{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE PatternSynonyms #-}
module Syntax where

import Data.Text (Text)
import Data.Data (Data, Typeable)

data Plicity
  = Im
  | Ex
  deriving (Eq, Show, Ord, Data, Typeable)

newtype Var = Bound Int
  deriving (Eq, Show, Ord, Data, Typeable)

data BoundDef = BDBound Text | BDDefined Text
  deriving (Eq, Show, Ord, Data, Typeable)

newtype MetaVar = MV { getMV :: Int }
  deriving (Eq, Show, Ord, Data, Typeable)

data Term
  = Var Var
  | Con Text
  | Let Text Term Term Term
  | Type | Prop

  | Pi  Plicity Text Term Term
  | Lam Plicity Text Term
  | App Plicity Term Term

  | Sigma Text Term Term
  | Pair Term Term
  | Proj1 Term
  | Proj2 Term

  | Meta    MetaVar
  | NewMeta MetaVar [BoundDef]

  | Id Term Term Term
  | Refl
  | Coe
  | Cong
  | Sym

  | Top | Unit
  deriving (Eq, Show, Ord, Typeable, Data)

pattern Bv :: Int -> Term
pattern Bv i = Var (Bound i)

data Telescope
  = End
  | Ext Telescope Text Term
  deriving (Eq, Show, Ord)

newtype Level = Lvl {unLvl :: Int}
  deriving (Eq, Show, Ord, Enum)

lvl2Ix :: Level -> Level -> Int
lvl2Ix (Lvl l) (Lvl x) = l - x - 1