module ahmed.day1 where

open import Data.Product

data Type : Set where
  Bool : Type
  _-→_ : Type → Type → Type

data Term : Set where
  True : Term
  False : Term
  If_Then_Else_ : Term → Term → Term → Term
  λ[_::_]_ : Term → Type → Term → Term
  _∙_ : Term → Term → Term

data isValue : Term → Set where
  TrueValue : isValue True
  FalseValue : isValue False
  LambdaValue : (x : Term) → (τ : Type) → (e : Term) → isValue (λ[ x :: τ ] e)

Value = Σ Term isValue

data evaluationContext : Set where
  dot : evaluationContext
  EIf_Then_Else_ : evaluationContext → Term → Term → evaluationContext
  EAppLeft : evaluationContext → Term → evaluationContext
  EAppRight : Value → evaluationContext → evaluationContext