Progress towards UFDs (#88)

Lists/Length.agda

@@ -0,0 +1,22 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import LogicalFormulae
+open import Functions
+open import Numbers.Naturals.Semiring -- for length
+open import Numbers.Naturals.Order
+open import Semirings.Definition
+open import Lists.Definition
+open import Lists.Fold.Fold
+
+module Lists.Length where
+
+length : {a : _} {A : Set a} (l : List A) → ℕ
+length [] = zero
+length (x :: l) = succ (length l)
+
+length' : {a : _} {A : Set a} → (l : List A) → ℕ
+length' = fold (λ _ → succ) 0
+
+length=length' : {a : _} {A : Set a} (l : List A) → length l ≡ length' l
+length=length' [] = refl
+length=length' (x :: l) = applyEquality succ (length=length' l)