(*  Title:      HOL/Tools/choice_specification.ML

     Author:     Sebastian Skalberg, TU Muenchen

 Package for defining constants by specification.

 *)

 signature CHOICE_SPECIFICATION =

 sig

   val close_form : term -> term

   val add_specification: string option -> (bstring * xstring * bool) list ->

     theory * thm -> theory * thm

 end

 structure Choice_Specification: CHOICE_SPECIFICATION =

 struct

 (* actual code *)

 fun close_form t =

     fold_rev (fn (s, T) => fn t => HOLogic.mk_all (s, T, t))

              (map dest_Free (OldTerm.term_frees t)) t

 local

     fun mk_definitional [] arg = arg

       | mk_definitional ((thname,cname,covld)::cos) (thy,thm) =

         case HOLogic.dest_Trueprop (concl_of thm) of

             Const(@{const_name Ex},_) $ P =>

             let

                 val ctype = domain_type (type_of P)

                 val cname_full = Sign.intern_const thy cname

                 val cdefname = if thname = ""

                                then Thm.def_name (Long_Name.base_name cname)

                                else thname

                 val def_eq = Logic.mk_equals (Const(cname_full,ctype),

                                               HOLogic.choice_const ctype $  P)

                 val (thms, thy') = Global_Theory.add_defs covld [((Binding.name cdefname, def_eq),[])] thy

                 val thm' = [thm,hd thms] MRS @{thm exE_some}

             in

                 mk_definitional cos (thy',thm')

             end

           | _ => raise THM ("Internal error: Bad specification theorem",0,[thm])

     fun mk_axiomatic axname cos arg =

         let

             fun process [] (thy,tm) =

                 let

                     val (thm, thy') =

                       Specification.axiom ((Binding.name axname, []), HOLogic.mk_Trueprop tm) thy

                 in

                     (thy', Drule.export_without_context thm)

                 end

               | process ((thname,cname,covld)::cos) (thy,tm) =

                 case tm of

                     Const(@{const_name Ex},_) $ P =>

                     let

                         val ctype = domain_type (type_of P)

                         val cname_full = Sign.intern_const thy cname

                         val cdefname = if thname = ""

                                        then Thm.def_name (Long_Name.base_name cname)

                                        else thname

                         val co = Const(cname_full,ctype)

                         val thy' = Theory.add_finals_i covld [co] thy

                         val tm' = case P of

                                       Abs(_, _, bodt) => subst_bound (co, bodt)

                                     | _ => P $ co

                     in

                         process cos (thy',tm')

                     end

                   | _ => raise TERM ("Internal error: Bad specification theorem",[tm])

         in

             process cos arg

         end

 in

 fun proc_exprop axiomatic cos arg =

     case axiomatic of

         SOME axname => mk_axiomatic axname cos (apsnd (HOLogic.dest_Trueprop o concl_of) arg)

       | NONE => mk_definitional cos arg

 end

 fun add_specification axiomatic cos =

     proc_exprop axiomatic cos

     #> apsnd Drule.export_without_context

 (* Collect all intances of constants in term *)

 fun collect_consts (        t $ u,tms) = collect_consts (u,collect_consts (t,tms))

   | collect_consts (   Abs(_,_,t),tms) = collect_consts (t,tms)

   | collect_consts (tm as Const _,tms) = insert (op aconv) tm tms

   | collect_consts (            _,tms) = tms

 (* Complementing Type.varify_global... *)

 fun unvarify_global t fmap =

     let

         val fmap' = map Library.swap fmap

         fun unthaw (f as (a, S)) =

             (case AList.lookup (op =) fmap' a of

                  NONE => TVar f

                | SOME (b, _) => TFree (b, S))

     in

         map_types (map_type_tvar unthaw) t

     end

 (* The syntactic meddling needed to setup add_specification for work *)

 fun process_spec axiomatic cos alt_props thy =

     let

         fun zip3 [] [] [] = []

           | zip3 (x::xs) (y::ys) (z::zs) = (x,y,z)::zip3 xs ys zs

           | zip3 _ _ _ = error "Choice_Specification.process_spec internal error"

         fun myfoldr f [x] = x

           | myfoldr f (x::xs) = f (x,myfoldr f xs)

           | myfoldr f [] = error "Choice_Specification.process_spec internal error"

         val rew_imps = alt_props |>

           map (Object_Logic.atomize o Thm.cterm_of thy o Syntax.read_prop_global thy o snd)

         val props' = rew_imps |>

           map (HOLogic.dest_Trueprop o term_of o snd o Thm.dest_equals o cprop_of)

         fun proc_single prop =

             let

                 val frees = OldTerm.term_frees prop

                 val _ = forall (fn v => Sign.of_sort thy (type_of v,HOLogic.typeS)) frees

                   orelse error "Specificaton: Only free variables of sort 'type' allowed"

                 val prop_closed = close_form prop

             in

                 (prop_closed,frees)

             end

         val props'' = map proc_single props'

         val frees = map snd props''

         val prop  = myfoldr HOLogic.mk_conj (map fst props'')

         val cprop = cterm_of thy (HOLogic.mk_Trueprop prop)

         val (vmap, prop_thawed) = Type.varify_global [] prop

         val thawed_prop_consts = collect_consts (prop_thawed,[])

         val (altcos,overloaded) = Library.split_list cos

         val (names,sconsts) = Library.split_list altcos

         val consts = map (Syntax.read_term_global thy) sconsts

         val _ = not (Library.exists (not o Term.is_Const) consts)

           orelse error "Specification: Non-constant found as parameter"

         fun proc_const c =

             let

                 val (_, c') = Type.varify_global [] c

                 val (cname,ctyp) = dest_Const c'

             in

                 case filter (fn t => let val (name,typ) = dest_Const t

                                      in name = cname andalso Sign.typ_equiv thy (typ, ctyp)

                                      end) thawed_prop_consts of

                     [] => error ("Specification: No suitable instances of constant \"" ^ Syntax.string_of_term_global thy c ^ "\" found")

                   | [cf] => unvarify_global cf vmap

                   | _ => error ("Specification: Several variations of \"" ^ Syntax.string_of_term_global thy c ^ "\" found (try applying explicit type constraints)")

             end

         val proc_consts = map proc_const consts

         fun mk_exist c prop =

             let

                 val T = type_of c

                 val cname = Long_Name.base_name (fst (dest_Const c))

                 val vname = if Syntax.is_identifier cname

                             then cname

                             else "x"

             in

                 HOLogic.exists_const T $ Abs(vname,T,Term.abstract_over (c,prop))

             end

         val ex_prop = fold_rev mk_exist proc_consts prop

         val cnames = map (fst o dest_Const) proc_consts

         fun post_process (arg as (thy,thm)) =

             let

                 fun inst_all thy v thm =

                     let

                         val cv = cterm_of thy v

                         val cT = ctyp_of_term cv

                         val spec' = instantiate' [SOME cT] [NONE,SOME cv] spec

                     in

                         thm RS spec'

                     end

                 fun remove_alls frees thm =

                     fold (inst_all (Thm.theory_of_thm thm)) frees thm

                 fun process_single ((name,atts),rew_imp,frees) args =

                     let

                         fun undo_imps thm =

                             Thm.equal_elim (Thm.symmetric rew_imp) thm

                         fun add_final (arg as (thy, thm)) =

                             if name = ""

                             then arg |> Library.swap

                             else (writeln ("  " ^ name ^ ": " ^ Display.string_of_thm_global thy thm);

                                   Global_Theory.store_thm (Binding.name name, thm) thy)

                     in

                         args |> apsnd (remove_alls frees)

                              |> apsnd undo_imps

                              |> apsnd Drule.export_without_context

                              |> Thm.theory_attributes (map (Attrib.attribute thy)

                                                            (Attrib.internal (K Nitpick_Choice_Specs.add) :: atts))

                              |> add_final

                              |> Library.swap

                     end

                 fun process_all [proc_arg] args =

                     process_single proc_arg args

                   | process_all (proc_arg::rest) (thy,thm) =

                     let

                         val single_th = thm RS conjunct1

                         val rest_th   = thm RS conjunct2

                         val (thy',_)  = process_single proc_arg (thy,single_th)

                     in

                         process_all rest (thy',rest_th)

                     end

                   | process_all [] _ = error "Choice_Specification.process_spec internal error"

                 val alt_names = map fst alt_props

                 val _ = if exists (fn(name,_) => not (name = "")) alt_names

                         then writeln "specification"

                         else ()

             in

                 arg |> apsnd Thm.unvarify_global

                     |> process_all (zip3 alt_names rew_imps frees)

             end

       fun after_qed [[thm]] = ProofContext.background_theory (fn thy =>

         #1 (post_process (add_specification axiomatic (zip3 names cnames overloaded) (thy, thm))));

     in

       thy

       |> ProofContext.init_global

       |> Variable.declare_term ex_prop

       |> Proof.theorem NONE after_qed [[(HOLogic.mk_Trueprop ex_prop, [])]]

     end;

 (* outer syntax *)

 val opt_name = Scan.optional (Parse.name --| Parse.$$$ ":") ""

 val opt_overloaded = Parse.opt_keyword "overloaded"

 val specification_decl =

   Parse.$$$ "(" |-- Scan.repeat1 (opt_name -- Parse.term -- opt_overloaded) --| Parse.$$$ ")" --

           Scan.repeat1 ((Parse_Spec.opt_thm_name ":" >> apfst Binding.name_of) -- Parse.prop)

 val _ =

   Outer_Syntax.command "specification" "define constants by specification" Keyword.thy_goal

     (specification_decl >> (fn (cos,alt_props) =>

                                Toplevel.print o (Toplevel.theory_to_proof

                                                      (process_spec NONE cos alt_props))))

 val ax_specification_decl =

     Parse.name --

     (Parse.$$$ "(" |-- Scan.repeat1 (opt_name -- Parse.term -- opt_overloaded) --| Parse.$$$ ")" --

            Scan.repeat1 ((Parse_Spec.opt_thm_name ":" >> apfst Binding.name_of) -- Parse.prop))

 val _ =

   Outer_Syntax.command "ax_specification" "define constants by specification" Keyword.thy_goal

     (ax_specification_decl >> (fn (axname,(cos,alt_props)) =>

                                Toplevel.print o (Toplevel.theory_to_proof

                                                      (process_spec (SOME axname) cos alt_props))))

 end