diff --git a/graph/graph/map.rkt b/graph/graph/map.rkt
new file mode 100644
index 00000000..270010bf
--- /dev/null
+++ b/graph/graph/map.rkt
@@ -0,0 +1,57 @@
+#lang typed/racket
+
+(require (for-syntax syntax/parse)
+         "../lib/low.rkt")
+
+(provide map:)
+
+(begin-for-syntax
+  (define-syntax-class lam
+    (pattern (~or (~literal λ) (~literal lambda)))))
+
+(define-syntax-rule (map:: TVar Element-Type f l)
+  ((λ #:∀ (TVar) ([lst : (Listof Element-Type)])
+     ((inst map TVar Element-Type) f lst)) l))
+
+(define-syntax (map: stx)
+  (syntax-parse stx
+    [(_ (~literal car) l) #'(map:: A (Pairof A Any) car l)]
+    [(_ (~literal cdr) l) #'(map:: B (Pairof Any B) cdr l)]
+    ;; TODO: add caar etc.
+    [(_ ((~literal values)) l) #'l]
+    [(_ ((~literal compose)) l) #'l]
+    [(_ ((~literal compose) f0 . fs) l) #'(map: f0 (map: (compose . fs) l))]
+    [(_ f . ls)
+     #'(map f . ls)]))
+
+(module* test typed/racket
+  (require (submod "..")
+           "../lib/low.rkt")
+  
+  (check-equal?: (map: car '((1 b x) (2 c) (3 d)))
+                 : (Listof Number)
+                 '(1 2 3))
+  (check-equal?: (map: cdr '((1 b x) (2 c) (3 d)))
+                 : (Listof Number)
+                 '((b x) (c) (d)))
+  (check-equal?: (map: car (map: cdr '((1 b x) (2 c) (3 d))))
+                 : (Listof Number)
+                 '(b c d))
+  (check-equal?: (map: (compose) '((1 b x) (2 c) (3 d)))
+                 : (Listof Number)
+                 '((1 b x) (2 c) (3 d)))
+  (check-equal?: (map: (compose car) '((1 b x) (2 c) (3 d)))
+                 : (Listof Number)
+                 '(1 2 3))
+  (check-equal?: (map: (compose cdr) '((1 b x) (2 c) (3 d)))
+                 : (Listof Number)
+                 '((b x) (c) (d)))
+  (check-equal?: (map: (compose car cdr) '((1 b x) (2 c) (3 d)))
+                 : (Listof Number)
+                 '(b c d))
+  (check-equal?: (map: (compose add1 car) '((1 b x) (2 c) (3 d)))
+                 : (Listof Number)
+                 '(2 3 4))
+  (check-equal?: (map: + '(1 2 3) '(4 5 6))
+                 : (Listof Number)
+                 '(5 7 9)))
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