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authorJJ2024-06-15 01:25:24 +0000
committerJJ2024-06-15 02:24:01 +0000
commite0b3fb41426ccebcb6e9c3556a90b276c65f9867 (patch)
tree3ac854360aba43c30d3a7f010354f9cde7def2c9
parent694abf3dfe03f801acd5c3f542de5fe0893b9206 (diff)
implement the standard simply-typed lambda calculus
-rw-r--r--stlc.rkt45
1 files changed, 45 insertions, 0 deletions
diff --git a/stlc.rkt b/stlc.rkt
new file mode 100644
index 0000000..bf65b73
--- /dev/null
+++ b/stlc.rkt
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+#lang racket
+(require "lib.rkt")
+
+;; The Simply-Typed Lambda Calculus
+
+;; (interpret Expr Table[Sym, Expr]): Value
+(define (interpret expr [ctx #hash()])
+ (interpret- (strip expr) ctx))
+(define (interpret- expr ctx)
+ (match expr
+ [x #:when (dict-has-key? ctx x) (dict-ref ctx x)]
+ [`(λ ,x ,e) `(λ ,x ,e ,ctx)]
+ [`(,e1 ,e2)
+ (match (interpret- e1 ctx)
+ [`(λ ,x ,e1 ,env) (interpret- e1 (dict-set env x (interpret- e2 ctx)))]
+ [e1 `(,e1 ,(interpret- e2 ctx))])]
+ [e e]))
+
+;; (check Expr Type Table[Sym, Type]): Bool
+(define (check expr with [Γ #hash()])
+ (match* (expr with)
+ [(x _) #:when (dict-has-key? Γ x)
+ (equal? (dict-ref Γ x) with)]
+ [(`(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()])
+ (match expr
+ [`(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)