diff --git a/src/typesystem/misc.ml b/src/typesystem/misc.ml
new file mode 100644
index 000000000..96baf197b
--- /dev/null
+++ b/src/typesystem/misc.ml
@@ -0,0 +1,57 @@
+open Core
+
+let pair_map = fun f (x , y) -> (f x , f y)
+
+module Substitution = struct
+
+  module Pattern = struct
+
+    (*
+       Computes `P[v := expr]`.
+    *)
+    let rec type_value ~tv ~v ~expr =
+      let self tv = type_value ~tv ~v ~expr in
+      match tv with
+      | P_variable v' when v' = v -> expr
+      | P_variable _ -> tv
+      | P_constant (x , lst) -> (
+          let lst' = List.map self lst in
+          P_constant (x , lst')
+        )
+      | P_apply ab -> (
+          let ab' = pair_map self ab in
+          P_apply ab'
+        )
+      | P_forall p -> (
+          let aux c = constraint_ ~c ~v ~expr in
+          let constraints = List.map aux p.constraints in
+          if (p.binder = v) then (
+            P_forall { p with constraints }
+          ) else (
+            let body = self p.body in
+            P_forall { p with constraints ; body }
+          )
+        )
+
+    and constraint_ ~c ~v ~expr =
+      match c with
+      | C_equation ab -> (
+          let ab' = pair_map (fun tv -> type_value ~tv ~v ~expr) ab in
+          C_equation ab'
+        )
+      | C_typeclass (tvs , tc) -> (
+          let tvs' = List.map (fun tv -> type_value ~tv ~v ~expr) tvs in
+          let tc' = typeclass ~tc ~v ~expr in
+          C_typeclass (tvs' , tc')
+        )
+      | C_access_label (tv , l , v') -> (
+          let tv' = type_value ~tv ~v ~expr in
+          C_access_label (tv' , l , v')
+        )
+
+    and typeclass ~tc ~v ~expr =
+      List.map (List.map (fun tv -> type_value ~tv ~v ~expr)) tc
+
+  end
+
+end
diff --git a/src/typesystem/typesystem.ml b/src/typesystem/typesystem.ml
index b97e373e9..75d8ee5b8 100644
--- a/src/typesystem/typesystem.ml
+++ b/src/typesystem/typesystem.ml
@@ -1,2 +1,3 @@
 module Core = Core
 module Shorthands = Shorthands
+module Misc = Misc