Add Church numerals

Computability/LambdaCalculus/ChurchNumeral.agda

@@ -0,0 +1,24 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import LogicalFormulae
+open import Lists.Lists
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+open import Decidable.Sets
+open import Numbers.Naturals.Definition
+open import Numbers.Naturals.Semiring
+
+module Computability.LambdaCalculus.ChurchNumeral where
+
+open import UnorderedSet.Definition ℕDecideEquality
+open import Computability.LambdaCalculus.Definition
+
+private
+  iter : ℕ → Term
+  iter zero = var 0
+  iter (succ n) = apply (var 1) (iter n)
+
+church : ℕ → Term
+church n = lam 1 (lam 0 (iter n))
+
+churchSucc : Term
+churchSucc = lam 0 (lam 1 (lam 2 (apply (var 1) (apply (apply (var 0) (var 1)) (var 2)))))

Computability/LambdaCalculus/Definition.agda

@@ -0,0 +1,17 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import LogicalFormulae
+open import Lists.Lists
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+open import Decidable.Sets
+open import Numbers.Naturals.Definition
+open import Numbers.Naturals.Semiring
+
+module Computability.LambdaCalculus.Definition where
+
+open import UnorderedSet.Definition (ℕDecideEquality)
+
+data Term : Set where
+  var : (v : ℕ) → Term
+  lam : (x : ℕ) → Term → Term
+  apply : Term → Term → Term

Everything/Safe.agda

@@ -156,6 +156,8 @@ open import Modules.PolynomialModule
 open import Modules.Lemmas
 open import Modules.DirectSum
 
+open import Computability.LambdaCalculus.ChurchNumeral
+
 open import ProjectEuler.Problem1
 
 module Everything.Safe where