src/ZF/Coind/Language.thy
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(*  Title:      ZF/Coind/Language.thy
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    Author:     Jacob Frost, Cambridge University Computer Laboratory
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    Copyright   1995  University of Cambridge
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*)
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theory Language imports ZF begin
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text\<open>these really can't be definitions without losing the abstraction\<close>
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axiomatization
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  Const :: i  and               (* Abstract type of constants *)
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  c_app :: "[i,i] \<Rightarrow> i"         (* Abstract constructor for fun application*)
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where
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  constNEE:  "c \<in> Const \<Longrightarrow> c \<noteq> 0" and
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  c_appI:    "\<lbrakk>c1 \<in> Const; c2 \<in> Const\<rbrakk> \<Longrightarrow> c_app(c1,c2) \<in> Const"
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consts
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  Exp   :: i                    (* Datatype of expressions *)
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  ExVar :: i                    (* Abstract type of variables *)
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datatype
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  "Exp" = e_const ("c \<in> Const")
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        | e_var ("x \<in> ExVar")
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        | e_fn ("x \<in> ExVar","e \<in> Exp")
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        | e_fix ("x1 \<in> ExVar","x2 \<in> ExVar","e \<in> Exp")
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        | e_app ("e1 \<in> Exp","e2 \<in> Exp")
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end