diff options
Diffstat (limited to 'stlc-ref.rkt')
| -rw-r--r-- | stlc-ref.rkt | 140 |
1 files changed, 101 insertions, 39 deletions
diff --git a/stlc-ref.rkt b/stlc-ref.rkt index 29f4527..6194728 100644 --- a/stlc-ref.rkt +++ b/stlc-ref.rkt @@ -1,52 +1,114 @@ #lang racket (require "lib.rkt") -;; the simply-typed lambda calculus with references +;; The Simply-Typed Lambda Calculus with references -(define (value? val) - (or (number? val) (string? val) (equal? 'sole val) (equal? 'true val) (equal? 'false val))) - -;; (interpret Expr Table[Sym, Expr]): Value -(define (interpret expr [ctx #hash()] [heap #hash()]) (interpret- (strip expr) ctx heap)) +;; (interpret Expr Table[Sym, Expr] Table[Sym, Expr]): Value +(define (interpret expr [ctx #hash()] [heap (make-hash)]) + (interpret- (strip (desugar expr)) ctx heap)) (define (interpret- expr ctx heap) + ; (print (format "interpret: ~a" (fmt expr))) + (match expr + ['sole 'sole] + [n #:when (natural? n) n] + [r #:when (dict-has-key? heap r) r] + [x #:when (dict-has-key? ctx x) (dict-ref ctx x)] + + [`(new ,e) + (let ([r (gensym)]) + (dict-set! heap r e) r)] + [`(! ,e) + (let ([r (interpret- e ctx heap)]) + (if (dict-has-key? heap r) + (interpret- (dict-ref heap r) ctx heap) + (err (format "attempting to deref unknown reference ~a" r))))] + [`(set ,e1 ,e2) + (let ([r (interpret- e1 ctx heap)]) + (if (dict-has-key? heap r) (dict-set! heap r (interpret- e2 ctx heap)) + (err (format "attempting to update unknown reference ~a" r)))) + 'sole] + + [`(λ ,x ,e) `(λ ,x ,e ,ctx)] + [`(λ ,x ,e ,env) `(λ ,x ,e ,env)] ; ??? + [`(,e1 ,e2) + (match (interpret- e1 ctx heap) + [`(λ ,x ,e1 ,env) + (interpret- e1 (dict-set env x (interpret- e2 ctx heap)) heap)] + [e1 (err (format "attempting to interpret arg ~a applied to unknown expression ~a" e2 e1))])] + + [e (err (format "attempting to interpret 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)] + + [(`(new ,e) `(Ref ,t)) (check- e t Γ)] + [(`(! ,e) t) (check- e `(Ref ,t) Γ)] + [(`(set ,e1 ,e2) 'Unit) + (match (infer- e1 Γ) + [`(Ref ,t) (check- e2 t Γ)] + [t (err (format "attempting to update non-reference ~a: ~a" e1 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 (err (format "expected → type on application body, got ~a" t))])] + + [(e t) (err (format "checking an unknown expression ~a with type ~a" e t))])) + +;; (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 - ; the simply-typed lambda calculus - [val #:when (value? val) val] ; values. strings, bools, ints, whatever - [val #:when (symbol? val) (cond ; identifiers. - [(dict-has-key? ctx val) (interpret- (dict-ref ctx val) ctx heap)] - [(dict-has-key? heap val) (interpret- (dict-ref heap val) ctx heap)] - [else val])] ; note: we do not distinguish between bound/unbound idents - [`(λ ,id ,body) `(λ ,id ,body ,ctx)] ; first class functions. returns the λ + ctx - [`(λ ,id ,body ,env) `(λ ,id ,body ,env)] - - ; references - [`(ref ,id) `(ref ,id)] ; refs. pointer to immutable bound value - [`(deref ,id) ; deref. accesses a stored reference from the heap - #:when (dict-has-key? heap id) - (interpret- (dict-ref heap id) ctx heap)] - [`(set ,id ,expr ,body) ; set. arbitrarily updates a reference to point elsewhere - ; note: MUST resolve the binding before applying!! !! - (interpret- body ctx (dict-set heap id (interpret- expr ctx heap)))] - - ; function application - [`(,body ,arg) - (match (interpret- body ctx heap) - [`(λ ,id ,body) - (interpret- body (dict-set ctx id (interpret- arg ctx heap)) heap)] - [`(λ ,id ,body ,env) - (interpret- body (dict-set env id (interpret- arg ctx heap)) heap)] - [expr `(,expr ,(interpret- arg ctx heap))])] - - ; desugaring and error handling - [`(let ,id ,expr ,body) (interpret- `((λ ,id ,body) ,expr) ctx heap)] - [`(deref ,id) (err (format "attempting to deref unknown reference ~a" id))] - [expr (err (format "interpreting an unknown expression ~a" expr))])) + ['sole 'Unit] + [n #:when (natural? n) 'Nat] + [x #:when (dict-has-key? Γ x) + (dict-ref Γ x)] + + [`(new ,e) `(Ref ,(infer- e Γ))] + [`(! ,e) + (match (infer- e Γ) + [`(Ref ,t) t] + [t (err "attempting to deref term not of Ref type!")])] + [`(set ,e1 ,e2) + (match (infer- e1 Γ) + [`(Ref ,t) + (if (check- e2 t Γ) 'Unit + (err (format "attempting to update ~a: ~a with term ~a: ~a of differing type" + e1 t e2 (infer- e2 Γ))))] + [t (err (format "attempting to update non-reference ~a: ~a" e1 t))])] + + [`(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))])) + +(provide interpret check infer) ; simple diverging program in STLC-ref ; https://www.youtube.com/watch?v=XNgE8kBfSz8 +#; (interpret ' (let id (: (→ Nat Nat)) (λ x x) - (let r (: (Ref (→ Nat Nat))) (ref id) - (let f (: (→ Nat Nat)) (λ x ((deref r) x)) + (let r (: (Ref (→ Nat Nat))) (new id) + (let f (: (→ Nat Nat)) (λ x ((! r) x)) (set r f (f 0)))))) |