section \<open>Concrete Syntax\<close>
theory RG_Syntax
imports RG_Hoare Quote_Antiquote
begin
abbreviation Skip :: "'a com" ("SKIP")
where "SKIP \ Basic id"
notation Seq ("(_;;/ _)" [60,61] 60)
syntax
"_Assign" :: "idt \ 'b \ 'a com" ("(\_ :=/ _)" [70, 65] 61)
"_Cond" :: "'a bexp \ 'a com \ 'a com \ 'a com" ("(0IF _/ THEN _/ ELSE _/FI)" [0, 0, 0] 61)
"_Cond2" :: "'a bexp \ 'a com \ 'a com" ("(0IF _ THEN _ FI)" [0,0] 56)
"_While" :: "'a bexp \ 'a com \ 'a com" ("(0WHILE _ /DO _ /OD)" [0, 0] 61)
"_Await" :: "'a bexp \ 'a com \ 'a com" ("(0AWAIT _ /THEN /_ /END)" [0,0] 61)
"_Atom" :: "'a com \ 'a com" ("(\_\)" 61)
"_Wait" :: "'a bexp \ 'a com" ("(0WAIT _ END)" 61)
translations
"\x := a" \ "CONST Basic \\(_update_name x (\_. a))\"
"IF b THEN c1 ELSE c2 FI" \<rightharpoonup> "CONST Cond \<lbrace>b\<rbrace> c1 c2"
"IF b THEN c FI" \<rightleftharpoons> "IF b THEN c ELSE SKIP FI"
"WHILE b DO c OD" \<rightharpoonup> "CONST While \<lbrace>b\<rbrace> c"
"AWAIT b THEN c END" \<rightleftharpoons> "CONST Await \<lbrace>b\<rbrace> c"
"\c\" \ "AWAIT CONST True THEN c END"
"WAIT b END" \<rightleftharpoons> "AWAIT b THEN SKIP END"
nonterminal prgs
syntax
"_PAR" :: "prgs \ 'a" ("COBEGIN//_//COEND" 60)
"_prg" :: "'a \ prgs" ("_" 57)
"_prgs" :: "['a, prgs] \ prgs" ("_//\//_" [60,57] 57)
translations
"_prg a" \<rightharpoonup> "[a]"
"_prgs a ps" \<rightharpoonup> "a # ps"
"_PAR ps" \<rightharpoonup> "ps"
syntax
"_prg_scheme" :: "['a, 'a, 'a, 'a] \ prgs" ("SCHEME [_ \ _ < _] _" [0,0,0,60] 57)
translations
"_prg_scheme j i k c" \<rightleftharpoons> "(CONST map (\<lambda>i. c) [j..<k])"
text \<open>Translations for variables before and after a transition:\<close>
syntax
"_before" :: "id \ 'a" ("\_")
"_after" :: "id \ 'a" ("\_")
translations
"\x" \ "x \CONST fst"
"\x" \ "x \CONST snd"
print_translation \<open>
let
fun quote_tr' f (t :: ts) =
Term.list_comb (f $ Syntax_Trans.quote_tr' \<^syntax_const>\_antiquote\ t, ts)
| quote_tr' _ _ = raise Match;
val assert_tr' = quote_tr' (Syntax.const \<^syntax_const>\<open>_Assert\<close>);
fun bexp_tr' name ((Const (\<^const_syntax>\Collect\, _) $ t) :: ts) =
quote_tr' (Syntax.const name) (t :: ts)
| bexp_tr' _ _ = raise Match;
fun assign_tr' (Abs (x, _, f $ k $ Bound 0) :: ts) =
quote_tr' (Syntax.const \<^syntax_const>\_Assign\ $ Syntax_Trans.update_name_tr' f)
(Abs (x, dummyT, Syntax_Trans.const_abs_tr' k) :: ts)
| assign_tr' _ = raise Match;
in
[(\<^const_syntax>\<open>Collect\<close>, K assert_tr'),
(\<^const_syntax>\<open>Basic\<close>, K assign_tr'),
(\<^const_syntax>\<open>Cond\<close>, K (bexp_tr' \<^syntax_const>\<open>_Cond\<close>)),
(\<^const_syntax>\<open>While\<close>, K (bexp_tr' \<^syntax_const>\<open>_While\<close>))]
end
\<close>
end
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