diff --git a/tapl/tests/stlc+overloading-tests.rkt b/tapl/tests/stlc+overloading-tests.rkt
new file mode 100644
index 0000000..217254c
--- /dev/null
+++ b/tapl/tests/stlc+overloading-tests.rkt
@@ -0,0 +1,52 @@
+#lang s-exp "../stlc+overloading.rkt"
+(require "rackunit-typechecking.rkt")
+
+;; -----------------------------------------------------------------------------
+;; --- syntax for ψ types
+
+(typecheck-fail
+ (signature (α) (→ α Str Str))
+ #:with-msg "We only support single-argument functions")
+
+(typecheck-fail
+ (signature (α) (→ Str Str))
+ #:with-msg "Variable 'α' must be free")
+
+(check-type
+ (signature (α) (→ α Str))
+ : (ψ (α) (→ α Str)))
+
+;; -----------------------------------------------------------------------------
+;; --- basic overloading
+
+;; -- creating a signature does nothing, at first
+;; (signature (to-string α) (→ α Str))
+
+;; (typecheck-fail
+;;  (to-string 1)
+;;  #:with-msg "no instance")
+
+;; (typecheck-fail
+;;  (to-string "yolo")
+;;  #:with-msg "no instance")
+
+;; ;; -- can later add cases to an overloaded name
+;; (instance (to-string Num)
+;;   (λ ([x : Num]) "num"))
+
+;; (instance (to-string Str)
+;;   (λ ([x : Str]) "string"))
+
+;; (check-type-and-result
+;;  (to-string 43)
+;;  : Str ⇒ "num")
+
+;; (check-type-and-result
+;;  (to-string (+ 2 2))
+;;  : Str ⇒ "num")
+
+;; (check-type-and-result
+;;  (to-string "hi")
+;;  : Str ⇒ "string")
+
+;; ;; --