Theory Language

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theory Language
imports Main

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

theory Language imports Main begin

consts
  Const :: i                    (* Abstract type of constants *)
  c_app :: "[i,i] => i"         (* Abstract constructor for fun application*)


text{*these really can't be definitions without losing the abstraction*}
axioms
  constNEE:  "c ∈ Const ==> c ≠ 0"
  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