# Theory WWellForm

```(*  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
```