First commit, a functional proof completeness of kripke structure for propositional logic

tests/test2.agda

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+module test2 where
+
+open import Data.Nat using (ℕ)
+open import Data.Vec using (Vec; _∷_)
+open import Data.Fin using (Fin; zero; suc)
+
+variable
+  A : Set
+  n : ℕ
+
+lookup : Vec A n → Fin n → A
+lookup (a ∷ as) zero = a
+lookup (a ∷ as) (suc i) = lookup as i

tests/test3.agda

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+module test3 where
+
+open import Data.Nat using (ℕ; _+_)
+open import Relation.Binary.PropositionalEquality using (_≡_)
+
++-assoc : Set
++-assoc = ∀ (x y z : ℕ) → x + (y + z) ≡ (x + y) + z
+
+open import Data.Nat using (zero; suc)
+open import Relation.Binary.PropositionalEquality using (refl; cong)
+
++-assoc-proof : +-assoc
+
++-assoc-proof zero y z = refl
++-assoc-proof (suc x') y z = cong suc (+-assoc-proof x' y z) 
+

tests/tests.agda

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+data Greeting : Set where
+  hello : Greeting
+
+greet : Greeting
+greet = hello
+
+module hello-world-dep where
+
+open import Data.Nat using (ℕ; zero; suc)
+
+data Vec (A : Set) : ℕ → Set where
+  []  : Vec A zero
+  _∷_ : ∀ {n} (x : A) (xs : Vec A n) → Vec A (suc n)
+
+infixr 5 _∷_
+
+