haskell-te: 5f3975c88a880608c6d395cbac2ad6d94bcecaaa

     1: ; Lists with Nil, Cons, append, reverse, length, map, foldl and foldr; various
     2: ; combinations of these have been used to test HipSpec
     3: (declare-datatypes (a)
     4:   ((List (Nil) (Cons (head a) (tail (List a))))))
     5: (declare-datatypes () ((Nat (Z) (S (p Nat)))))
     6: 
     7: ; Functions equivalent to the constructors
     8: (define-fun
     9:   (par (a)
    10:     (constructor-Nil () (List a)
    11:       (as Nil (List a)))))
    12: 
    13: (define-fun
    14:   (par (a)
    15:     (constructor-Cons ((local-head a) (local-tail (List a))) (List a)
    16:       (as (Cons local-head local-tail) (List a)))))
    17: 
    18: (define-fun constructor-Z () Nat
    19:   (as Z Nat))
    20: 
    21: (define-fun constructor-S ((local-p Nat)) Nat
    22:   (as (S local-p) Nat))
    23: 
    24: ; Functions equivalent to the destructors
    25: (define-fun
    26:   (par (a)
    27:     (destructor-head ((local-x (List a))) a
    28:       (match local-x
    29:         (case (Cons local-head local-tail) local-head)))))
    30: 
    31: (define-fun
    32:   (par (a)
    33:     (destructor-tail ((local-x (List a))) (List a)
    34:       (match local-x
    35:         (case (Cons local-head local-tail) local-tail)))))
    36: 
    37: (define-fun destructor-p ((local-x Nat)) Nat
    38:   (match local-x
    39:     (case (S local-p) local-p)))
    40: 
    41: ; Other functions
    42: (define-fun-rec
    43:   (par (a)
    44:     (append
    45:        ((x (List a)) (y (List a))) (List a)
    46:        (match x
    47:          (case Nil y)
    48:          (case (Cons z xs) (Cons z (append xs y)))))))
    49: (define-fun-rec
    50:   (par (a)
    51:     (reverse
    52:        ((x (List a))) (List a)
    53:        (match x
    54:          (case Nil (as Nil (List a)))
    55:          (case (Cons z xs) (append (reverse xs) (Cons z (as Nil (List a)))))))))
    56: (define-fun-rec
    57:   (par (a)
    58:     (length
    59:        ((x (List a))) (Nat)
    60:        (match x
    61:          (case Nil Z)
    62:          (case (Cons z xs) (S (length xs)))))))
    63: (define-fun-rec
    64:   (par (a b)
    65:     (map
    66:        ((x (=> a b)) (y (List a))) (List b)
    67:        (match y
    68:          (case Nil (as Nil (List b)))
    69:          (case (Cons z xs) (as (Cons (@ x z) (map x xs)) (List b)))))))
    70: (define-fun-rec
    71:   (par (a b)
    72:     (foldl
    73:        ((f (=> b (=> a b))) (x b) (y (List a))) b
    74:        (match y
    75:          (case Nil x)
    76:          (case (Cons z xs) (foldl f (@ (@ f x) z) xs))))))
    77: (define-fun-rec
    78:   (par (a b)
    79:     (foldr
    80:        ((f (=> a (=> b b))) (y (List a)) (x b)) b
    81:        (match y
    82:          (case Nil x)
    83:          (case (Cons h t) (@ (@ f h) (foldr f t x)))))))
    84: (check-sat)