src/HOL/Tools/function_package/fundef_package.ML
author krauss
Mon Oct 29 10:37:09 2007 +0100 (2007-10-29)
changeset 25222 78943ac46f6d
parent 25201 e6fe58b640ce
child 26129 14f6dbb195c4
permissions -rw-r--r--
fun/function: generate case names for induction rules
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(*  Title:      HOL/Tools/function_package/fundef_package.ML
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    ID:         $Id$
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    Author:     Alexander Krauss, TU Muenchen
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A package for general recursive function definitions.
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Isar commands.
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*)
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signature FUNDEF_PACKAGE =
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sig
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    val add_fundef :  (string * string option * mixfix) list
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                      -> ((bstring * Attrib.src list) * string) list 
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                      -> FundefCommon.fundef_config
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                      -> bool list
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                      -> local_theory
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                      -> Proof.state
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    val add_fundef_i:  (string * typ option * mixfix) list
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                       -> ((bstring * Attrib.src list) * term) list
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                       -> FundefCommon.fundef_config
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                       -> bool list
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                       -> local_theory
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                       -> Proof.state
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    val setup_termination_proof : string option -> local_theory -> Proof.state
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    val setup : theory -> theory
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    val get_congs : theory -> thm list
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end
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structure FundefPackage : FUNDEF_PACKAGE =
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struct
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open FundefLib
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open FundefCommon
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val note_theorem = LocalTheory.note Thm.theoremK
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fun mk_defname fixes = fixes |> map (fst o fst) |> space_implode "_" 
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fun add_simps fnames post sort label moreatts simps lthy =
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    let
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      val atts = Attrib.internal (K Simplifier.simp_add) :: moreatts
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      val spec = post simps
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                   |> map (apfst (apsnd (append atts)))
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      val (saved_spec_simps, lthy) =
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        fold_map note_theorem spec lthy
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      val saved_simps = flat (map snd saved_spec_simps)
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      val simps_by_f = sort saved_simps
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      fun add_for_f fname simps =
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        note_theorem ((NameSpace.qualified fname label, []), simps) #> snd
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    in
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      (saved_simps,
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       fold2 add_for_f fnames simps_by_f lthy)
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    end
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fun fundef_afterqed config fixes post defname cont sort_cont cnames [[proof]] lthy =
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    let
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      val FundefResult {fs, R, psimps, trsimps, subset_pinducts, simple_pinducts, termination, domintros, cases, ...} = 
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          cont (Goal.close_result proof)
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      val fnames = map (fst o fst) fixes
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      val qualify = NameSpace.qualified defname
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      val addsmps = add_simps fnames post sort_cont
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      val (((psimps', pinducts'), (_, [termination'])), lthy) =
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          lthy
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            |> addsmps "psimps" [] psimps
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            ||> fold_option (snd oo addsmps "simps" []) trsimps
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            ||>> note_theorem ((qualify "pinduct",
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                   [Attrib.internal (K (RuleCases.case_names cnames)),
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                    Attrib.internal (K (RuleCases.consumes 1)),
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                    Attrib.internal (K (Induct.induct_pred ""))]), simple_pinducts)
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            ||>> note_theorem ((qualify "termination", []), [termination])
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            ||> (snd o note_theorem ((qualify "cases", 
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                   [Attrib.internal (K (RuleCases.case_names cnames))]), [cases]))
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            ||> fold_option (snd oo curry note_theorem (qualify "domintros", [])) domintros
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      val cdata = FundefCtxData { add_simps=addsmps, case_names=cnames, psimps=psimps',
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                                  pinducts=snd pinducts', termination=termination', fs=fs, R=R, defname=defname }
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      val _ = Specification.print_consts lthy (K false) (map fst fixes)
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    in
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      lthy 
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        |> LocalTheory.declaration (add_fundef_data o morph_fundef_data cdata)
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    end
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fun gen_add_fundef prep fixspec eqnss config flags lthy =
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    let
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      val ((fixes, spec), ctxt') = prep fixspec (map (fn (n_a, eq) => [(n_a, [eq])]) eqnss) lthy
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      val (eqs, post, sort_cont, cnames) = FundefCommon.get_preproc lthy config flags ctxt' fixes spec
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      val defname = mk_defname fixes
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      val ((goalstate, cont), lthy) =
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          FundefMutual.prepare_fundef_mutual config defname fixes eqs lthy
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      val afterqed = fundef_afterqed config fixes post defname cont sort_cont cnames
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    in
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      lthy
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        |> Proof.theorem_i NONE afterqed [[(Logic.unprotect (concl_of goalstate), [])]]
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        |> Proof.refine (Method.primitive_text (fn _ => goalstate)) |> Seq.hd
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    end
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fun total_termination_afterqed data [[totality]] lthy =
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    let
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      val FundefCtxData { add_simps, case_names, psimps, pinducts, defname, ... } = data
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      val totality = Goal.close_result totality
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      val remove_domain_condition = full_simplify (HOL_basic_ss addsimps [totality, True_implies_equals])
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      val tsimps = map remove_domain_condition psimps
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      val tinduct = map remove_domain_condition pinducts
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      val has_guards = exists ((fn (Const ("Trueprop", _) $ _) => false | _ => true) o prop_of) tsimps
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      val allatts = if has_guards then [] else [Attrib.internal (K RecfunCodegen.add_default)]
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      val qualify = NameSpace.qualified defname;
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    in
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      lthy
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        |> add_simps "simps" allatts tsimps |> snd
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        |> note_theorem ((qualify "induct", [Attrib.internal (K (RuleCases.case_names case_names))]), tinduct) |> snd
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    end
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fun setup_termination_proof term_opt lthy =
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    let
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      val data = the (case term_opt of
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                        SOME t => import_fundef_data (Syntax.read_term lthy t) (Context.Proof lthy)
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                      | NONE => import_last_fundef (Context.Proof lthy))
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          handle Option.Option => raise ERROR ("Not a function: " ^ quote (the_default "" term_opt))
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        val FundefCtxData {termination, R, ...} = data
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        val domT = domain_type (fastype_of R)
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        val goal = HOLogic.mk_Trueprop (HOLogic.mk_all ("x", domT, mk_acc domT R $ Free ("x", domT)))
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    in
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      lthy
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        |> ProofContext.note_thmss_i "" [(("", [ContextRules.rule_del]), [([allI], [])])] |> snd
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        |> ProofContext.note_thmss_i "" [(("", [ContextRules.intro_bang (SOME 1)]), [([allI], [])])] |> snd
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        |> ProofContext.note_thmss_i ""
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          [(("termination", [ContextRules.intro_bang (SOME 0)]),
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            [([Goal.norm_result termination], [])])] |> snd
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        |> Proof.theorem_i NONE (total_termination_afterqed data) [[(goal, [])]]
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    end
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val add_fundef = gen_add_fundef Specification.read_specification
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val add_fundef_i = gen_add_fundef Specification.check_specification
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(* Datatype hook to declare datatype congs as "fundef_congs" *)
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fun add_case_cong n thy =
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    Context.theory_map (FundefCtxTree.map_fundef_congs (Thm.add_thm
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                          (DatatypePackage.get_datatype thy n |> the
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                           |> #case_cong
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                           |> safe_mk_meta_eq)))
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                       thy
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val case_cong = fold add_case_cong
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val setup_case_cong = DatatypePackage.interpretation case_cong
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(* ad-hoc method to convert elimination-style goals to existential statements *)
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fun insert_int_goal thy subg st =
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    let
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      val goal = hd (prems_of st)
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      val (ps, imp) = dest_all_all goal
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      val cps = map (cterm_of thy) ps
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      val imp_subg = fold (fn p => fn t => betapply (t,p)) ps subg
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      val new_subg = implies $ imp_subg $ imp
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                      |> fold_rev mk_forall ps
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                      |> cterm_of thy 
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                      |> assume 
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      val sg2 = imp_subg
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                 |> fold_rev mk_forall ps
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                 |> cterm_of thy 
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                 |> assume
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      val t' = new_subg
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                |> fold forall_elim cps
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                |> Thm.elim_implies (fold forall_elim cps sg2)
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                |> fold_rev forall_intr cps
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      val st' = implies_elim st t'
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                 |> implies_intr (cprop_of sg2)
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                 |> implies_intr (cprop_of new_subg)
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    in
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      Seq.single st'
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    end
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fun mk_cases_statement thy t =
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    let
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      fun mk_clause t = 
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          let 
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            val (qs, imp) = dest_all_all t
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          in 
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            Logic.strip_imp_prems imp
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             |> map (ObjectLogic.atomize_term thy)
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             |> foldr1 HOLogic.mk_conj
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             |> fold_rev (fn Free (v,T) => fn t => HOLogic.mk_exists (v,T,t)) qs
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          end
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      val (ps, imp) = dest_all_all t
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    in 
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      Logic.strip_imp_prems imp
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       |> map mk_clause
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       |> foldr1 HOLogic.mk_disj
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       |> HOLogic.mk_Trueprop
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       |> fold_rev lambda ps
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    end
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fun elim_to_cases1 ctxt st =
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    let
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      val thy = theory_of_thm st
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      val [subg] = prems_of st
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      val cex = mk_cases_statement thy subg
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    in
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      (insert_int_goal thy cex
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       THEN REPEAT_ALL_NEW (Tactic.ematch_tac [disjE, exE, conjE]) 1
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       THEN REPEAT (Goal.assume_rule_tac ctxt 1)
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    (*   THEN REPEAT (etac thin_rl 1)*)) st
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    end
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fun elim_to_cases_tac ctxt = SELECT_GOAL (elim_to_cases1 ctxt)
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val elim_to_cases_setup = Method.add_methods
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  [("elim_to_cases", Method.ctxt_args (Method.SIMPLE_METHOD' o elim_to_cases_tac),
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    "convert elimination-style goal to a disjunction of existentials")]
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(* setup *)
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val setup =
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  Attrib.add_attributes
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    [("fundef_cong", Attrib.add_del_args FundefCtxTree.cong_add FundefCtxTree.cong_del,
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      "declaration of congruence rule for function definitions")]
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  #> setup_case_cong
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  #> FundefRelation.setup
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  #> elim_to_cases_setup
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val get_congs = FundefCtxTree.get_fundef_congs o Context.Theory
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(* outer syntax *)
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local structure P = OuterParse and K = OuterKeyword in
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val _ = OuterSyntax.keywords ["otherwise"];
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val _ =
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  OuterSyntax.command "function" "define general recursive functions" K.thy_goal
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  (fundef_parser default_config
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     >> (fn ((config, fixes), (flags, statements)) =>
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            Toplevel.local_theory_to_proof (target_of config) (add_fundef fixes statements config flags)
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            #> Toplevel.print));
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val _ =
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  OuterSyntax.command "termination" "prove termination of a recursive function" K.thy_goal
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  (P.opt_target -- Scan.option P.term
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    >> (fn (target, name) =>
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           Toplevel.print o
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           Toplevel.local_theory_to_proof target (setup_termination_proof name)));
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end;
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end