src/HOL/Tools/function_package/fundef_package.ML

check validity of class target improvement

(*  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 extra_qualify label moreatts simps lthy =
    let
      val atts = Attrib.internal (K Simplifier.simp_add) :: moreatts
      val spec = post simps
                   |> map (apfst (apsnd (append atts)))
                   |> map (apfst (apfst extra_qualify))

      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 do_print fixes post defname cont sort_cont cnames [[proof]] lthy =
    let
      val FundefResult {fs, R, psimps, trsimps,  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 (NameSpace.qualified "partial") "psimps" [] psimps
            ||> fold_option (snd oo addsmps I "simps" []) trsimps
            ||>> note_theorem ((qualify "pinduct",
                   [Attrib.internal (K (RuleCases.case_names cnames)),
                    Attrib.internal (K (RuleCases.consumes 1)),
                    Attrib.internal (K (Induct.induct_pred ""))]), simple_pinducts)
            ||>> note_theorem ((qualify "termination", []), [termination])
            ||> (snd o note_theorem ((qualify "cases", 
                   [Attrib.internal (K (RuleCases.case_names cnames))]), [cases]))
            ||> fold_option (snd oo curry note_theorem (qualify "domintros", [])) domintros

      val cdata = FundefCtxData { add_simps=addsmps, case_names=cnames, psimps=psimps',
                                  pinducts=snd pinducts', termination=termination', fs=fs, R=R, defname=defname }
      val _ =
        if not do_print then ()
        else Specification.print_consts lthy (K false) (map fst fixes)
    in
      lthy 
        |> LocalTheory.declaration (add_fundef_data o morph_fundef_data cdata)
    end


fun gen_add_fundef is_external prep fixspec eqnss config flags lthy =
    let
      val ((fixes, spec), ctxt') = prep fixspec (map (fn (n_a, eq) => [(n_a, [eq])]) eqnss) lthy
      val (eqs, post, sort_cont, cnames) = 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 is_external fixes post defname cont sort_cont cnames
    in
      lthy
        |> is_external ? LocalTheory.set_group (serial_string ())
        |> 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, case_names, 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 I "simps" allatts tsimps |> snd
        |> note_theorem ((qualify "induct", [Attrib.internal (K (RuleCases.case_names case_names))]), 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

fun termination_cmd term_opt lthy =
  lthy
  |> LocalTheory.set_group (serial_string ())
  |> setup_termination_proof term_opt;

val add_fundef = gen_add_fundef true Specification.read_specification
val add_fundef_i = gen_add_fundef false 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

(* 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

val get_congs = FundefCtxTree.get_fundef_congs o Context.Theory


(* outer syntax *)

local structure P = OuterParse and K = OuterKeyword in

val _ = OuterSyntax.keywords ["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 (termination_cmd name)));

end;


end