Theory RG_Syntax

theory RG_Syntax
imports RG_Hoare Quote_Antiquote
header {* \section{Concrete Syntax} *}

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" \<rightharpoonup> "CONST Basic «´(_update_name x (λ_. 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⟩" \<rightleftharpoons> "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" ("_//\<parallel>//_" [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 (λi. c) [j..<k])"

text {* Translations for variables before and after a transition: *}

syntax
"_before" :: "id => 'a" ("º_")
"_after" :: "id => 'a" ("ª_")

translations
"ºx" \<rightleftharpoons> "x ´CONST fst"
"ªx" \<rightleftharpoons> "x ´CONST snd"

print_translation {*
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 "_Assert"});

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 Collect}, K assert_tr'),
(@{const_syntax Basic}, K assign_tr'),
(@{const_syntax Cond}, K (bexp_tr' @{syntax_const "_Cond"})),
(@{const_syntax While}, K (bexp_tr' @{syntax_const "_While"}))]
end
*}


end