# Theory OG_Syntax

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theory OG_Syntax
imports OG_Tactics Quote_Antiquote
begin

    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}. *}

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

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

    syntax
      "_AnnSkip"     :: "'a assn => 'a ann_com"              ("_//SKIP" [90] 63)
      "_AnnSeq"      :: "'a ann_com => 'a ann_com => 'a ann_com"  ("_;;/ _" [60,61] 60)

      "_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)

      "_Skip"        :: "'a com"                 ("SKIP" 63)
      "_Seq"         :: "'a com => 'a com => 'a com" ("_,,/ _" [55, 56] 55)
      "_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
      "SKIP" \<rightleftharpoons> "Basic id"
      "c_1,, c_2" \<rightleftharpoons> "Seq c_1 c_2"

      "IF b THEN c1 ELSE c2 FI" \<rightharpoonup> "Cond .{b}. c1 c2"
      "IF b THEN c FI" \<rightleftharpoons> "IF b THEN c ELSE SKIP FI"
      "WHILE b INV i DO c OD" \<rightharpoonup> "While .{b}. i c"
      "WHILE b DO c OD" \<rightleftharpoons> "WHILE b INV arbitrary DO c OD"

      "r SKIP" \<rightleftharpoons> "AnnBasic r id"
      "c_1;; c_2" \<rightleftharpoons> "AnnSeq c_1 c_2"
      "r IF b THEN c1 ELSE c2 FI" \<rightharpoonup> "AnnCond1 r .{b}. c1 c2"
      "r IF b THEN c FI" \<rightharpoonup> "AnnCond2 r .{b}. c"
      "r WHILE b INV i DO c OD" \<rightharpoonup> "AnnWhile r .{b}. i c"
      "r AWAIT b THEN c END" \<rightharpoonup> "AnnAwait r .{b}. c"
      "r ⟨c⟩" \<rightleftharpoons> "r AWAIT True THEN c END"
      "r WAIT b END" \<rightleftharpoons> "r AWAIT b THEN SKIP END"

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

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

    print_translation {*
      let
        fun quote_tr' f (t :: ts) =
              Term.list_comb (f $ Syntax.quote_tr' "_antiquote" t, ts)
          | quote_tr' _ _ = raise Match;

        fun annquote_tr' f (r :: t :: ts) =
              Term.list_comb (f $ r $ Syntax.quote_tr' "_antiquote" t, ts)
          | annquote_tr' _ _ = raise Match;

        val assert_tr' = quote_tr' (Syntax.const "_Assert");

        fun bexp_tr' name ((Const ("Collect", _) $ t) :: ts) =
              quote_tr' (Syntax.const name) (t :: ts)
          | bexp_tr' _ _ = raise Match;

        fun annbexp_tr' name (r :: (Const ("Collect", _) $ t) :: ts) =
              annquote_tr' (Syntax.const name) (r :: t :: ts)
          | annbexp_tr' _ _ = raise Match;

        fun upd_tr' (x_upd, T) =
          (case try (unsuffix RecordPackage.updateN) x_upd of
            SOME x => (x, if T = dummyT then T else Term.domain_type T)
          | NONE => raise Match);

        fun update_name_tr' (Free x) = Free (upd_tr' x)
          | update_name_tr' ((c as Const ("_free", _)) $ Free x) =
              c $ Free (upd_tr' x)
          | update_name_tr' (Const x) = Const (upd_tr' x)
          | update_name_tr' _ = raise Match;

        fun assign_tr' (Abs (x, _, f $ t $ Bound 0) :: ts) =
              quote_tr' (Syntax.const "_Assign" $ update_name_tr' f)
                (Abs (x, dummyT, t) :: ts)
          | assign_tr' _ = raise Match;

        fun annassign_tr' (r :: Abs (x, _, f $ t $ Bound 0) :: ts) =
              quote_tr' (Syntax.const "_AnnAssign" $ r $ update_name_tr' f)
                (Abs (x, dummyT, t) :: ts)
          | annassign_tr' _ = raise Match;

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

    fun Parallel_tr' ts = Syntax.const "_PAR" $ Parallel_PAR ts;
      in
        [("Collect", assert_tr'), ("Basic", assign_tr'),
          ("Cond", bexp_tr' "_Cond"), ("While", bexp_tr' "_While_inv"),
          ("AnnBasic", annassign_tr'),
          ("AnnWhile", annbexp_tr' "_AnnWhile"), ("AnnAwait", annbexp_tr' "_AnnAwait"),
          ("AnnCond1", annbexp_tr' "_AnnCond1"), ("AnnCond2", annbexp_tr' "_AnnCond2")]

      end

    *}

    end