krauss@19564: (*  Title:      HOL/Tools/function_package/fundef_package.ML
krauss@19564:     ID:         $Id$
krauss@19564:     Author:     Alexander Krauss, TU Muenchen
krauss@19564: 
wenzelm@20363: A package for general recursive function definitions.
krauss@19564: Isar commands.
krauss@19564: 
krauss@19564: *)
krauss@19564: 
wenzelm@20363: signature FUNDEF_PACKAGE =
krauss@19564: sig
wenzelm@20877:     val add_fundef :  (string * string option * mixfix) list
krauss@23203:                       -> ((bstring * Attrib.src list) * string) list 
wenzelm@20877:                       -> FundefCommon.fundef_config
krauss@23203:                       -> bool list
wenzelm@20877:                       -> local_theory
krauss@22733:                       -> Proof.state
krauss@20523: 
wenzelm@20877:     val add_fundef_i:  (string * typ option * mixfix) list
krauss@23203:                        -> ((bstring * Attrib.src list) * term) list
krauss@22170:                        -> FundefCommon.fundef_config
krauss@23203:                        -> bool list
wenzelm@20877:                        -> local_theory
krauss@22733:                        -> Proof.state
krauss@21211: 
krauss@21211:     val setup_termination_proof : string option -> local_theory -> Proof.state
krauss@19564: 
krauss@19564:     val setup : theory -> theory
krauss@21235:     val setup_case_cong_hook : theory -> theory
krauss@19770:     val get_congs : theory -> thm list
krauss@19564: end
krauss@19564: 
krauss@19564: 
krauss@23203: structure FundefPackage : FUNDEF_PACKAGE =
krauss@19564: struct
krauss@19564: 
krauss@21051: open FundefLib
krauss@19564: open FundefCommon
krauss@19564: 
wenzelm@21435: val note_theorem = LocalTheory.note Thm.theoremK
wenzelm@21435: 
krauss@22166: fun mk_defname fixes = fixes |> map (fst o fst) |> space_implode "_" 
krauss@22166: 
krauss@23819: fun add_simps fnames post sort label moreatts simps lthy =
krauss@19564:     let
krauss@23819:       val atts = Attrib.internal (K Simplifier.simp_add) :: moreatts
krauss@23819:       val spec = post simps
krauss@23819:                    |> map (apfst (apsnd (append atts)))
krauss@21255: 
krauss@22166:       val (saved_spec_simps, lthy) =
krauss@23819:         fold_map note_theorem spec lthy
krauss@23819: 
krauss@22498:       val saved_simps = flat (map snd saved_spec_simps)
krauss@22166:       val simps_by_f = sort saved_simps
krauss@19564: 
krauss@22166:       fun add_for_f fname simps =
krauss@23819:         note_theorem ((NameSpace.qualified fname label, []), simps) #> snd
krauss@19564:     in
krauss@22166:       (saved_simps,
krauss@22166:        fold2 add_for_f fnames simps_by_f lthy)
krauss@19564:     end
krauss@19564: 
krauss@23203: fun fundef_afterqed config fixes post defname cont sort_cont [[proof]] lthy =
krauss@20523:     let
krauss@22733:       val FundefResult {fs, R, psimps, trsimps, subset_pinducts, simple_pinducts, termination, domintros, cases, ...} = 
krauss@22166:           cont (Goal.close_result proof)
krauss@22166: 
krauss@23819:       val fnames = map (fst o fst) fixes
wenzelm@21391:       val qualify = NameSpace.qualified defname
krauss@23819:       val addsmps = add_simps fnames post sort_cont
wenzelm@21602: 
wenzelm@21602:       val (((psimps', pinducts'), (_, [termination'])), lthy) =
krauss@21255:           lthy
krauss@22170:             |> addsmps "psimps" [] psimps
krauss@22170:             ||> fold_option (snd oo addsmps "simps" []) trsimps
krauss@22166:             ||>> note_theorem ((qualify "pinduct",
krauss@22166:                                 [Attrib.internal (K (InductAttrib.induct_set ""))]), simple_pinducts)
krauss@22166:             ||>> note_theorem ((qualify "termination", []), [termination])
krauss@22166:             ||> (snd o note_theorem ((qualify "cases", []), [cases]))
krauss@22166:             ||> fold_option (snd oo curry note_theorem (qualify "domintros", [])) domintros
krauss@21255: 
krauss@22170:       val cdata = FundefCtxData { add_simps=addsmps, psimps=psimps',
krauss@22733:                                   pinducts=snd pinducts', termination=termination', fs=fs, R=R, defname=defname }
wenzelm@22668:       val cdata' = cdata |> morph_fundef_data (LocalTheory.target_morphism lthy);  (* FIXME !? *)
krauss@20523:     in
krauss@22623:       lthy 
krauss@22733:         |> LocalTheory.declaration (fn phi => add_fundef_data (morph_fundef_data phi cdata)) (* save in target *)
krauss@22733:         |> Context.proof_map (add_fundef_data cdata') (* also save in local context *)
krauss@20523:     end (* FIXME: Add cases for induct and cases thm *)
krauss@20523: 
krauss@20523: 
krauss@23203: fun prepare_spec prep fixspec eqnss lthy = (* FIXME: obsolete when "read_specification" etc. is there *)
krauss@19564:     let
krauss@23203:       val eqns = map (apsnd single) eqnss
krauss@22498: 
krauss@23203:       val ((fixes, _), ctxt') = prep fixspec [] lthy             
krauss@23203:       fun prep_eqn e = the_single (snd (fst (prep [] [e] ctxt')))
krauss@23189: 
krauss@23203:       val spec = map prep_eqn eqns
krauss@23203:                  |> map (apsnd (map (fn t => fold_rev (mk_forall o Free) (frees_in_term ctxt' t) t))) (* Add quantifiers *)
krauss@20523:     in
krauss@20523:       ((fixes, spec), ctxt')
krauss@20523:     end
krauss@20523: 
krauss@23203: fun gen_add_fundef prep fixspec eqnss config flags lthy =
krauss@20523:     let
krauss@23203:       val ((fixes, spec), ctxt') = prepare_spec prep fixspec eqnss lthy
krauss@23819:       val (eqs, post, sort_cont) = FundefCommon.get_preproc lthy config flags ctxt' fixes spec
krauss@22166: 
krauss@22166:       val defname = mk_defname fixes
krauss@22166: 
krauss@23819:       val ((goalstate, cont), lthy) =
krauss@23203:           FundefMutual.prepare_fundef_mutual config defname fixes eqs lthy
krauss@20523: 
krauss@23203:       val afterqed = fundef_afterqed config fixes post defname cont sort_cont
krauss@20523:     in
krauss@22733:       lthy
krauss@22733:         |> Proof.theorem_i NONE afterqed [[(Logic.unprotect (concl_of goalstate), [])]]
krauss@22733:         |> Proof.refine (Method.primitive_text (fn _ => goalstate)) |> Seq.hd
krauss@20523:     end
krauss@20523: 
krauss@22733: fun total_termination_afterqed data [[totality]] lthy =
krauss@20523:     let
krauss@22733:       val FundefCtxData { add_simps, psimps, pinducts, defname, ... } = data
krauss@21255: 
krauss@22166:       val totality = Goal.close_result totality
krauss@19564: 
krauss@21255:       val remove_domain_condition = full_simplify (HOL_basic_ss addsimps [totality, True_implies_equals])
krauss@19564: 
krauss@22166:       val tsimps = map remove_domain_condition psimps
krauss@22166:       val tinduct = map remove_domain_condition pinducts
krauss@19770: 
krauss@21511:       val has_guards = exists ((fn (Const ("Trueprop", _) $ _) => false | _ => true) o prop_of) tsimps
haftmann@24624:       val allatts = if has_guards then [] else [Attrib.internal (K RecfunCodegen.add_default)]
wenzelm@21602: 
krauss@21511:       val qualify = NameSpace.qualified defname;
krauss@19564:     in
krauss@21511:       lthy
krauss@22166:         |> add_simps "simps" allatts tsimps |> snd
krauss@22166:         |> note_theorem ((qualify "induct", []), tinduct) |> snd
wenzelm@20363:     end
krauss@19564: 
krauss@19564: 
krauss@22733: fun setup_termination_proof term_opt lthy =
krauss@20523:     let
krauss@22733:       val data = the (case term_opt of
wenzelm@24508:                         SOME t => import_fundef_data (Syntax.read_term lthy t) (Context.Proof lthy)
krauss@22733:                       | NONE => import_last_fundef (Context.Proof lthy))
krauss@22733:           handle Option.Option => raise ERROR ("Not a function: " ^ quote (the_default "" term_opt))
krauss@20523: 
krauss@22166:         val FundefCtxData {termination, R, ...} = data
krauss@22325:         val domT = domain_type (fastype_of R)
krauss@22325:         val goal = HOLogic.mk_Trueprop (HOLogic.mk_all ("x", domT, mk_acc domT R $ Free ("x", domT)))
krauss@20523:     in
wenzelm@20877:       lthy
krauss@22325:         |> ProofContext.note_thmss_i "" [(("", [ContextRules.rule_del]), [([allI], [])])] |> snd
krauss@22325:         |> ProofContext.note_thmss_i "" [(("", [ContextRules.intro_bang (SOME 1)]), [([allI], [])])] |> snd
wenzelm@21602:         |> ProofContext.note_thmss_i ""
krauss@22325:           [(("termination", [ContextRules.intro_bang (SOME 0)]),
wenzelm@21602:             [([Goal.norm_result termination], [])])] |> snd
krauss@22733:         |> Proof.theorem_i NONE (total_termination_afterqed data) [[(goal, [])]]
krauss@20523:     end
krauss@20523: 
krauss@20523: 
krauss@20523: val add_fundef = gen_add_fundef Specification.read_specification
krauss@20523: val add_fundef_i = gen_add_fundef Specification.cert_specification
krauss@19611: 
krauss@19564: 
krauss@21235: (* Datatype hook to declare datatype congs as "fundef_congs" *)
krauss@21235: 
krauss@21235: 
wenzelm@21602: fun add_case_cong n thy =
krauss@24168:     Context.theory_map (FundefCtxTree.map_fundef_congs (Thm.add_thm
krauss@21235:                           (DatatypePackage.get_datatype thy n |> the
krauss@21235:                            |> #case_cong
wenzelm@21602:                            |> safe_mk_meta_eq)))
krauss@21235:                        thy
krauss@21235: 
krauss@21235: val case_cong_hook = fold add_case_cong
krauss@21235: 
wenzelm@21602: val setup_case_cong_hook =
krauss@21235:     DatatypeHooks.add case_cong_hook
krauss@21235:     #> (fn thy => case_cong_hook (Symtab.keys (DatatypePackage.get_datatypes thy)) thy)
krauss@19564: 
krauss@23819: 
krauss@23473: (* ad-hoc method to convert elimination-style goals to existential statements *)
krauss@23473: 
krauss@23473: fun insert_int_goal thy subg st =
krauss@23473:     let
krauss@23473:       val goal = hd (prems_of st)
krauss@23473:       val (ps, imp) = dest_all_all goal
krauss@23473:       val cps = map (cterm_of thy) ps
krauss@23473: 
krauss@23473:       val imp_subg = fold (fn p => fn t => betapply (t,p)) ps subg
krauss@23473:       val new_subg = implies $ imp_subg $ imp
krauss@23473:                       |> fold_rev mk_forall ps
krauss@23473:                       |> cterm_of thy 
krauss@23473:                       |> assume 
krauss@23473: 
krauss@23473:       val sg2 = imp_subg
krauss@23473:                  |> fold_rev mk_forall ps
krauss@23473:                  |> cterm_of thy 
krauss@23473:                  |> assume
krauss@23473: 
krauss@23473:       val t' = new_subg
krauss@23473:                 |> fold forall_elim cps
krauss@23473:                 |> flip implies_elim (fold forall_elim cps sg2)
krauss@23473:                 |> fold_rev forall_intr cps
krauss@23473: 
krauss@23473:       val st' = implies_elim st t'
krauss@23473:                  |> implies_intr (cprop_of sg2)
krauss@23473:                  |> implies_intr (cprop_of new_subg)
krauss@23473:     in
krauss@23473:       Seq.single st'
krauss@23473:     end
krauss@23473: 
krauss@23473: fun mk_cases_statement thy t =
krauss@23473:     let
krauss@23473:       fun mk_clause t = 
krauss@23473:           let 
krauss@23473:             val (qs, imp) = dest_all_all t
krauss@23473:           in 
krauss@23473:             Logic.strip_imp_prems imp
krauss@23473:              |> map (ObjectLogic.atomize_term thy)
krauss@23473:              |> foldr1 HOLogic.mk_conj
krauss@23473:              |> fold_rev (fn Free (v,T) => fn t => HOLogic.mk_exists (v,T,t)) qs
krauss@23473:           end
krauss@23473: 
krauss@23473:       val (ps, imp) = dest_all_all t
krauss@23473:     in 
krauss@23473:       Logic.strip_imp_prems imp
krauss@23473:        |> map mk_clause
krauss@23473:        |> foldr1 HOLogic.mk_disj
krauss@23473:        |> HOLogic.mk_Trueprop
krauss@23473:        |> fold_rev lambda ps
krauss@23473:     end
krauss@23473: 
krauss@23473: fun elim_to_cases1 ctxt st =
krauss@23473:     let
krauss@23473:       val thy = theory_of_thm st
krauss@23473:       val [subg] = prems_of st
krauss@23473:       val cex = mk_cases_statement thy subg
krauss@23473:     in
krauss@23473:       (insert_int_goal thy cex
krauss@23473:        THEN REPEAT_ALL_NEW (Tactic.ematch_tac [disjE, exE, conjE]) 1
krauss@23473:        THEN REPEAT (Goal.assume_rule_tac ctxt 1)
krauss@23473:     (*   THEN REPEAT (etac thin_rl 1)*)) st
krauss@23473:     end
krauss@23473: 
krauss@23473: fun elim_to_cases_tac ctxt = SELECT_GOAL (elim_to_cases1 ctxt)
krauss@23473: 
krauss@23473: val elim_to_cases_setup = Method.add_methods
krauss@23473:   [("elim_to_cases", Method.ctxt_args (Method.SIMPLE_METHOD' o elim_to_cases_tac),
krauss@23473:     "convert elimination-style goal to a disjunction of existentials")]
krauss@23473: 
krauss@19564: (* setup *)
krauss@19564: 
wenzelm@21602: val setup =
wenzelm@22846:   Attrib.add_attributes
krauss@24168:     [("fundef_cong", Attrib.add_del_args FundefCtxTree.cong_add FundefCtxTree.cong_del,
wenzelm@22846:       "declaration of congruence rule for function definitions")]
wenzelm@22846:   #> setup_case_cong_hook
wenzelm@22846:   #> FundefRelation.setup
krauss@23473:   #> elim_to_cases_setup
krauss@19564: 
krauss@24168: val get_congs = FundefCtxTree.get_fundef_congs o Context.Theory
krauss@19770: 
krauss@21235: 
krauss@19564: (* outer syntax *)
krauss@19564: 
krauss@19564: local structure P = OuterParse and K = OuterKeyword in
krauss@19564: 
krauss@19564: val functionP =
krauss@19564:   OuterSyntax.command "function" "define general recursive functions" K.thy_goal
krauss@22498:   (fundef_parser default_config
krauss@23203:      >> (fn ((config, fixes), (flags, statements)) =>
krauss@23203:             Toplevel.local_theory_to_proof (target_of config) (add_fundef fixes statements config flags)
krauss@21211:             #> Toplevel.print));
krauss@20523: 
krauss@19564: val terminationP =
krauss@19564:   OuterSyntax.command "termination" "prove termination of a recursive function" K.thy_goal
krauss@22733:   (P.opt_target -- Scan.option P.term
wenzelm@21000:     >> (fn (target, name) =>
wenzelm@21000:            Toplevel.print o
krauss@21211:            Toplevel.local_theory_to_proof target (setup_termination_proof name)));
krauss@19564: 
krauss@19564: val _ = OuterSyntax.add_parsers [functionP];
krauss@19564: val _ = OuterSyntax.add_parsers [terminationP];
krauss@20654: val _ = OuterSyntax.add_keywords ["sequential", "otherwise"];
krauss@19564: 
krauss@19564: end;
krauss@19564: 
krauss@19564: 
wenzelm@19585: end