aboutsummaryrefslogtreecommitdiff
path: root/stlc-rec.rkt
diff options
context:
space:
mode:
Diffstat (limited to 'stlc-rec.rkt')
-rw-r--r--stlc-rec.rkt94
1 files changed, 94 insertions, 0 deletions
diff --git a/stlc-rec.rkt b/stlc-rec.rkt
new file mode 100644
index 0000000..24bbb8f
--- /dev/null
+++ b/stlc-rec.rkt
@@ -0,0 +1,94 @@
+#lang racket
+(require "lib.rkt")
+
+;; The Simply-Typed Lambda Calculus with iso-recursive types
+
+; Γ ⊢ e: [x ↦ μx.t] t
+; ------------------------
+; Γ ⊢ fold [μx.t] e: μx.t
+
+; Γ ⊢ e: μx.t
+; -----------------------------------
+; Γ ⊢ unfold [μx.t] e: [x ↦ μx.t] t
+
+;; (interpret Expr Table[Sym, Expr]): Value
+(define (interpret expr [ctx #hash()])
+ (interpret- (strip (desugar expr)) ctx))
+(define (interpret- expr ctx)
+ (match expr
+ ['sole 'sole]
+ [n #:when (natural? n) n]
+ [x #:when (dict-has-key? ctx x) (dict-ref ctx x)]
+
+ [`(fold ,t ,e) `(fold ,t ,(interpret- e))]
+ [`(unfold ,t ,e) `(unfold ,t ,(interpret- e))]
+
+ [`(λ ,x ,e) `(λ ,x ,e ,ctx)]
+ [`(,e1 ,e2)
+ (match (interpret- e1 ctx)
+ [`(λ ,x ,e ,env)
+ (interpret- e (dict-set env x (interpret- e2 ctx)))]
+ [e (err (format "applying arg ~a to unknown expression ~a" e2 e))])]
+
+ [e (err (format "interpreting an unknown expression ~a" e))]))
+
+;; (check Expr Type Table[Sym, Type]): Bool
+(define (check expr with [Γ #hash()])
+ (check- (desugar expr) with Γ))
+(define (check- expr with Γ)
+ ; (print (format "check: ~a" (fmt expr)))
+ (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)]
+
+ [(`(fold (μ ,x ,t) ,e) `(μ ,x ,t))
+ (check- e t (dict-set Γ x `(μ ,x ,t)))]
+ [(`(unfold (μ ,x ,t) ,e) with)
+ (and (check- e `(μ ,x ,t) Γ)
+ (equiv? with t #hash() #hash((x . `(μ ,x ,t)))))]
+
+ [(`(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 #f])]
+
+ [(e t) #f]))
+
+;; (infer Expr Table[Sym, Type]): Type
+(define (infer expr [Γ #hash()])
+ (infer- (desugar expr) Γ))
+(define (infer- expr Γ)
+ ; (print (format "infer: ~a" (fmt expr)))
+ (match expr
+ ['sole 'Unit]
+ [n #:when (natural? n) 'Nat]
+ [b #:when (boolean? b) 'Bool]
+ [x #:when (dict-has-key? Γ x)
+ (dict-ref Γ x)]
+
+ [`(fold (μ ,x ,t) ,e)
+ (if (check- e t (dict-set Γ x `(μ ,x ,t))) `(μ ,x ,t)
+ (err (format ("expected ~a to be of type ~a, got ~a"
+ e t (infer e (dict-set Γ x `(μ ,x ,t)))))))]
+ [`(unfold (μ ,x ,t) ,e)
+ (if (check- e `(μ ,x ,t)) (α-convert t #hash((x . `(μ ,x ,t))))
+ (err (format ("expected ~a to be of type ~a, got ~a"
+ e `(μ ,x ,t) (infer- e Γ)))))]
+
+ [`(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))]))