(*  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 (Misc_Legacy.term_frees t)) t

fun add_final overloaded (c, T) thy =

  let

    val ctxt = Syntax.init_pretty_global thy;

    val _ = Theory.check_overloading ctxt overloaded (c, T);

  in Theory.add_deps ctxt "" (c, T) [] thy end;

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 thy' = add_final covld (cname_full,ctype) thy

                        val co = Const (cname_full,ctype)

                        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 = Misc_Legacy.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 Lexicon.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 (thm, thy) =

                            if name = ""

                            then (thm, thy)

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

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

                    in

                        swap args

                             |> apfst (remove_alls frees)

                             |> apfst undo_imps

                             |> apfst Drule.export_without_context

                             |-> Thm.theory_attributes

                                (map (Attrib.attribute thy)

                                  (@{attributes [nitpick_choice_spec]} @ atts))

                             |> add_final

                             |> 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]] = Proof_Context.background_theory (fn thy =>

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

    in

      thy

      |> Proof_Context.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 --| @{keyword ":"}) ""

val opt_overloaded = Parse.opt_keyword "overloaded"

val _ =

  Outer_Syntax.command @{command_spec "specification"} "define constants by specification"

    (@{keyword "("} |-- Scan.repeat1 (opt_name -- Parse.term -- opt_overloaded) --| @{keyword ")"} --

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

      >> (fn (cos, alt_props) => Toplevel.print o

          (Toplevel.theory_to_proof (process_spec NONE cos alt_props))))

val _ =

  Outer_Syntax.command @{command_spec "ax_specification"} "define constants by specification"

    (Parse.name --

      (@{keyword "("} |-- Scan.repeat1 (opt_name -- Parse.term -- opt_overloaded) --| @{keyword ")"} --

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

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

           Toplevel.print o (Toplevel.theory_to_proof (process_spec (SOME axname) cos alt_props))))

end