1 files changed, 86 insertions, 0 deletions
diff --git a/simple/fix.rkt b/simple/fix.rkt
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+++ b/simple/fix.rkt
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+#lang racket
+(require "../lib.rkt")
+(require (only-in "stlc.rkt" stlc/type?))
+
+;; The Simply-Typed Lambda Calculus, with general recursion
+
+;; Checks an expression for syntactic well-formedness.
+(define/contract (stlc-fix/expr? expr)
+  (-> any/c boolean?)
+  (match expr
+    [x #:when (symbol? x) #t]
+    [`(fix ,e) (stlc-fix/expr? e)]
+    [`(λ (,x : ,t) ,e) (and (symbol? x) (stlc/type? t) (stlc-fix/expr? e))]
+    [`(,e1 ,e2) (and (stlc-fix/expr? e1) (stlc-fix/expr? e2))]
+    [_ #f]))
+
+;; Checks a value for syntactic well-formedness.
+(define (stlc-fix/value? value)
+  (match value
+    [x #:when (symbol? x) #t]
+    [`(,v1 ,v2) (and (stlc-fix/value? v1) (stlc-fix/value? v2))]
+    [`(λ ,x ,e ,env) (and (symbol? x) (stlc-fix/expr? e) (dict? env))]
+    [_ #f]))
+
+;; Interprets an expression down to a value, in a given context.
+(define (interpret expr)
+  (interpret/core (desugar expr) #hash()))
+(define/contract (interpret/core expr Γ)
+  (-> stlc-fix/expr? dict? stlc-fix/value?)
+  (match expr
+    ['sole 'sole]
+    [x #:when (dict-has-key? Γ x) (dict-ref Γ x)]
+    [x #:when (symbol? x) x]
+
+    [`(fix ,e)
+      (match (interpret/core e Γ)
+        [`(λ ,x ,e ,env)
+          ; FIXME: unsure what should be Γ and what should be env
+          (interpret/core e (dict-set env x `(fix (λ ,x ,e ,Γ))))]
+        [e (err (format "applying fix to unknown expression ~a" e))])]
+
+    [`(λ (,id : ,t) ,body) `(λ ,id ,body ,Γ)]
+    [`(,body ,arg)
+      (match (interpret/core body Γ)
+        [`(λ ,id ,body ,env)
+          (interpret/core body (dict-set env id (interpret/core arg Γ)))]
+        [e (err (format "applying arg ~a to unknown expression ~a" arg e))])]))
+
+;; Checks an expression against some type, in a given context.
+(define (check expr with)
+  (check/core (desugar expr) with #hash()))
+(define/contract (check/core expr with Γ) ; FIXME
+  (-> stlc-fix/expr? stlc/type? dict? boolean?)
+  (let ([with (if (dict-has-key? Γ with) (dict-ref Γ with) with)])
+  (match expr
+    [`(fix ,e)
+      (check/core (infer/core e) `(,with → ,with) Γ)]
+    [`(λ (,x : ,t) ,e)
+      (match with
+        [`(,t1 → ,t2)
+          (and (equal? t1 t)
+            (check/core e t2 (dict-set Γ x t1)))]
+        [_ #f])]
+    [_ (equal? (infer/core expr Γ) with)])))
+
+;; Infers a type from some expression, in a given context.
+(define (infer expr)
+  (infer/core (desugar expr) #hash()))
+(define/contract (infer/core expr Γ)
+  (-> stlc-fix/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))]
+    [`(fix ,e)
+      (match (infer/core e Γ)
+        [`(,t → ,t) t]
+        [t (err (format "fix expects a term of type t → t, got ~a" t))])]
+    [`(λ (,x : ,t) ,e)
+      `(,t → ,(infer/core e (dict-set Γ x t)))]
+    [`(,e1 ,e2)
+      (match (infer/core e1 Γ)
+        [`(,t1 → ,t2)
+          (if (check/core 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))])]))