import BidirTT.Syntax

namespace BidirTT

mutual
  inductive Val where
    | var  : Nat → Val
    | app  : Val → Val → Val
    | fst  : Val → Val
    | snd  : Val → Val
    | lam  : Closure → Val
    | pi   : Val → Closure → Val
    | sig  : Val → Closure → Val
    | pair : Val → Val → Val
    | univ : Nat → Val

  inductive Closure where
    | mk : List Val → Tm → Closure
end

abbrev Env := List Val
abbrev Lvl := Nat

instance : Inhabited Val := ⟨.univ 0⟩
instance : Inhabited Closure := ⟨.mk [] (.univ 0)⟩

end BidirTT