diff --git a/src/Data/Vec.hs b/src/Data/Vec.hs
index 489c3c1..b4191e8 100644
--- a/src/Data/Vec.hs
+++ b/src/Data/Vec.hs
@@ -320,6 +320,28 @@ drop' SZ     x         = x
 drop' (SS n) (x :- xs) = drop' n xs
 
 
+-- * Searching vectors
+-- Searching by equality
+
+-- | Does the element occur in the structure?
+elem ∷ Eq a ⇒ Vec a n → a → 𝔹
+elem Nil       _ = F
+elem (x :- xs) y = (x ≡ y) ∨ (elem xs y)
+
+
+-- | 'notElem' is the negation of 'elem'.
+notElem ∷ Eq a ⇒ Vec a n → a → 𝔹
+notElem xs = (¬) ∘ elem xs
+
+
+-- | 'lookup' key assocs looks up a key in an association vector.
+lookup ∷ Eq a ⇒ a → Vec (a, b) n → Maybe b
+lookup t Nil          = Nothing
+lookup t ((k,v) :- x) =
+  if t ≡ k
+    then Just v
+    else lookup t x
+
 
 -- * Zipping and unzipping vectors