theory FSet3

imports "../../../Nominal/FSet"

begin

(* TBD *)

text {* syntax for fset comprehensions (adapted from lists) *}

nonterminals fsc_qual fsc_quals

syntax

"_fsetcompr" :: "'a \<Rightarrow> fsc_qual \<Rightarrow> fsc_quals \<Rightarrow> 'a fset"  ("{|_ . __")

"_fsc_gen" :: "'a \<Rightarrow> 'a fset \<Rightarrow> fsc_qual" ("_ <- _")

"_fsc_test" :: "bool \<Rightarrow> fsc_qual" ("_")

"_fsc_end" :: "fsc_quals" ("|}")

"_fsc_quals" :: "fsc_qual \<Rightarrow> fsc_quals \<Rightarrow> fsc_quals" (", __")

"_fsc_abs" :: "'a => 'b fset => 'b fset"

syntax (xsymbols)

"_fsc_gen" :: "'a \<Rightarrow> 'a fset \<Rightarrow> fsc_qual" ("_ \<leftarrow> _")

syntax (HTML output)

"_fsc_gen" :: "'a \<Rightarrow> 'a fset \<Rightarrow> fsc_qual" ("_ \<leftarrow> _")

parse_translation (advanced) {*

let

  val femptyC = Syntax.const @{const_name fempty};

  val finsertC = Syntax.const @{const_name finsert};

  val fmapC = Syntax.const @{const_name fmap};

  val fconcatC = Syntax.const @{const_name fconcat};

  val IfC = Syntax.const @{const_name If};

  fun fsingl x = finsertC $ x $ femptyC;

  fun pat_tr ctxt p e opti = (* %x. case x of p => e | _ => [] *)

    let

      val x = Free (Name.variant (fold Term.add_free_names [p, e] []) "x", dummyT);

      val e = if opti then fsingl e else e;

      val case1 = Syntax.const "_case1" $ p $ e;

      val case2 = Syntax.const "_case1" $ Syntax.const Term.dummy_patternN

                                        $ femptyC;

      val cs = Syntax.const "_case2" $ case1 $ case2

      val ft = Datatype_Case.case_tr false Datatype.info_of_constr

                 ctxt [x, cs]

    in lambda x ft end;

  fun abs_tr ctxt (p as Free(s,T)) e opti =

        let val thy = ProofContext.theory_of ctxt;

            val s' = Sign.intern_const thy s

        in if Sign.declared_const thy s'

           then (pat_tr ctxt p e opti, false)

           else (lambda p e, true)

        end

    | abs_tr ctxt p e opti = (pat_tr ctxt p e opti, false);

  fun fsc_tr ctxt [e, Const("_fsc_test",_) $ b, qs] =

        let 

          val res = case qs of 

                      Const("_fsc_end",_) => fsingl e

                    | Const("_fsc_quals",_)$ q $ qs => fsc_tr ctxt [e, q, qs];

        in 

          IfC $ b $ res $ femptyC 

        end

    | fsc_tr ctxt [e, Const("_fsc_gen",_) $ p $ es, Const("_fsc_end",_)] =

         (case abs_tr ctxt p e true of

            (f,true) => fmapC $ f $ es

          | (f, false) => fconcatC $ (fmapC $ f $ es))

    | fsc_tr ctxt [e, Const("_fsc_gen",_) $ p $ es, Const("_fsc_quals",_) $ q $ qs] =

        let

          val e' = fsc_tr ctxt [e, q, qs];

        in 

          fconcatC $ (fmapC $ (fst (abs_tr ctxt p e' false)) $ es) 

        end

in [("_fsetcompr", fsc_tr)] end

*}

(* NEEDS FIXING *)

(* examles *)

(*

term "{|(x,y,z). b|}"

term "{|x. x \<leftarrow> xs|}"

term "{|(x,y,z). x\<leftarrow>xs|}"

term "{|e x y. x\<leftarrow>xs, y\<leftarrow>ys|}"

term "{|(x,y,z). x<a, x>b|}"

term "{|(x,y,z). x\<leftarrow>xs, x>b|}"

term "{|(x,y,z). x<a, x\<leftarrow>xs|}"

term "{|(x,y). Cons True x \<leftarrow> xs|}"

term "{|(x,y,z). Cons x [] \<leftarrow> xs|}"

term "{|(x,y,z). x<a, x>b, x=d|}"

term "{|(x,y,z). x<a, x>b, y\<leftarrow>ys|}"

term "{|(x,y,z). x<a, x\<leftarrow>xs,y>b|}"

term "{|(x,y,z). x<a, x\<leftarrow>xs, y\<leftarrow>ys|}"

term "{|(x,y,z). x\<leftarrow>xs, x>b, y<a|}"

term "{|(x,y,z). x\<leftarrow>xs, x>b, y\<leftarrow>ys|}"

term "{|(x,y,z). x\<leftarrow>xs, y\<leftarrow>ys,y>x|}"

term "{|(x,y,z). x\<leftarrow>xs, y\<leftarrow>ys,z\<leftarrow>zs|}"

*)

(* BELOW CONSTRUCTION SITE *)

end