oplss2024/ahmed/day1.agda

module Ahmed.Day1 where

open import Data.Empty
open import Data.Unit
open import Relation.Nullary using (Dec; yes; no)

data type : Set where
  bool : type
  _-→_ : type -> type -> type

data term : Set where
  true : term

data ctx : Set where
  nil : ctx
  cons : ctx -> type -> ctx

data substitution : Set where
  nil : substitution
  cons : substitution -> term -> substitution

isGoodSubstitution : (Γ : ctx) -> (γ : substitution) -> Set
isGoodSubstitution nil nil = ⊤
isGoodSubstitution nil (cons γ x) = ⊥
isGoodSubstitution (cons Γ x) nil = ⊥
isGoodSubstitution (cons Γ x) (cons γ x₁) = {!   !}