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+#lang racket
+(require "../lib.rkt")
+(provide (all-defined-out))
+
+;; The Simply-Typed Lambda Calculus
+
+;; Checks an expression for syntactic well-formedness.
+(define (stlc/expr? expr)
+  (match expr
+    [x #:when (symbol? x) #t]
+    [`(,e1 ,e2) (and (stlc/expr? e1) (stlc/expr? e2))]
+    [`(λ (,x : ,t) ,e) (and (symbol? x) (stlc/type? t) (stlc/expr? e))]
+    [_ #f]))
+
+;; Checks a type for syntactic well-formedness.
+(define (stlc/type? type)
+  (match type
+    [t #:when (symbol? t) #t]
+    [`(,t1 → ,t2) (and (stlc/type? t1) (stlc/type? t2))]
+    [_ #f]))
+
+;; Checks a value for syntactic well-formedness.
+(define (stlc/value? value)
+  (match value
+    [x #:when (symbol? x) #t]
+    [`(,v1 ,v2) (and (stlc/value? v1) (stlc/value? v2))]
+    [`(λ ,x ,e ,env) (and (symbol? x) (stlc/expr? e) (dict? env))]
+    [_ #f]))
+
+;; Interprets an expression down to a value, in a given context.
+(define/contract (interpret expr [Γ #hash()])
+  (->* (stlc/expr?) (dict?) stlc/value?)
+  (match expr
+    [x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
+    [f #:when (symbol? f) f]
+    [`(λ (,x : ,t) ,e) `(λ ,x ,e ,Γ)]
+    [`(,e1 ,e2)
+      (match (interpret e1 Γ)
+        [`(λ ,x ,e ,env) (interpret e (dict-set env x (interpret e2 Γ)))]
+        [e `(,e ,(interpret e2 Γ))])]))
+
+;; Checks an expression against some type, in a given context.
+(define/contract (check expr with [Γ #hash()])
+  (->* (stlc/expr? stlc/type?) (dict?) boolean?)
+  (match expr
+    [`(λ (,x : ,t) ,e)
+      (match with
+        [`(,t1 → ,t2)
+          (and (equal? t t1) (check e t2 (dict-set Γ x t)))]
+        [_ #f])]
+    [_ (equal? with (infer with Γ))]))
+
+;; Infers a type from some expression, in a given context.
+(define/contract (infer expr [Γ #hash()])
+  (->* (stlc/expr?) (dict?) stlc/type?)
+  (match expr
+    [x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
+    [f #:when (symbol? f)
+      (err (format "attempting to infer type of free variable ~a" f))]
+    [`(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))])]))