Theory OG_Syntax

theory OG_Syntax
imports OG_Tactics Quote_Antiquote
theory OG_Syntax
imports OG_Tactics Quote_Antiquote
begin

text{* Syntax for commands and for assertions and boolean expressions in
commands @{text com} and annotated commands @{text ann_com}. *}


abbreviation Skip :: "'a com" ("SKIP" 63)
where "SKIP ≡ Basic id"

abbreviation AnnSkip :: "'a assn => 'a ann_com" ("_//SKIP" [90] 63)
where "r SKIP ≡ AnnBasic r id"

notation
Seq ("_,,/ _" [55, 56] 55) and
AnnSeq ("_;;/ _" [60,61] 60)

syntax
"_Assign" :: "idt => 'b => 'a com" ("(´_ :=/ _)" [70, 65] 61)
"_AnnAssign" :: "'a assn => idt => 'b => 'a com" ("(_ ´_ :=/ _)" [90,70,65] 61)

translations
"´x := a" \<rightharpoonup> "CONST Basic «´(_update_name x (λ_. a))»"
"r ´x := a" \<rightharpoonup> "CONST AnnBasic r «´(_update_name x (λ_. a))»"

syntax
"_AnnCond1" :: "'a assn => 'a bexp => 'a ann_com => 'a ann_com => 'a ann_com"
("_ //IF _ /THEN _ /ELSE _ /FI" [90,0,0,0] 61)
"_AnnCond2" :: "'a assn => 'a bexp => 'a ann_com => 'a ann_com"
("_ //IF _ /THEN _ /FI" [90,0,0] 61)
"_AnnWhile" :: "'a assn => 'a bexp => 'a assn => 'a ann_com => 'a ann_com"
("_ //WHILE _ /INV _ //DO _//OD" [90,0,0,0] 61)
"_AnnAwait" :: "'a assn => 'a bexp => 'a com => 'a ann_com"
("_ //AWAIT _ /THEN /_ /END" [90,0,0] 61)
"_AnnAtom" :: "'a assn => 'a com => 'a ann_com" ("_//⟨_⟩" [90,0] 61)
"_AnnWait" :: "'a assn => 'a bexp => 'a ann_com" ("_//WAIT _ END" [90,0] 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" ("IF _ THEN _ FI" [0,0] 56)
"_While_inv" :: "'a bexp => 'a assn => 'a com => 'a com"
("(0WHILE _/ INV _ //DO _ /OD)" [0, 0, 0] 61)
"_While" :: "'a bexp => 'a com => 'a com"
("(0WHILE _ //DO _ /OD)" [0, 0] 61)

translations
"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 INV i DO c OD" \<rightharpoonup> "CONST While \<lbrace>b\<rbrace> i c"
"WHILE b DO c OD" \<rightleftharpoons> "WHILE b INV CONST undefined DO c OD"

"r IF b THEN c1 ELSE c2 FI" \<rightharpoonup> "CONST AnnCond1 r \<lbrace>b\<rbrace> c1 c2"
"r IF b THEN c FI" \<rightharpoonup> "CONST AnnCond2 r \<lbrace>b\<rbrace> c"
"r WHILE b INV i DO c OD" \<rightharpoonup> "CONST AnnWhile r \<lbrace>b\<rbrace> i c"
"r AWAIT b THEN c END" \<rightharpoonup> "CONST AnnAwait r \<lbrace>b\<rbrace> c"
"r ⟨c⟩" \<rightleftharpoons> "r AWAIT CONST True THEN c END"
"r WAIT b END" \<rightleftharpoons> "r AWAIT b THEN SKIP END"

nonterminal prgs

syntax
"_PAR" :: "prgs => 'a" ("COBEGIN//_//COEND" [57] 56)
"_prg" :: "['a, 'a] => prgs" ("_//_" [60, 90] 57)
"_prgs" :: "['a, 'a, prgs] => prgs" ("_//_//\<parallel>//_" [60,90,57] 57)

"_prg_scheme" :: "['a, 'a, 'a, 'a, 'a] => prgs"
("SCHEME [_ ≤ _ < _] _// _" [0,0,0,60, 90] 57)

translations
"_prg c q" \<rightleftharpoons> "[(CONST Some c, q)]"
"_prgs c q ps" \<rightleftharpoons> "(CONST Some c, q) # ps"
"_PAR ps" \<rightleftharpoons> "CONST Parallel ps"

"_prg_scheme j i k c q" \<rightleftharpoons> "CONST map (λi. (CONST Some c, q)) [j..<k]"

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;

fun annquote_tr' f (r :: t :: ts) =
Term.list_comb (f $ r $ Syntax_Trans.quote_tr' @{syntax_const "_antiquote"} t, ts)
| annquote_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 annbexp_tr' name (r :: (Const (@{const_syntax Collect}, _) $ t) :: ts) =
annquote_tr' (Syntax.const name) (r :: t :: ts)
| annbexp_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;

fun annassign_tr' (r :: Abs (x, _, f $ k $ Bound 0) :: ts) =
quote_tr' (Syntax.const @{syntax_const "_AnnAssign"} $ r $ Syntax_Trans.update_name_tr' f)
(Abs (x, dummyT, Syntax_Trans.const_abs_tr' k) :: ts)
| annassign_tr' _ = raise Match;

fun Parallel_PAR [(Const (@{const_syntax Cons}, _) $
(Const (@{const_syntax Pair}, _) $ (Const (@{const_syntax Some},_) $ t1 ) $ t2) $
Const (@{const_syntax Nil}, _))] = Syntax.const @{syntax_const "_prg"} $ t1 $ t2
| Parallel_PAR [(Const (@{const_syntax Cons}, _) $
(Const (@{const_syntax Pair}, _) $ (Const (@{const_syntax Some}, _) $ t1) $ t2) $ ts)] =
Syntax.const @{syntax_const "_prgs"} $ t1 $ t2 $ Parallel_PAR [ts]
| Parallel_PAR _ = raise Match;

fun Parallel_tr' ts = Syntax.const @{syntax_const "_PAR"} $ Parallel_PAR ts;
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_inv"})),
(@{const_syntax AnnBasic}, K annassign_tr'),
(@{const_syntax AnnWhile}, K (annbexp_tr' @{syntax_const "_AnnWhile"})),
(@{const_syntax AnnAwait}, K (annbexp_tr' @{syntax_const "_AnnAwait"})),
(@{const_syntax AnnCond1}, K (annbexp_tr' @{syntax_const "_AnnCond1"})),
(@{const_syntax AnnCond2}, K (annbexp_tr' @{syntax_const "_AnnCond2"}))]
end;
*}


end