(* Title: JinjaDCI/J/WWellForm.thy
Author: Tobias Nipkow, Susannah Mansky
Copyright 2003 Technische Universitaet Muenchen, 2019-20 UIUC
Based on the Jinja theory J/WWellForm.thy by Tobias Nipkow
*)
section ‹ Weak well-formedness of Jinja programs ›
theory WWellForm imports "../Common/WellForm" Expr begin
definition wwf_J_mdecl :: "J_prog → cname → J_mb mdecl → bool"
where
"wwf_J_mdecl P C ≡ λ(M,b,Ts,T,(pns,body)).
length Ts = length pns ∧ distinct pns ∧ ¬sub_RI body ∧
(case b of
NonStatic → this ∉ set pns ∧ fv body ⊆ {this} ∪ set pns
| Static → fv body ⊆ set pns)"
lemma wwf_J_mdecl_NonStatic[simp]:
"wwf_J_mdecl P C (M,NonStatic,Ts,T,pns,body) =
(length Ts = length pns ∧ distinct pns ∧ ¬sub_RI body ∧ this ∉ set pns ∧ fv body ⊆ {this} ∪ set pns)"
(*<*)by(simp add:wwf_J_mdecl_def)(*>*)
lemma wwf_J_mdecl_Static[simp]:
"wwf_J_mdecl P C (M,Static,Ts,T,pns,body) =
(length Ts = length pns ∧ distinct pns ∧ ¬sub_RI body ∧ fv body ⊆ set pns)"
(*<*)by(simp add:wwf_J_mdecl_def)(*>*)
abbreviation
wwf_J_prog :: "J_prog → bool" where
"wwf_J_prog ≡ wf_prog wwf_J_mdecl"
lemma sees_wwf_nsub_RI:
"[ wwf_J_prog P; P ⊨ C sees M,b : Ts→T = (pns, body) in D ] ==> ¬sub_RI body"
(*<*)by(auto dest!: sees_wf_mdecl simp: wwf_J_mdecl_def wf_mdecl_def)(*>*)
end
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