Add some unit test cases

nbe-test.rkt

@@ -0,0 +1,11 @@
+#lang racket
+
+(require rackunit "nbe.rkt")
+(define tm-id '(λ (var 0)))
+(define tm-fst '(λ (λ (var 1))))
+(define tm-snd '(λ (λ (var 0))))
+(define tm-pair '(λ (λ (λ (app (app (var 0) (var 2)) (var 1))))))
+
+(check-equal? (normalize `(app ,tm-id ,tm-id)) tm-id)
+(check-equal? (normalize `(app (app (app ,tm-pair ,tm-id) ,tm-fst) ,tm-snd)) tm-fst)
+(check-equal? (normalize `(app (app (app ,tm-pair ,tm-id) ,tm-fst) ,tm-fst)) tm-id)

nbe.rkt

@@ -1,39 +1,54 @@
 #lang racket
-(require racket/treelist)
-
 ;; Grammar (Λ)
 ;; t := λ t | app t t | i
 
 ;; Domain
-;; D ≃ Λ + [D → D]
+;; D ≃ neu D_ne | fun [D → D]
 ;; D_ne = var i | app D_ne D
 ;; Define as we go
+
 (define (ap a b)
   (match a
-    [`(fun ,f) (f b)]))
+    [`(fun ,f) (f identity b)]
+    [`(neu ,u) `(neu (app ,u ,b))]))
+
+(define compose-ren compose)
+(define (compose-ren-sub ξ ρ) (compose (curry ren-dom ξ) ρ))
+(define (ext ρ a)
+  (lambda (i)
+    (if (zero? i)
+        a
+        (ρ (- i 1)))))
 
 (define (ren-ne-dom ξ a)
   (match a
-    [`(var ,i) `(var ,(treelist-ref ξ i))]
+    [`(var ,i) `(var ,(ξ i))]
     [`(app ,a ,b) `(app ,(ren-ne-dom ξ a) ,(ren-dom ξ b))]))
 
 (define (ren-dom ξ a)
   (match a
-    [`(neu ,a) `(neu ,(ren-ne-dom a))]
+    [`(neu ,a) `(neu ,(ren-ne-dom ξ a))]
-    [`(fun ,f) `(fun ,(λ (ξ0 α) (f (compose ξ0 ξ) α)))]))
+    [`(fun ,f) `(fun ,(λ (ξ0 α) (f (compose-ren ξ0 ξ) α)))]))
 
 (define (interp a ρ)
   (match a
-    [`(var ,i) (treelist-ref ρ i)]
+    [`(var ,i) (ρ i)]
-    [`(λ ,a)  (list 'fun (λ (ξ x) (interp a (treelist-cons (compose ren-dom ρ) x))))]
+    [`(λ ,a)  (list 'fun (λ (ξ x) (interp a (ext (compose-ren-sub ξ ρ) x))))]
     [`(app ,a ,b) (ap (interp a ρ) (interp b ρ))]))
 
-
-
-(define (reflect a)
-  (list 'neu a))
-
-
 (define (reify a)
   (match a
-    [`(fun ,f) (reify (f (reflect '(var 0))))]))
+    [`(fun ,f) (list 'λ (reify (f  (curry + 1) '(neu (var 0)))))]
+    [`(neu ,a) (reify-neu a)]))
+
+(define (reify-neu a)
+  (match a
+    [`(app ,u ,v) (list 'app (reify-neu u) (reify a))]
+    [`(var ,i) a]))
+
+(define (idsub i) `(neu (var ,i)))
+
+(define (normalize a)
+  (reify (interp a idsub)))
+
+(provide normalize)