implement the standard simply-typed lambda calculus

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
@@ -0,0 +1,45 @@
+#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)