moved Pure/Isar/induct_attrib.ML and Provers/induct_method.ML to Tools/induct.ML;
(* 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_set ""))]), 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 functionP =
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 terminationP =
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)));
val _ = OuterSyntax.add_parsers [functionP];
val _ = OuterSyntax.add_parsers [terminationP];
val _ = OuterSyntax.add_keywords ["sequential", "otherwise"];
end;
end