type var = Ix of int
type name = string

type icit
  = Imp
  | Exp

type ast
  = Var of var

  | Type

  | T0
  | Ind0 of ast * ast

  | T1
  | T1tr (* Unit eta rule instead of elimination principle *)

  | TNat
  | Zero
  | Suc  of ast
  | IndN of ast * ast * ast * ast

  | TBool
  | True
  | False
  | IndB of ast * ast * ast * ast (* ordered true, false *)

  | Pi   of icit * ast * ast
  | Lam  of icit * ast
  | App  of icit * ast

  | Sg   of ast * ast
  | Pair of ast * ast
  | Fst  of ast
  | Snd  of ast

  | Let  of ast * ast * ast (* tr : ty in sc *)