ensures(Result() >= 0)
+    if n == 0:
+        return 0
+    else:
+        return (count7__r(n - 1) if ((n - 1) % 11 == 0 or (n - 1) % 13 == 0) else 0) + fizz_buzz_fun(n - 1)
+
+
+def count7(x : int) -> int:
+    Requires(x >= 0)
+    Ensures(Result() >= 0)
+    Ensures((Result()) == (count7__r(x)))
+    count = int(0) # type : int
+    count = 0
+    d_6_y_ = int(0) # type : int
+    d_6_y_ = x
+    while (d_6_y_) > (0):
+        Invariant(((0) <= (d_6_y_)) and ((d_6_y_) <= (x)))
+        Invariant(((count) + (count7__r(d_6_y_))) == (count7__r(x)))
+        if ((d_6_y_ % 10)) == (7):
+            count = (count) + (1)
+        d_6_y_ = d_6_y_ // 10
+    return count
+
+@Pure
+def count7__r(x : int) -> int :
+    Requires(x >= 0)
+    Ensures(Result() >= 0)
+    if x == 0:
+        return 0
+    else:
+        return (x % 10 == 7) + count7__r(x // 10)

Bench/161-solve.py

@@ -0,0 +1,76 @@
+from typing import List
+from nagini_contracts.contracts import *
+
+def solve(s : List[int]) -> List[int]:
+    Requires(Acc(list_pred(s), 1/2))
+    Ensures(Acc(list_pred(Result()), 1/2))
+    Ensures(Acc(list_pred(s), 1/2))
+    Ensures((len(s)) == (len(Result())))
+    Ensures(Implies(Forall(int, lambda d_0_i_:
+        not (((0) <= (d_0_i_)) and ((d_0_i_) < (len(s)))) or (not(is__alpha((s)[d_0_i_])))), Forall(int, lambda d_1_i_:
+        not (((0) <= (d_1_i_)) and ((d_1_i_) < (len(s)))) or (((s)[d_1_i_]) == ((Result())[((len(Result())) - (1)) - (d_1_i_)])))))
+    Ensures(Implies(Exists(int, lambda d_2_i_:
+        (((0) <= (d_2_i_)) and ((d_2_i_) < (len(s)))) and (is__alpha((s)[d_2_i_]))), Forall(int, lambda d_3_i_:
+        not (((0) <= (d_3_i_)) and ((d_3_i_) < (len(Result())))) or ((((Result())[d_3_i_]) == (flip__case((s)[d_3_i_])) if is__alpha((s)[d_3_i_]) else ((Result())[d_3_i_]) == ((s)[d_3_i_]))))))
+    t : List[int] = []
+    d_4_flag_ = False # type : bool
+    d_5_i_ = int(0) # type : int
+    d_5_i_ = 0
+    while (d_5_i_) < (len(s)):
+        Invariant(Acc(list_pred(t)))
+        Invariant(Acc(list_pred(s), 1/2))
+        Invariant(((0) <= (d_5_i_)) and ((d_5_i_) <= (len(s))))
+        Invariant((len(t)) == (d_5_i_))
+        Invariant(Implies(d_4_flag_, Exists(int, lambda d_6_j_:
+            (((0) <= (d_6_j_)) and ((d_6_j_) < (d_5_i_))) and (is__alpha((s)[d_6_j_])))))
+        Invariant(Implies(Exists(int, lambda d_6_j_:
+            (((0) <= (d_6_j_)) and ((d_6_j_) < (d_5_i_))) and (is__alpha((s)[d_6_j_]))), d_4_flag_))
+        Invariant(Implies(not(d_4_flag_), Forall(int, lambda d_7_j_:
+            Implies(((0) <= (d_7_j_)) and (d_7_j_) < (d_5_i_), not(is__alpha((s)[d_7_j_]))))))
+        Invariant(Implies(Forall(int, lambda d_7_j_:
+            Implies(((0) <= (d_7_j_)) and (d_7_j_) < (d_5_i_), not(is__alpha((s)[d_7_j_])))), not(d_4_flag_)))
+        Invariant(Forall(int, lambda d_7_j_:
+            (Implies(((0) <= (d_7_j_)) and ((d_7_j_) < (d_5_i_)), ((t)[d_7_j_]) == ((flip__case((s)[d_7_j_]) if is__alpha((s)[d_7_j_]) else (s)[d_7_j_]))), [[]])))
+        if is__alpha((s)[d_5_i_]):
+            t = (t) + [flip__case((s)[d_5_i_])]
+            d_4_flag_ = True
+        else:
+            t = (t) + [(s)[d_5_i_]]
+        d_5_i_ = (d_5_i_) + (1)
+    if not(d_4_flag_):
+        t = reverse(t)
+    return t
+
+def reverse(str : List[int]) -> List[int]:
+    Requires(Acc(list_pred(str), 1/2))
+    Ensures(Acc(list_pred(str), 1/2))
+    Ensures(Acc(list_pred(Result())))
+    Ensures(str == Old(str))
+    Ensures((len(Result())) == (len(str)))
+    Ensures(Forall(int, lambda d_11_k_:
+        not (((0) <= (d_11_k_)) and ((d_11_k_) < (len(str)))) or (((Result())[d_11_k_]) == ((str)[((len(str)) - (1)) - (d_11_k_)]))))
+    rev = list([int(0)] * 0) # type : List[int]
+    rev = []
+    d_12_i_ = int(0) # type : int
+    d_12_i_ = 0
+    while (d_12_i_) < (len(str)):
+        Invariant(Acc(list_pred(str), 1/2))
+        Invariant(Acc(list_pred(rev)))
+        Invariant(((d_12_i_) >= (0)) and ((d_12_i_) <= (len(str))))
+        Invariant((len(rev)) == (d_12_i_))
+        Invariant(Forall(int, lambda d_13_k_:
+            not (((0) <= (d_13_k_)) and ((d_13_k_) < (d_12_i_))) or (((rev)[d_13_k_]) == ((str)[(len(str) - (1)) - (d_13_k_)]))))
+        rev = (rev) + [(str)[(len(str) - (d_12_i_)) - (1)]]
+        d_12_i_ = (d_12_i_) + (1)
+    return rev
+
+@Pure
+def is__alpha(c : int) -> bool :
+    return (((97) <= (c)) and ((c) <= (122))) or (((65) <= (c)) and ((c) <= (90)))
+
+@Pure
+def flip__case(c : int) -> int :
+    if ((97) <= (c)) and ((c) <= (122)):
+        return ((c) - (97)) + (65)
+    elif True:
+        return ((c) - (65)) + (97)

README.md

@@ -19,7 +19,7 @@ Current status:
 - [x] 13. greatest_common_divisor
 - [ ] 14. all_prefixes
 - [ ] 15. string_sequence
-- [ ] 16. count_distinct_characters
+- [x] 16. count_distinct_characters
 - [ ] 17. parse_music
 - [ ] 18. how_many_times
 - [ ] 19. sort_numbers
@@ -39,7 +39,7 @@ Current status:
 - [x] 33. sort_third
 - [x] 34. unique
 - [x] 35. max_element
-- [ ] 36. fizz_buzz
+- [x] 36. fizz_buzz
 - [x] 37. sort_even
 - [ ] 38. encode_cyclic
 - [ ] 39. prime_fib
@@ -78,7 +78,7 @@ Current status:
 - [x] 72. will_it_fly
 - [x] 73. smallest_change
 - [ ] 74. total_match
-- [x] 75. is_multiply_prime
+- [ ] 75. is_multiply_prime
 - [ ] 76. is_simple_power
 - [ ] 77. iscube
 - [x] 78. hex_key
@@ -164,6 +164,6 @@ Current status:
 - [ ] 158. find_max
 - [x] 159. eat
 - [ ] 160. do_algebra
-- [ ] 161. solve
+- [x] 161. solve
 - [ ] 162. string_to_md5
 - [x] 163. generate_integers

WIP/077-is_cube.py

@@ -10,21 +10,28 @@ def cube__root(N : int) -> int:
     # Ensures(Forall(int, lambda d_0_r_: Implies(0 <= d_0_r_ and d_0_r_ < r, cube(d_0_r_) < N)))
     r = int(0) # type : int
     r = 0
-    Assert(Forall(int, lambda x: x < (x + 1)))
+    # Assert(Forall(int, lambda x: x < (x + 1)))
     # Assert(Forall(int, lambda x: Implies(0 <= x and x < N, x * x < (x + 1) * (x + 1))))
-    Assert(Forall(int, lambda x: x * x * x < (x + 1) * (x + 1) * (x + 1)))
+    # Assert(Forall(int, lambda x: x * x * x < (x + 1) * (x + 1) * (x + 1)))
     # Assert(Forall(int, lambda x: (Implies(0 <= x and x < N, cube(x) < cube(x + 1)), [[cube(x)]])))
     while (cube((r) + (1))) <= (N):
         Invariant(N >= 0)
         Invariant(r >= 0 and r <= N)
         Invariant((cube(r)) <= (N))
-        # Invariant(Forall(int, lambda x: (Implies(0 <= x, cube(x) < cube(x + 1)), [[cube(x)]])))
-        # Invariant(Forall(int, lambda x: (Implies(0 <= x and x < r, cube(x) < cube(r)), [[cube(x) < cube(r)]])))
+        Invariant(Forall(int, lambda x: (Implies(0 <= x and x <= N, cube_less(x, x + 1)), [[cube_less(x, x + 1)]])))
+        Invariant(Forall(int, lambda x: (Implies(0 <= x and x < r, cube_less(x, r)), [[cube_less(x, r)]])))
+        Invariant(cube_less(r, r + 1))
+        # Invariant(Forall(int, lambda x: (Implies(r < x and x <= N, cube_less(r, x)), [[]])))
         # Invariant(Forall(int, lambda x: Forall(int, lambda y : (Implies(0 <= x and x < y, cube(x) < cube(y)), [[cube(x) < cube(y)]]))))
         # Invariant(Forall(int, lambda d_0_r_: (Implies(0 <= d_0_r_ and d_0_r_ < r, cube(d_0_r_) < N), [[cube(d_0_r_)]])))
         r = (r) + (1)
     return r
 
+@Pure
+def cube_less(a : int, b : int) -> bool:
+    Requires(a >= 0)
+    Requires(b >= 0)
+    return cube(a) < cube(b)
 
 def is__cube(n : int) -> bool:
     Requires(n >= (0))