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Diffstat (limited to 'stlc-rec.rkt')
-rw-r--r-- | stlc-rec.rkt | 94 |
1 files changed, 94 insertions, 0 deletions
diff --git a/stlc-rec.rkt b/stlc-rec.rkt new file mode 100644 index 0000000..24bbb8f --- /dev/null +++ b/stlc-rec.rkt @@ -0,0 +1,94 @@ +#lang racket +(require "lib.rkt") + +;; The Simply-Typed Lambda Calculus with iso-recursive types + +; Γ ⊢ e: [x ↦ μx.t] t +; ------------------------ +; Γ ⊢ fold [μx.t] e: μx.t + +; Γ ⊢ e: μx.t +; ----------------------------------- +; Γ ⊢ unfold [μx.t] e: [x ↦ μx.t] t + +;; (interpret Expr Table[Sym, Expr]): Value +(define (interpret expr [ctx #hash()]) + (interpret- (strip (desugar expr)) ctx)) +(define (interpret- expr ctx) + (match expr + ['sole 'sole] + [n #:when (natural? n) n] + [x #:when (dict-has-key? ctx x) (dict-ref ctx x)] + + [`(fold ,t ,e) `(fold ,t ,(interpret- e))] + [`(unfold ,t ,e) `(unfold ,t ,(interpret- e))] + + [`(λ ,x ,e) `(λ ,x ,e ,ctx)] + [`(,e1 ,e2) + (match (interpret- e1 ctx) + [`(λ ,x ,e ,env) + (interpret- e (dict-set env x (interpret- e2 ctx)))] + [e (err (format "applying arg ~a to unknown expression ~a" e2 e))])] + + [e (err (format "interpreting an unknown expression ~a" e))])) + +;; (check Expr Type Table[Sym, Type]): Bool +(define (check expr with [Γ #hash()]) + (check- (desugar expr) with Γ)) +(define (check- expr with Γ) + ; (print (format "check: ~a" (fmt expr))) + (match* (expr with) + [('sole 'Unit) #t] + [(n 'Nat) #:when (natural? n) #t] + [(x _) #:when (dict-has-key? Γ x) + (equal? (dict-ref Γ x) with)] + + [(`(fold (μ ,x ,t) ,e) `(μ ,x ,t)) + (check- e t (dict-set Γ x `(μ ,x ,t)))] + [(`(unfold (μ ,x ,t) ,e) with) + (and (check- e `(μ ,x ,t) Γ) + (equiv? with t #hash() #hash((x . `(μ ,x ,t)))))] + + [(`(λ ,x (: ,t) ,e) `(→ ,t1 ,t2)) + (and (equal? t t1) (check- e t2 (dict-set Γ x t1)))] + + [(`(,e1 ,e2) t) + (match (infer- e1 Γ) + [`(→ ,t1 ,t2) + (and (equal? t2 t) (equal? t1 (infer- e2 Γ)))] + [t #f])] + + [(e t) #f])) + +;; (infer Expr Table[Sym, Type]): Type +(define (infer expr [Γ #hash()]) + (infer- (desugar expr) Γ)) +(define (infer- expr Γ) + ; (print (format "infer: ~a" (fmt expr))) + (match expr + ['sole 'Unit] + [n #:when (natural? n) 'Nat] + [b #:when (boolean? b) 'Bool] + [x #:when (dict-has-key? Γ x) + (dict-ref Γ x)] + + [`(fold (μ ,x ,t) ,e) + (if (check- e t (dict-set Γ x `(μ ,x ,t))) `(μ ,x ,t) + (err (format ("expected ~a to be of type ~a, got ~a" + e t (infer e (dict-set Γ x `(μ ,x ,t)))))))] + [`(unfold (μ ,x ,t) ,e) + (if (check- e `(μ ,x ,t)) (α-convert t #hash((x . `(μ ,x ,t)))) + (err (format ("expected ~a to be of type ~a, got ~a" + e `(μ ,x ,t) (infer- e Γ)))))] + + [`(λ ,x (: ,t) ,e) + `(→ ,t ,(infer- e (dict-set Γ x t)))] + + [`(,e1 ,e2) + (match (infer- e1 Γ) + [`(→ ,t1 ,t2) + (if (check- e2 t1 Γ) t2 + (err (format "inferred argument type ~a does not match arg ~a" t1 e2)))] + [t (err (format "expected → type on application body, got ~a" t))])] + + [e (err (format "attempting to infer an unknown expression ~a" e))])) |