reorganize and add plfa

plfa/Naturals.agda

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+module Naturals where
+
+import Relation.Binary.PropositionalEquality as Eq
+open Eq using (_≡_; refl)
+open Eq.≡-Reasoning using (begin_; _≡⟨⟩_; _∎)
+
+data ℕ : Set where
+  zero : ℕ
+  suc  : ℕ → ℕ
+
+{-# BUILTIN NATURAL ℕ #-}
+
+_+_ : ℕ → ℕ → ℕ
+zero + n  = n
+suc m + n = suc (m + n)
+
+_*_ : ℕ → ℕ → ℕ
+zero  * n = zero
+suc m * n = n + (m * n)
+
+_^_ : ℕ → ℕ → ℕ
+n ^ 0     = 1
+n ^ suc m = n * (n ^ m)
+
+_∸_ : ℕ → ℕ → ℕ
+m ∸ zero      = m
+zero ∸ suc n  = zero
+suc m ∸ suc n = m ∸ n
+
+infixl 6  _+_  _∸_
+infixl 7  _*_
+
+{-# BUILTIN NATPLUS _+_ #-}
+{-# BUILTIN NATTIMES _*_ #-}
+{-# BUILTIN NATMINUS _∸_ #-}
+
+-- Bin stretch exercise
+
+data Bin : Set where
+  ⟨⟩ : Bin
+  _O : Bin → Bin
+  _I : Bin → Bin
+
+inc : Bin → Bin
+inc ⟨⟩ = ⟨⟩ I
+inc (m O) =  m I
+inc (m I) = (inc m) O
+
+_ : inc (⟨⟩ I O I I) ≡ ⟨⟩ I I O O
+_ = refl
+
+_ : inc (⟨⟩ I)  ≡ ⟨⟩ I O
+_ = refl
+
+to : ℕ -> Bin
+to 0 = ⟨⟩
+to (suc n) = inc (to n)
+
+_ : to 11 ≡ ⟨⟩ I O I I
+_ = refl
+
+from : Bin -> ℕ
+from ⟨⟩ = 0
+from (m O) = 2 * from m
+from (m I) = 1 + 2 * from m
+
+_ : from (⟨⟩ I O I I) ≡ 11
+_ = refl

plfa/README.md

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+# PLFA
+
+I’m following along [PLFA](https://plfa.github.io/). This repo only contains the
+stretch exercises and supporting materials.