Theory Language

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


theory Language imports Main 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