(* Title: ZF/Coind/Dynamic.thy
Author: Jacob Frost, Cambridge University Computer Laboratory
Copyright 1995 University of Cambridge
*)
theory Dynamic imports Values begin
consts
EvalRel :: i
inductive
domains "EvalRel" <= "ValEnv * Exp * Val"
intros
eval_constI:
" [| ve \<in> ValEnv; c \<in> Const |] ==>
<ve,e_const(c),v_const(c)>:EvalRel"
eval_varI:
" [| ve \<in> ValEnv; x \<in> ExVar; x \<in> ve_dom(ve) |] ==>
<ve,e_var(x),ve_app(ve,x)>:EvalRel"
eval_fnI:
" [| ve \<in> ValEnv; x \<in> ExVar; e \<in> Exp |] ==>
<ve,e_fn(x,e),v_clos(x,e,ve)>:EvalRel "
eval_fixI:
" [| ve \<in> ValEnv; x \<in> ExVar; e \<in> Exp; f \<in> ExVar; cl \<in> Val;
v_clos(x,e,ve_owr(ve,f,cl))=cl |] ==>
<ve,e_fix(f,x,e),cl>:EvalRel "
eval_appI1:
" [| ve \<in> ValEnv; e1 \<in> Exp; e2 \<in> Exp; c1 \<in> Const; c2 \<in> Const;
<ve,e1,v_const(c1)>:EvalRel;
<ve,e2,v_const(c2)>:EvalRel |] ==>
<ve,e_app(e1,e2),v_const(c_app(c1,c2))>:EvalRel "
eval_appI2:
" [| ve \<in> ValEnv; vem \<in> ValEnv; e1 \<in> Exp; e2 \<in> Exp; em \<in> Exp; xm \<in> ExVar; v \<in> Val;
<ve,e1,v_clos(xm,em,vem)>:EvalRel;
<ve,e2,v2>:EvalRel;
<ve_owr(vem,xm,v2),em,v>:EvalRel |] ==>
<ve,e_app(e1,e2),v>:EvalRel "
type_intros c_appI ve_appI ve_empI ve_owrI Exp.intros Val_ValEnv.intros
end