diff --git a/nbe-test.rkt b/nbe-test.rkt
index 49ff739..51eb93c 100644
--- a/nbe-test.rkt
+++ b/nbe-test.rkt
@@ -1,11 +1,43 @@
 #lang racket
 
 (require rackunit "nbe.rkt")
+
+(define-syntax tm-app
+  (syntax-rules ()
+    [(tm-app a) a]
+    [(tm-app a b c ...)
+     (tm-app `(app ,a ,b) c ...)]))
+
+(define-syntax-rule (tm-var a) `(var ,a))
+(define-syntax-rule (tm-abs a) `(λ ,a))
+
 (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))))))
+
+(define tm-pair `(λ (λ (λ ,(tm-app '(var 0) '(var 2) '(var 1))))))
+
+(define tm-y
+  (let ([g (tm-abs (tm-app (tm-var 1) (tm-app (tm-var 0) (tm-var 0))))])
+    (tm-abs (tm-app g g))))
+
+(define tm-zero tm-snd)
+
+(define (tm-suc a) (tm-abs (tm-abs (tm-app (tm-var 1) (tm-app a (tm-var 1) (tm-var 0))))))
+
+(define (tm-add a b)
+  (tm-abs (tm-abs
+           (tm-app b (tm-var 1) (tm-app a (tm-var 1) (tm-var 0))))))
+
+(define (tm-nat n)
+  (if (positive? n)
+      (tm-suc (tm-nat (- n 1)))
+      tm-zero))
 
 (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)
+(check-equal? (normalize (tm-app tm-snd (tm-app tm-pair tm-id tm-fst) tm-fst)) tm-fst)
+(check-equal? (normalize (tm-add (tm-nat 100) (tm-nat 40))) (normalize (tm-add (tm-nat 40) (tm-nat 100))))
diff --git a/nbe.rkt b/nbe.rkt
index 7a8da91..841cef8 100644
--- a/nbe.rkt
+++ b/nbe.rkt
@@ -43,7 +43,7 @@
 
 (define (reify-neu a)
   (match a
-    [`(app ,u ,v) (list 'app (reify-neu u) (reify a))]
+    [`(app ,u ,v) (list 'app (reify-neu u) (reify v))]
     [`(var ,i) a]))
 
 (define (idsub i) `(neu (var ,i)))
@@ -51,4 +51,11 @@
 (define (normalize a)
   (reify (interp a idsub)))
 
-(provide normalize)
+(define (tm? a)
+  (match a
+    [`(λ ,a) (tm? a)]
+    [`(app ,a ,b) (and (tm? a) (tm? b))]
+    [`(var ,i) (exact-nonnegative-integer? i)]
+    [_ false]))
+
+(provide reify interp normalize tm?)