diff --git a/nbe.rkt b/nbe.rkt
index 86f2917..9c6701d 100644
--- a/nbe.rkt
+++ b/nbe.rkt
@@ -2,6 +2,7 @@
 
 (define-type denv (-> V (Promise D)))
 (define-type V Nonnegative-Integer)
+
 (define-type Term (∪ 'zero
                      'nat
                      (List 'succ Term)
@@ -12,6 +13,24 @@
                      (List 'Π Term Term)
                      'U))
 
+(define-type Neu (∪ (List 'ind Neu Norm Norm)
+                    (List 'var V)
+                    (List 'app Neu Norm)))
+
+(define-type Norm (∪ Neu
+                     'zero
+                     'nat
+                     (List 'λ Norm)
+                     (List 'U V)
+                     (List 'succ Norm)
+                     (List 'Π Norm Norm)))
+
+(: embed (-> Neu Term))
+(define (embed a) a)
+
+(: embed-norm (-> Norm Term))
+(define (embed-norm a) a)
+
 (define-type D (∪ 'zero
                   (List 'Π (Promise D) (-> (Promise D) D))
                   (List 'succ (Promise D))
@@ -101,7 +120,7 @@
                                                  (compare (+ n 2) (open-dom2 n c0) (open-dom2 n c1)))]
     [_ #f]))
 
-(: reify (-> V D Term))
+(: reify (-> V D Norm))
 (define (reify n a)
   (match a
     [`(Π ,A ,B) `(Π ,(reify n (force A)) ,(reify (+ n 1) (B (delay `(neu (idx ,n))))))]
@@ -118,7 +137,7 @@
         (error "variable to index conversion failed")
         ret)))
 
-(: reify-neu (-> V D-ne Term))
+(: reify-neu (-> V D-ne Neu))
 (define (reify-neu n a)
   (match a
     [`(ind ,a ,b ,c) (list 'ind
diff --git a/type-checker.rkt b/type-checker.rkt
index d895735..5b42c9c 100644
--- a/type-checker.rkt
+++ b/type-checker.rkt
@@ -23,7 +23,11 @@
 
 (: synth (-> context Term Term))
 (define (synth Γ a)
-  (error "unimplmented"))
+  (match a
+    [`(var ,i) (context-get Γ i)]
+    [`(app ,a ,b)
+     (let ([A (synth Γ a)]
+           [D (interp-with-scope (context-len Γ) A)]))]))
 
 (: check (-> context Term D Boolean))
 (define (check Γ a A)