Created
February 16, 2015 02:47
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(declare-datatypes () ( | |
(Ty (base (idx Int)) | |
(arrow (src Ty) (tar Ty)) | |
(prod (c1 Ty) (c2 Ty)) | |
))) | |
(declare-datatypes () ( | |
(Expr exprA | |
exprAtoBtoC | |
exprB | |
exprAtoCtoD | |
(ap (ap1 Expr) (ap2 Expr)) | |
) | |
)) | |
(declare-fun hastype (Expr Ty) Bool) | |
(assert (forall ((a Expr) (b Expr) (t1 Ty) (t2 Ty)) | |
(=> (and (hastype a (arrow t1 t2)) (hastype b t1)) | |
(hastype (ap a b) t2)))) | |
(define-fun A () Ty (base 0)) | |
(define-fun B () Ty (base 1)) | |
(define-fun C () Ty (base 2)) | |
(define-fun D () Ty (base 3)) | |
(assert (hastype exprAtoBtoC (arrow A (arrow B C)))) | |
(assert (hastype exprA A)) | |
(assert (hastype exprB B)) | |
(assert (hastype exprAtoCtoD (arrow A (arrow C D)))) | |
(define-fun is-appl ((a Expr) (t Ty)) Bool | |
(exists ((s Ty) (f Expr) (b Expr)) | |
(and (hastype f (arrow s t)) | |
(hastype b s) | |
(= a (ap f b)) | |
) | |
) | |
) | |
(define-fun disjointness ((e Expr) (t Ty)) Bool | |
(forall ((e1 Expr)) | |
(=> (hastype e1 t) | |
(or (= e1 e) (is-appl e1 t)) | |
) | |
) | |
) | |
(assert (disjointness exprA A)) | |
(assert (disjointness exprB B)) | |
(assert (disjointness exprAtoBtoC (arrow A (arrow B C)))) | |
(assert (disjointness exprAtoCtoD (arrow A (arrow C D)))) | |
(assert (forall ((a Expr) (t1 Ty) (t2 Ty)) | |
(=> (and (hastype a t1) (hastype a t2)) (= t1 t2)) | |
)) | |
(declare-const z Expr) | |
(assert (hastype z D)) | |
(check-sat) | |
(get-model) |
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