Theory Language

(*  Title:      ZF/Coind/Language.thy
    Author:     Jacob Frost, Cambridge University Computer Laboratory
    Copyright   1995  University of Cambridge
*)

theory Language imports ZF begin


text‹these really can't be definitions without losing the abstraction›

axiomatization
  Const :: i  and               (* Abstract type of constants *)
  c_app :: "[i,i] ⇒ i"         (* Abstract constructor for fun application*)
where
  constNEE:  "c ∈ Const ⟹ c ≠ 0" and
  c_appI:    "⟦c1 ∈ Const; c2 ∈ Const⟧ ⟹ c_app(c1,c2) ∈ Const"


consts
  Exp   :: i                    (* Datatype of expressions *)
  ExVar :: i                    (* Abstract type of variables *)

datatype
  "Exp" = e_const ("c ∈ Const")
        | e_var ("x ∈ ExVar")
        | e_fn ("x ∈ ExVar","e ∈ Exp")
        | e_fix ("x1 ∈ ExVar","x2 ∈ ExVar","e ∈ Exp")
        | e_app ("e1 ∈ Exp","e2 ∈ Exp")

end