(*  Title:      HOL/Tools/function_package/fundef_package.ML

    ID:         $Id$

    Author:     Alexander Krauss, TU Muenchen

A package for general recursive function definitions.

Isar commands.

*)

signature FUNDEF_PACKAGE =

sig

    val add_fundef :  (string * string option * mixfix) list

                      -> ((bstring * Attrib.src list) * string) list 

                      -> FundefCommon.fundef_config

                      -> bool list

                      -> local_theory

                      -> Proof.state

    val add_fundef_i:  (string * typ option * mixfix) list

                       -> ((bstring * Attrib.src list) * term) list

                       -> FundefCommon.fundef_config

                       -> bool list

                       -> local_theory

                       -> Proof.state

    val setup_termination_proof : string option -> local_theory -> Proof.state

    val setup : theory -> theory

    val get_congs : theory -> thm list

end

structure FundefPackage : FUNDEF_PACKAGE =

struct

open FundefLib

open FundefCommon

val note_theorem = LocalTheory.note Thm.theoremK

fun mk_defname fixes = fixes |> map (fst o fst) |> space_implode "_" 

fun add_simps fnames post sort label moreatts simps lthy =

    let

      val atts = Attrib.internal (K Simplifier.simp_add) :: moreatts

      val spec = post simps

                   |> map (apfst (apsnd (append atts)))

      val (saved_spec_simps, lthy) =

        fold_map note_theorem spec lthy

      val saved_simps = flat (map snd saved_spec_simps)

      val simps_by_f = sort saved_simps

      fun add_for_f fname simps =

        note_theorem ((NameSpace.qualified fname label, []), simps) #> snd

    in

      (saved_simps,

       fold2 add_for_f fnames simps_by_f lthy)

    end

fun fundef_afterqed config fixes post defname cont sort_cont [[proof]] lthy =

    let

      val FundefResult {fs, R, psimps, trsimps, subset_pinducts, simple_pinducts, termination, domintros, cases, ...} = 

          cont (Goal.close_result proof)

      val fnames = map (fst o fst) fixes

      val qualify = NameSpace.qualified defname

      val addsmps = add_simps fnames post sort_cont

      val (((psimps', pinducts'), (_, [termination'])), lthy) =

          lthy

            |> addsmps "psimps" [] psimps

            ||> fold_option (snd oo addsmps "simps" []) trsimps

            ||>> note_theorem ((qualify "pinduct",

                                [Attrib.internal (K (Induct.induct_pred ""))]), simple_pinducts)

            ||>> note_theorem ((qualify "termination", []), [termination])

            ||> (snd o note_theorem ((qualify "cases", []), [cases]))

            ||> fold_option (snd oo curry note_theorem (qualify "domintros", [])) domintros

      val cdata = FundefCtxData { add_simps=addsmps, psimps=psimps',

                                  pinducts=snd pinducts', termination=termination', fs=fs, R=R, defname=defname }

      val cdata' = cdata |> morph_fundef_data (LocalTheory.target_morphism lthy);  (* FIXME !? *)

    in

      lthy 

        |> LocalTheory.declaration (fn phi => add_fundef_data (morph_fundef_data phi cdata)) (* save in target *)

        |> Context.proof_map (add_fundef_data cdata') (* also save in local context *)

    end (* FIXME: Add cases for induct and cases thm *)

fun prepare_spec prep fixspec eqnss lthy = (* FIXME: obsolete; use Specification.read/check_specification *)

    let

      val eqns = map (apsnd single) eqnss

      val ((fixes, _), ctxt') = prep fixspec [] lthy             

      fun prep_eqn e = the_single (snd (fst (prep [] [[e]] ctxt')))

      val spec = map prep_eqn eqns

                 |> map (apsnd (map (fn t => fold_rev (mk_forall o Free) (frees_in_term ctxt' t) t))) (* Add quantifiers *)

    in

      ((fixes, spec), ctxt')

    end

fun gen_add_fundef prep fixspec eqnss config flags lthy =

    let

      val ((fixes, spec), ctxt') = prepare_spec prep fixspec eqnss lthy

      val (eqs, post, sort_cont) = FundefCommon.get_preproc lthy config flags ctxt' fixes spec

      val defname = mk_defname fixes

      val ((goalstate, cont), lthy) =

          FundefMutual.prepare_fundef_mutual config defname fixes eqs lthy

      val afterqed = fundef_afterqed config fixes post defname cont sort_cont

    in

      lthy

        |> Proof.theorem_i NONE afterqed [[(Logic.unprotect (concl_of goalstate), [])]]

        |> Proof.refine (Method.primitive_text (fn _ => goalstate)) |> Seq.hd

    end

fun total_termination_afterqed data [[totality]] lthy =

    let

      val FundefCtxData { add_simps, psimps, pinducts, defname, ... } = data

      val totality = Goal.close_result totality

      val remove_domain_condition = full_simplify (HOL_basic_ss addsimps [totality, True_implies_equals])

      val tsimps = map remove_domain_condition psimps

      val tinduct = map remove_domain_condition pinducts

      val has_guards = exists ((fn (Const ("Trueprop", _) $ _) => false | _ => true) o prop_of) tsimps

      val allatts = if has_guards then [] else [Attrib.internal (K RecfunCodegen.add_default)]

      val qualify = NameSpace.qualified defname;

    in

      lthy

        |> add_simps "simps" allatts tsimps |> snd

        |> note_theorem ((qualify "induct", []), tinduct) |> snd

    end

fun setup_termination_proof term_opt lthy =

    let

      val data = the (case term_opt of

                        SOME t => import_fundef_data (Syntax.read_term lthy t) (Context.Proof lthy)

                      | NONE => import_last_fundef (Context.Proof lthy))

          handle Option.Option => raise ERROR ("Not a function: " ^ quote (the_default "" term_opt))

        val FundefCtxData {termination, R, ...} = data

        val domT = domain_type (fastype_of R)

        val goal = HOLogic.mk_Trueprop (HOLogic.mk_all ("x", domT, mk_acc domT R $ Free ("x", domT)))

    in

      lthy

        |> ProofContext.note_thmss_i "" [(("", [ContextRules.rule_del]), [([allI], [])])] |> snd

        |> ProofContext.note_thmss_i "" [(("", [ContextRules.intro_bang (SOME 1)]), [([allI], [])])] |> snd

        |> ProofContext.note_thmss_i ""

          [(("termination", [ContextRules.intro_bang (SOME 0)]),

            [([Goal.norm_result termination], [])])] |> snd

        |> Proof.theorem_i NONE (total_termination_afterqed data) [[(goal, [])]]

    end

val add_fundef = gen_add_fundef Specification.read_specification

val add_fundef_i = gen_add_fundef Specification.check_specification

(* Datatype hook to declare datatype congs as "fundef_congs" *)

fun add_case_cong n thy =

    Context.theory_map (FundefCtxTree.map_fundef_congs (Thm.add_thm

                          (DatatypePackage.get_datatype thy n |> the

                           |> #case_cong

                           |> safe_mk_meta_eq)))

                       thy

val case_cong = fold add_case_cong

val setup_case_cong = DatatypePackage.interpretation case_cong

(* ad-hoc method to convert elimination-style goals to existential statements *)

fun insert_int_goal thy subg st =

    let

      val goal = hd (prems_of st)

      val (ps, imp) = dest_all_all goal

      val cps = map (cterm_of thy) ps

      val imp_subg = fold (fn p => fn t => betapply (t,p)) ps subg

      val new_subg = implies $ imp_subg $ imp

                      |> fold_rev mk_forall ps

                      |> cterm_of thy 

                      |> assume 

      val sg2 = imp_subg

                 |> fold_rev mk_forall ps

                 |> cterm_of thy 

                 |> assume

      val t' = new_subg

                |> fold forall_elim cps

                |> flip implies_elim (fold forall_elim cps sg2)

                |> fold_rev forall_intr cps

      val st' = implies_elim st t'

                 |> implies_intr (cprop_of sg2)

                 |> implies_intr (cprop_of new_subg)

    in

      Seq.single st'

    end

fun mk_cases_statement thy t =

    let

      fun mk_clause t = 

          let 

            val (qs, imp) = dest_all_all t

          in 

            Logic.strip_imp_prems imp

             |> map (ObjectLogic.atomize_term thy)

             |> foldr1 HOLogic.mk_conj

             |> fold_rev (fn Free (v,T) => fn t => HOLogic.mk_exists (v,T,t)) qs

          end

      val (ps, imp) = dest_all_all t

    in 

      Logic.strip_imp_prems imp

       |> map mk_clause

       |> foldr1 HOLogic.mk_disj

       |> HOLogic.mk_Trueprop

       |> fold_rev lambda ps

    end

fun elim_to_cases1 ctxt st =

    let

      val thy = theory_of_thm st

      val [subg] = prems_of st

      val cex = mk_cases_statement thy subg

    in

      (insert_int_goal thy cex

       THEN REPEAT_ALL_NEW (Tactic.ematch_tac [disjE, exE, conjE]) 1

       THEN REPEAT (Goal.assume_rule_tac ctxt 1)

    (*   THEN REPEAT (etac thin_rl 1)*)) st

    end

fun elim_to_cases_tac ctxt = SELECT_GOAL (elim_to_cases1 ctxt)

val elim_to_cases_setup = Method.add_methods

  [("elim_to_cases", Method.ctxt_args (Method.SIMPLE_METHOD' o elim_to_cases_tac),

    "convert elimination-style goal to a disjunction of existentials")]

(* setup *)

val setup =

  Attrib.add_attributes

    [("fundef_cong", Attrib.add_del_args FundefCtxTree.cong_add FundefCtxTree.cong_del,

      "declaration of congruence rule for function definitions")]

  #> setup_case_cong

  #> FundefRelation.setup

  #> elim_to_cases_setup

val get_congs = FundefCtxTree.get_fundef_congs o Context.Theory

(* outer syntax *)

local structure P = OuterParse and K = OuterKeyword in

val _ = OuterSyntax.keywords ["sequential", "otherwise"];

val _ =

  OuterSyntax.command "function" "define general recursive functions" K.thy_goal

  (fundef_parser default_config

     >> (fn ((config, fixes), (flags, statements)) =>

            Toplevel.local_theory_to_proof (target_of config) (add_fundef fixes statements config flags)

            #> Toplevel.print));

val _ =

  OuterSyntax.command "termination" "prove termination of a recursive function" K.thy_goal

  (P.opt_target -- Scan.option P.term

    >> (fn (target, name) =>

           Toplevel.print o

           Toplevel.local_theory_to_proof target (setup_termination_proof name)));

end;

end