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step-c.rkt
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step-c.rkt
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#lang racket
(require redex/reduction-semantics)
(require "lang.rkt" "meta.rkt" "check.rkt" "util.rkt")
(provide c)
(test-suite test step-c)
(define c
(reduction-relation
λcρ #:domain (D σ)
(--> ((ANYCON ρ <= LAB_1 LAB_2 V_1 LAB_3 D) σ)
(D σ)
any/c-drop)
;; FLAT CONTRACTS
(--> ((FLAT ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ) ; FIXME: first V_1 was V-or-AE
((if (@ (-- (↓ (flat-check (FLAT ρ) V) ρ)) V Λ)
V_2
(blame LAB_1 LAB_3 V_1 (FLAT ρ) V))
σ)
(where V_2 (remember-contract V (FLAT ρ)))
(side-condition (not (redex-match λcρ ANYCON (term FLAT))))
flat-check)
;; HIGHER-ORDER CONTRACTS
(--> (((or/c FLAT HOC) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
((if (@ (-- (↓ (flat-check (FLAT ρ) V) (env))) V Λ)
V_2
(HOC ρ <= LAB_1 LAB_2 V_1 LAB_3 V))
σ)
(where V_2 (remember-contract V (FLAT ρ)))
or/c-hoc)
(--> (((and/c CON_0 CON_1) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
((CON_1 ρ <= LAB_1 LAB_2 V_1 LAB_3
(CON_0 ρ <= LAB_1 LAB_2 V_1 LAB_3 V))
σ)
(where HOC (and/c CON_0 CON_1))
and/c-hoc)
(--> (((rec/c X CON) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
(((unroll HOC) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
(where HOC (rec/c X CON))
unroll-HOC)
;; PAIR CONTRACTS
;; FIXME: forgets what's known about the pair.
(--> (((cons/c CON_0 CON_1) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
((@ (-- (↓ cons (env)))
(CON_0 ρ <= LAB_1 LAB_2 V_1 LAB_3 V_car)
(CON_1 ρ <= LAB_1 LAB_2 V_1 LAB_3 V_cdr)
Λ)
σ)
(where HOC (cons/c CON_0 CON_1))
(where #t (∈ #t (δ cons? V)))
(where (any_0 ... V_car any_1 ...) (δ car V))
(where (any_2 ... V_cdr any_3 ...) (δ cdr V))
check-cons-pass)
(--> (((cons/c CON_0 CON_1) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
((blame LAB_1 LAB_3 V_1 (HOC ρ) V) σ)
(where HOC (cons/c CON_0 CON_1))
(where #t (∈ #f (δ cons? V)))
check-cons-fail)
;; STRUCT CONTRACTS
;; FIXME: forgets what's known about the struct.
(--> (((struct/c X_m X_tag CON ...) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
((@ (-- (↓ (s-cons X_m X_tag ,(length (term (CON ...)))) (env)))
(CON ρ <= LAB_1 LAB_2 V_r LAB_3 V_1) ...
Λ)
σ)
(where HOC (struct/c X_m X_tag CON ...))
(where #t (∈ #t (δ (s-pred X_m X_tag) V)))
(where (natural_1 ...) ,(for/list ([i (length (term (CON ...)))]) i))
(where ((any_0 ... V_r any_1 ...) ...) ((δ (s-ref X_m X_tag natural_1) V) ...))
check-struct-pass)
(--> (((struct/c X_m X_tag CON ...) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
((blame LAB_1 LAB_3 V_1 (HOC ρ) V) σ)
(where HOC (struct/c X_m X_tag CON ...))
(where #t (∈ #f (δ (s-pred X_m X_tag) V)))
check-struct-fail)
;; PROCEDURE CONTRACTS
(--> ((@ ((CON_0 ..._1 --> (λ (X ..._1) CON_1)) ρ <= LAB_1 LAB_2 V_2 LAB_3 V) V_1 ..._1 LAB) σ)
((CON_1 ρ_1 ; lax
<= LAB_1 LAB_2 V_2 LAB_3
(@ (remember-contract V ((CON_0 ... -> (λ (X ...) CON_1)) ρ))
(CON_0 ρ <= LAB_2 LAB_1 V_1 LAB_3 V_1) ... Λ))
σ_1)
(where (ρ_1 σ_1) (bind-vars ρ σ (X V_1) ...))
blessed-β-dep)
(--> ((@ ((CON_0 ..._1 --> CON_1) ρ <= LAB_1 LAB_2 V_2 LAB_3 V) V_1 ..._1 LAB) σ)
((CON_1 ρ <= LAB_1 LAB_2 V_2 LAB_3
(@ (remember-contract V ((CON_0 ... -> CON_1) ρ))
(CON_0 ρ <= LAB_2 LAB_1 V_1 LAB_3 V_1) ... Λ))
σ)
blessed-β)
(--> ((@ ((CON_0 ..._1 CON_r -->* CON_1) ρ <= LAB_1 LAB_2 V_2 LAB_3 V) V_1 ..._1 V_r ... LAB) σ)
((CON_1 ρ <= LAB_1 LAB_2 V_2 LAB_3
(@* (remember-contract V ((CON_0 ... CON_r ->* CON_1) ρ))
(CON_0 ρ <= LAB_2 LAB_1 V_1 LAB_3 V_1)
...
(CON_r ρ <= LAB_2 LAB_1 V_ls LAB_3 V_ls) ;; This isn't right -- double turning into a list.
Λ))
σ)
(where V_ls (list->list-value (V_r ...)))
blessed-β*)
(--> ((@* V_1 ... V_r LAB) σ)
((@ V_1 ... V ... LAB) σ)
(where (V ...) (list-value->list V_r))
@*)
;; BLESSING
(--> ((CARROW ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
(((bless CARROW) ρ <= LAB_1 LAB_2 V_1 LAB_3
(remember-contract V ((pred procedure? Λ) (env))))
σ)
(side-condition (term (∈ #t (δ procedure? V))))
chk-fun-pass)
;; DAMNING
(--> (((CON_1 ... -> any) ρ <= LAB_1 LAB_2 V_1 LAB_3 V) σ)
((blame LAB_1 LAB_3 V_1 ((CON_1 ... -> any) (env)) V) σ)
(side-condition (term (∈ #f (δ procedure? V))))
chk-fun-fail-flat)))
(define-metafunction λcρ
bless : CARROW -> BARROW
[(bless (CON_1 ... -> any)) (CON_1 ... --> any)]
[(bless (CON_1 ... ->* any)) (CON_1 ... -->* any)])
(test
(test/σ--> c ; (nat? <= 5) -- provable
(term ((pred exact-nonnegative-integer? f)
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ 5 (env)))))
(term (if (@ (-- (↓ (flat-check ((pred exact-nonnegative-integer? f) (env))
(-- (↓ 5 (env))))
(env)))
(-- (↓ 5 (env)))
Λ)
(remember-contract (-- (↓ 5 (env)))
((pred exact-nonnegative-integer? f) (env)))
(blame f f (-- (↓ 0 (env)))
((pred exact-nonnegative-integer? f) (env))
(-- (↓ 5 (env)))))))
(test/σ--> c ; (prime? <= 5) -- runable
(term ((pred (prime? ^ h j) f)
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ 5 (env)))))
(term (if (@ (-- (↓ (flat-check ((pred (prime? ^ h j) f) (env))
(-- (↓ 5 (env))))
(env)))
(-- (↓ 5 (env)))
Λ)
(remember-contract (-- (↓ 5 (env)))
((pred (prime? ^ h j) f) (env)))
(blame f f (-- (↓ 0 (env)))
((pred (prime? ^ h j) f) (env))
(-- (↓ 5 (env)))))))
(test/σ--> c ; ((or/c prime? string?) <= 5)
(term ((or/c (pred (prime? ^ f g) f) (pred string? f))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ 5 (env)))))
(term (if (@ (-- (↓ (flat-check ((or/c (pred (prime? ^ f g) f)
(pred string? f))
(env))
(-- (↓ 5 (env))))
(env)))
(-- (↓ 5 (env)))
Λ)
(remember-contract (-- (↓ 5 (env))
((pred (prime? ^ f g) f) (env))))
(blame f f (-- (↓ 0 (env)))
((or/c (pred (prime? ^ f g) f) (pred string? f)) (env))
(-- (↓ 5 (env))))))
(term (if (@ (-- (↓ (flat-check ((or/c (pred (prime? ^ f g) f)
(pred string? f))
(env))
(-- (↓ 5 (env))))
(env)))
(-- (↓ 5 (env)))
Λ)
(remember-contract (-- (↓ 5 (env)))
((pred string? f) (env)))
(blame f f (-- (↓ 0 (env)))
((or/c (pred (prime? ^ f g) f) (pred string? f)) (env))
(-- (↓ 5 (env)))))))
(test/σ--> c ; ((-> string?) <= 5)
(term ((-> (pred string? †))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ 5 (env)))))
(term (blame f f (-- (↓ 0 (env)))
((-> (pred string? †)) (env))
(-- (↓ 5 (env))))))
(test/σ--> c ; ((or/c string? (-> string?)) <= (λ () "x")))
(term ((or/c (pred string? f)
(-> (pred string? f)))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ (λ () "x") (env)))))
(term (if (@ (-- (↓ (flat-check ((pred string? f) (env))
(-- (↓ (λ () "x") (env))))
(env)))
(-- (↓ (λ () "x") (env)))
Λ)
(remember-contract (-- (↓ (λ () "x") (env)))
((pred string? f) (env)))
((-> (pred string? f))
(env) <= f g
(-- (↓ 0 (env))) f
(-- (↓ (λ () "x") (env)))))))
(test/σ--> c ; ((and/c (-> string?) (-> string?)) <= (λ () "x")))
(term ((and/c (-> (pred string? f))
(-> (pred string? f)))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ (λ () "x") (env)))))
(term ((-> (pred string? f))
(env) <= f g (-- (↓ 0 (env))) f
((-> (pred string? f))
(env) <= f g
(-- (↓ 0 (env))) f
(-- (↓ (λ () "x") (env)))))))
(test/σ--> c ; ((cons/c (-> string?) (-> string?)) <= (cons (λ () "x") (λ () "y")))
(term ((cons/c (-> (pred string? f))
(-> (pred string? g)))
(env) <= f g (-- (↓ 0 (env))) f
(-- (cons (-- (↓ (λ () "x") (env)))
(-- (↓ (λ () "y") (env)))))))
(term (@ (-- (↓ cons (env)))
((-> (pred string? f))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ (λ () "x") (env))))
((-> (pred string? g))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ (λ () "y") (env))))
Λ)))
(test/σ--> c ; ((rec/c x (or/c string? (-> x)) <= "x")
(term ((rec/c x (or/c (pred string? f) (-> x)))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ "x" (env)))))
(term ((or/c (pred string? f)
(-> (rec/c x (or/c (pred string? f) (-> x)))))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ "x" (env))))))
(test/σ--> c ; ((cons/c (-> string?) (-> string?)) <= 3)
(term ((cons/c (-> (pred string? f))
(-> (pred string? g)))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ 3 (env)))))
(term (blame f f (-- (↓ 0 (env)))
((cons/c (-> (pred string? f))
(-> (pred string? g)))
(env))
(-- (↓ 3 (env))))))
(test--> c ; (@ ((string? --> (λ (x) (pred (λ (y) x)))) <= (λ (x) x)) "q")
(term ((@ (((pred string? g) --> (λ (x) (pred (λ (y) x) f)))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ (λ (x) x) (env))))
(-- (↓ "q" (env)))
†)
(sto)))
(redex-let
λcρ
([(ρ σ) (term (bind-vars (env) (sto) (x (-- (↓ "q" (env))))))])
(term (((pred (λ (y) x) f) ρ
<= f g (-- (↓ 0 (env))) f
(@ (-- (↓ (λ (x) x) (env))
(((pred string? g) -> (λ (x) (pred (λ (y) x) f))) (env)))
((pred string? g)
(env) <= g f (-- (↓ "q" (env))) f
(-- (↓ "q" (env))))
Λ))
σ))))
(test/σ--> c ; (@ ((string? --> string?) <= (λ () "x")))
(term (@ (((pred string? g) --> (pred string? f))
(env) <= f g (-- (↓ 0 (env))) f (-- (↓ (λ (x) x) (env))))
(-- (↓ "x" (env)))
†))
(term ((pred string? f)
(env) <= f g (-- (↓ 0 (env))) f
(@ (-- (↓ (λ (x) x) (env))
(((pred string? g) -> (pred string? f)) (env)))
((pred string? g)
(env) <= g f (-- (↓ "x" (env))) f
(-- (↓ "x" (env))))
Λ))))
(test/σ--> c ; ((-> string) <= (λ () 1))
(term ((-> (pred string? f))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ (λ () 1) (env)))))
(term ((--> (pred string? f))
(env) <= f g (-- (↓ 0 (env))) f
(-- (↓ (λ () 1) (env)))))))