{-# OPTIONS --prop #-}

module Zdancewic.Day1 where

open import Data.Bool
open import Data.Nat
open import Data.String

mem = String -> ℕ

infixl 20 _∙_

data aexp : Set where
data bexp : Set where
data com : Set where
  `_:=_ : String → ℕ → com
  `if_then_else_ : bexp → com → com → com
  `skip : com
  _∙_ : com → com → com

beval : mem → bexp → Bool

denote : com → mem → mem
denote `skip st = st
denote (`if x then c else c₁) st = if beval st x then denote c st else denote c₁ st
denote (` x := n) st = λ y → if x == y then n else st x
denote (c ∙ c₁) st = denote c₁ (denote c st)

data ceval : com → mem → mem → Prop where
  E_skip : ∀ {st} → ceval `skip st st