diff --git a/stlc-tests.rkt b/stlc-tests.rkt
index 4287c70..d112317 100644
--- a/stlc-tests.rkt
+++ b/stlc-tests.rkt
@@ -1,16 +1,16 @@
 #lang s-exp "stlc.rkt"
 
-(check-type-error ((λ (x : Int) (+ x 1)) "10"))
-(check-type ((λ (x : Int) (+ x 1)) 10) : Int)
-(check-equal? ((λ (x : Int) (+ x 1)) 10) 11)
-(check-type-and-result ((λ (x : Int) (+ x 1)) 10) : Int => 11)
+(check-type-error ((λ ([x : Int]) (+ x 1)) "10"))
+(check-type ((λ ([x : Int]) (+ x 1)) 10) : Int)
+(check-equal? ((λ ([x : Int]) (+ x 1)) 10) 11)
+(check-type-and-result ((λ ([x : Int]) (+ x 1)) 10) : Int => 11)
 
 ; HO fn
-(check-type-and-result ((λ (f : (→ Int Int)) (f 10)) (λ (x : Int) (+ x 1))) : Int => 11)
-(check-type (λ (f : (→ Int Int)) (f 10)) : (→ (→ Int Int) Int))
-(check-type (λ (f : (→ Int Int)) (λ (x : Int) (f (f x)))) : (→ (→ Int Int) (→ Int Int)))
+(check-type-and-result ((λ ([f : (→ Int Int)]) (f 10)) (λ ([x : Int]) (+ x 1))) : Int => 11)
+(check-type (λ ([f : (→ Int Int)]) (f 10)) : (→ (→ Int Int) Int))
+(check-type (λ ([f : (→ Int Int)]) (λ ([x : Int]) (f (f x)))) : (→ (→ Int Int) (→ Int Int)))
 (check-type-error (λ (f : (→ Int Int)) (λ (x : String) (f (f x)))))
 
 ;; shadowed var
-(check-type-error ((λ (x : Int) ((λ (x : String) x) x)) 10))
-(check-type-and-result ((λ (x : String) ((λ (x : Int) (+ x 1)) 10)) "ten") : Int => 11)
\ No newline at end of file
+(check-type-error ((λ ([x : Int]) ((λ ([x : String]) x) x)) 10))
+(check-type-and-result ((λ ([x : String]) ((λ ([x : Int]) (+ x 1)) 10)) "ten") : Int => 11)
\ No newline at end of file
diff --git a/stlc.rkt b/stlc.rkt
index 2f64cc5..152cccb 100644
--- a/stlc.rkt
+++ b/stlc.rkt
@@ -1,14 +1,18 @@
 #lang racket
-(require (for-syntax syntax/parse syntax/id-table))
-(provide (except-out (all-from-out racket) λ #%app + #%datum))
+(require (for-syntax syntax/parse syntax/id-table syntax/stx racket/list
+                     "stx-utils.rkt"))
+(provide (except-out (all-from-out racket) λ #%app + #%datum let))
 
-(provide (rename-out [myλ λ] [myapp #%app] [my+ +] [mydatum #%datum]))
+(provide (rename-out [myλ λ] [myapp #%app] [my+ +] [mydatum #%datum] #;[mylet let]))
 
-(provide Int String Bool →)
+(provide Int String Bool → Listof)
 (define Int #f)
 (define String #f)
 (define Bool #f)
 (define → #f)
+(define Listof #f) 
+
+(define-for-syntax TYPE-ENV-PROP 'Γ)
 
 (require (for-syntax rackunit))
 (provide check-type-error check-type check-type-and-result)
@@ -71,6 +75,15 @@
   (local-expand 
    #`(λ (#,x) #,(syntax-property e 'Γ (hash-set Γ (syntax->datum x) τ)))
    'expression null))
+(define-for-syntax (expand/Γ/:=s e outer-e x:τs)
+  (define Γ (or (syntax-property outer-e TYPE-ENV-PROP) (hash)))
+  (define xs (stx-map stx-car x:τs))
+  (define τs (stx-map stx-cadr x:τs))
+  (local-expand
+   #`(λ #,xs #,(syntax-property e TYPE-ENV-PROP 
+                 (apply hash-set* Γ 
+                   (append-map (λ (x τ) (list (syntax->datum x) τ)) xs τs))))
+   'expression null))
 
 (define-syntax (mydatum stx)
   (syntax-parse stx
@@ -83,34 +96,40 @@
 
 (define-syntax (my+ stx)
   (syntax-parse stx
-    [(_ e1 e2)
-     #:with e1+ (expand/Γ #'e1 stx)
-     #:with e2+ (expand/Γ #'e2 stx)
-     #:when (assert-type #'e1+ #'Int)
-     #:when (assert-type #'e2+ #'Int)
-     (⊢ (syntax/loc stx (+ e1 e2)) #'Int)]))
+    [(_ e ...)
+;    [(_ e1 e2)
+;     #:with e1+ (expand/Γ #'e1 stx)
+;     #:with e2+ (expand/Γ #'e2 stx)
+     #:with (e+ ...) (stx-map (λ (estx) (expand/Γ estx stx)) #'(e ...))
+;     #:when (assert-type #'e1+ #'Int)
+;     #:when (assert-type #'e2+ #'Int)
+     #:when (andmap (λ (estx) (assert-type estx #'Int)) (syntax->list #'(e+ ...)))
+     (⊢ (syntax/loc stx (+ e+ ...)) #'Int)]))
+;     (⊢ (syntax/loc stx (+ e1+ e2+)) #'Int)]))
 
 
 (define-syntax (myλ stx)
   (syntax-parse stx #:datum-literals (:)
-    [(_ (x:id : τ1) e)
+    [(_ ([x:id : τ] ...) e)
      ;; - can't use free-identifier=? for the hash table (or free-id-table)
      ;;   because I have to set the table now, but once I get under the λ, the
      ;;   x's won't be free-id=? to the one in the table
      ;; use symbols instead of identifiers for now --- should be fine because
      ;; I'm manually managing the environment
-     #:with (lam xs e+) (expand/Γ/:= #'e stx #'x #'τ1)
-;     (expand/Γ/:= #'(λ (x) #,(syntax-property #'e 'Γ (hash-set
-;                                                                 (or (syntax-property stx 'Γ) (hash))
-;                                                                 (syntax->datum #'x) #'τ1))) stx)
+     #:with (lam xs e+) (expand/Γ/:=s #'e stx #'((x τ) ...))
      #:with τ2 (typeof #'e+)
-     (⊢ (syntax/loc stx (lam xs e+)) #'(→ τ1 τ2))]))
+     (⊢ (syntax/loc stx (lam xs e+)) #'(→ τ ... τ2))]))
+
+;(define-syntax (mylet stx)
+;  (syntax-parse stx #:datum-literals (:)
+;    [(_ ([x:id : τ]) e)
+;     #:
 
 (define-syntax (myapp stx)
   (syntax-parse stx #:literals (→)
-    [(_ e1 e2)
-     #:with e1+ (expand/Γ #'e1 stx)
-     #:with e2+ (expand/Γ #'e2 stx)
-     #:with (→ τ1 τ2) (typeof #'e1+)
-     #:when (assert-type #'e2+ #'τ1)
-     (⊢ (syntax/loc stx (#%app e1+ e2+)) #'τ2)]))
+    [(_ e_fn e_arg ...)
+     #:with e_fn+ (expand/Γ #'e_fn stx)
+     #:with (e_arg+ ...) (stx-map (λ (e) (expand/Γ e stx)) #'(e_arg ...))
+     #:with (→ τ ... τ_res) (typeof #'e_fn+)
+     #:when (andmap assert-type (syntax->list #'(e_arg+ ...)) (syntax->list #'(τ ...)))
+     (⊢ (syntax/loc stx (#%app e_fn+ e_arg+ ...)) #'τ_res)]))