stlc-let: reimplement

1 files changed, 45 insertions, 90 deletions

diff --git a/stlc-let.rkt b/stlc-let.rkt
index 23f697c..ab42711 100644
--- a/stlc-let.rkt
+++ b/stlc-let.rkt
@@ -1,106 +1,61 @@
 #lang racket
 (require "lib.rkt")
 
-;; The Simply-Typed Lambda Calculus, with let sugar
+;; The Simply-Typed Lambda Calculus, with let sugar and some base types
 
-(define (value? val) (or (number? val) (string? val) (symbol? val)))
-
-; note: no function overloading ;_;
 ;;      (interpret Expr Table[Sym, Expr]): Value
-(define (interpret expr) (interpret- (strip expr) '()))
+(define (interpret expr [ctx #hash()])
+  (interpret- (strip (desugar expr)) ctx))
 (define (interpret- expr ctx)
   (match expr
-    [`(λ ,id ,body) `(λ ,id ,body ,ctx)]
-    [`(λ ,id ,body ,env) `(λ ,id ,body ,env)]
-    [`((λ ,id ,body) ,arg)
-      (interpret- body (dict-set ctx id (interpret- arg ctx)))]
-    [`((λ ,id ,body ,env) ,arg)
-      (interpret- body (dict-set env id (interpret- arg ctx)))]
-    [`(,id ,arg) #:when (dict-has-key? ctx id)
-      (interpret- `(,(interpret- (dict-ref ctx id) ctx) ,arg) ctx)]
-    [`(,body ,arg) ; todo: how to recognize an irreducible term? this is kinda cheating, i think
-      (let ([reduced (interpret- body ctx)])
-        (if (equal? body reduced)
-          `(,reduced ,(interpret- arg ctx))
-          (interpret- `(,reduced ,arg) ctx)))]
-    [id #:when (dict-has-key? ctx id)
-      (interpret- (dict-ref ctx id) ctx)]
-    [val #:when (value? val) val]
-    [`(let ,id ,expr ,body) (interpret- `((λ ,id ,body) ,expr) ctx)]
-    [expr (err (format "interpreting an unknown expression ~a" expr))]))
+    ['sole 'sole]
+    [n #:when (natural? n) n]
+    [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 [ctx #hash()])
-  (match expr
-    [val #:when (or (value? val) (symbol? val))
-      (equiv with (infer val ctx))]
-    [`(λ ,id ,body)
-      (match with
-        [`(→ ,a ,b) (check body b (dict-set ctx id a))]
-        [_ (err (format "expected → type to check λ with but received ~a" with))])]
-    [`((λ ,id ,body) ,arg)
-      (note "unable to check arg type from λ lacking annotation")
-      (check body with ctx)] ; hmm
-    [`(λ ,id (: ,type) ,body)
-      (and (check `(λ ,id ,body) type ctx) (equiv with type))]
-    [`((λ ,id (: (→ ,a ,b)) ,body) ,arg)
-      (and (check arg a ctx) (equiv with b)
-        (check `(λ ,id ,body) `(→ ,a ,b) (dict-set ctx id a)))]
-    ; desugaring and error handling
-    [`(let ,id ,expr ,body)
-      (check `((λ ,id ,body) ,expr) with ctx)]
-    [`(let ,id (: ,type) ,expr ,body)
-      (check `((λ ,id (: ,type) ,body) ,expr) with ctx)]
-    [`(λ ,id (: ,type) ,body)
-      (err (format "expected → type on λ but received ~a" type))]
-    [`((λ ,id (: ,type) ,body) ,arg)
-      (err (format "expected → type on λ but received ~a" type))]
-    [expr (err (format "inferring an unknown expression ~a" expr))]))
-
-;;      (equiv Type Type): Bool
-(define (equiv a b)
-  (match* (a b)
-    [[`(→ ,a ,c) `(→ ,b ,d)] (and (equiv a b) (equiv c d))]
-    [[a b] (equal? a b)]))
-
-;;      (infer Expr Table[Sym, Type]) → Type
-(define (infer expr [ctx #hash()])
+(define (check expr with [Γ #hash()])
+  (check- (desugar expr) with Γ))
+(define (check- expr 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)]
+    [(`(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()])
+  (infer- (desugar expr) Γ))
+(define (infer- expr Γ)
   (match expr
-    [val #:when (string? val) 'Str]
-    [val #:when (and (number? val) (>= val 0)) 'Nat]
-    [val #:when (symbol? val) (dict-get ctx val)]
-    [`((λ ,id ,body) ,arg)
-      (infer body (dict-set ctx id (infer arg ctx)))]
-    [`(λ ,id (: (→ ,a ,b)) ,body)
-      (note "unable to infer arg type from λ lacking annotation")
-      (if (check body b (dict-set ctx id a))
-        `(→ ,a ,b)
-        (err (format "inferred return type of ~a does not match annotated type ~a"
-          `(λ ,id ,body) b)))]
-    [`((λ ,id (: (→ ,a ,b)) ,body) ,arg)
-      (if (check `((λ ,id ,body) ,arg) `(→ ,a ,b) ctx)
-        b
-        (err (format "inferred type of ~a does not match annotated type ~a"
-          `((λ ,id ,body) ,arg) `(: (→ ,a ,b)))))]
-    [`(let ,id ,expr ,body) ; desugaring
-      (infer `((λ ,id ,expr) ,body) ctx)]
-    [`(let ,id (: ,type) ,expr ,body)
-      (infer `((λ ,id (: ,type) ,expr) ,body) ctx)]
-    [`(λ ,id ,body) ; error handling
-      (err "unable to infer type from λ lacking annotation")] ; hmm
-    [`(λ ,id (: ,type) ,body)
-      (err (format "expected → type on λ but received ~a" type))]
-    [`((λ ,id (: ,type) ,body) ,arg)
-      (err (format "expected → type on λ but received ~a" type))]
-    [expr (err (format "inferring an unknown expression ~a" expr))]))
-
-(define (dict-get dict key)
-  (dict-ref dict key (λ () (err (format "identifier ~a not found" key)))))
+    ['sole 'Unit]
+    [n #:when (natural? n) 'Nat]
+    [`(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)
 
 (require rackunit)
 (check-equal? (interpret '(λ x x)) '(λ x x #hash()))
 (check-equal? (interpret '((λ a a) (x y))) '(x y))
 (check-equal? (interpret '((λ a (x y)) (λ z z))) '(x y))
 (check-equal? (interpret '((λ a (a y)) x)) '(x y))
-
-; todo: inference tests