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| -rw-r--r-- | README.md | 2 | ||||
| -rw-r--r-- | stlc-imp.rkt | 110 |
2 files changed, 111 insertions, 1 deletions
@@ -13,7 +13,7 @@ For an introduction, see [*Explaining Lisp's quoting without getting tangled*](q * [ ] STLC-rec: Recursive types. Also sums, products, ascryption. * [x] STLC-ref: References. * [x] STLC-pred: Higher-order *predicative* references. Terminating. -* [ ] STLC-imp: Higher-order *impredicative* references. Terminating. +* [x] STLC-imp: Higher-order *impredicative* references. Terminating. * [ ] STLC-rc: References with reference counting. * [ ] STLC-gc: References with a tracing garbage collector. * [ ] STLC-own: References with first-class ownership, Rust-style. diff --git a/stlc-imp.rkt b/stlc-imp.rkt new file mode 100644 index 0000000..4d16188 --- /dev/null +++ b/stlc-imp.rkt @@ -0,0 +1,110 @@ +#lang racket +(require "lib.rkt") + +;; The Simply-Typed Lambda Calculus with higher-order *impredicative* references + +(require (only-in "stlc-ref.rkt" interpret)) + +;; (check Expr Type Table[Sym, Type]): Bool +(define (check expr with [Γ #hash()]) + (check- (desugar expr) with Γ)) +(define (check- expr with Γ) + ; (check- expr (dict-ref Γ with) Γ) + (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 #f])] + + [(`(λ ,x (: ,t) ,e) `(→ ,k ,t1 ,t2)) + (and + (equal? t t1) + (> k (max-level e (dict-set Γ x t1) t1 t2)) ; KNOB + (check- e t2 (dict-set Γ x t1)))] + [(`(,e1 ,e2) t) + (match (infer- e1 Γ) + [`(→ ,k ,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] + [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 (: ,t1) ,e) + (let ([t2 (infer- e (dict-set Γ x t1))]) + (let ([k (+ 1 (max-level e (dict-set Γ x t1) t1 t2))]) ; KNOB + `(→ ,k ,t1 ,t2)))] + [`(,e1 ,e2) + (match (infer- e1 Γ) + [`(→ ,k ,t1 ,t2) + (if (check- e2 t1 Γ) t2 + (err (format "inferred argument type ~a does not match arg ~a of type ~a" t1 e2 (infer- e2 Γ))))] + [t (err (format "expected → type on application body, got ~a" t))])] + + [e (err (format "attempting to infer an unknown expression ~a" e))])) + +;; (max-level Table[Sym, Type] Expr Type Type): Natural +(define (max-level e Γ t1 t2) + (max + (level-type t1) + (level-type t2) + (level-body e Γ))) + +;; (level-type Type): Natural +(define (level-type t) + (match t + ['Unit 0] + ['Nat 0] + [`(→ ,k ,t1 ,t2) + (if (or (< k (level-type t1)) (< k (level-type t2))) + (err (format "annotated level ~a is less than inferred levels of ~a and ~a!" + k t1 t2)) + k)] + [`(Ref ,t) + (let ([k (level-type t)]) + (if (zero? k) 0 ((+ 1 k))))] ; KNOB + [t (err (format "attempting to infer the level of unknown type ~a" t))])) + +;; (level-body Expr Table[Sym, Type]): Natural +(define (level-body e Γ) + (match e + ['sole 0] + [n #:when (natural? n) 0] + [x #:when (dict-has-key? Γ x) + (level-type (dict-ref Γ x))] + [`(new ,e) (level-body e Γ)] + [`(! ,e) (level-body e Γ)] + [`(set ,e1 ,e2) (max (level-body e1 Γ) (level-body e2 Γ))] + [`(λ ,x (: ,t) ,e) (level-body e (dict-set Γ x t))] ; todo: should be 0? + [`(,e1 ,e2) (max (level-body e1 Γ) (level-body e2 Γ))])) |