(* 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 * bool) list) list list
-> FundefCommon.fundef_config
-> local_theory
-> string * Proof.state
val add_fundef_i: (string * typ option * mixfix) list
-> ((bstring * Attrib.src list) * (term * bool) list) list list
-> FundefCommon.fundef_config
-> local_theory
-> string * Proof.state
val setup_termination_proof : string option -> local_theory -> Proof.state
val cong_add: attribute
val cong_del: attribute
val setup : theory -> theory
val setup_case_cong_hook : 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 burrow_snd f ps = (* ('a list -> 'b list) -> ('c * 'a) list -> ('c * 'b) list *)
let val (xs, ys) = split_list ps
in xs ~~ f ys end
fun restore_spec_structure reps spec =
(burrow o burrow_snd o burrow o K) reps spec
fun add_simps fixes spec sort label moreatts simps lthy =
let
val fnames = map (fst o fst) fixes
val (saved_spec_simps, lthy) =
fold_map (fold_map note_theorem) (restore_spec_structure simps spec) lthy
val saved_simps = flat (map snd (flat saved_spec_simps))
val simps_by_f = sort saved_simps
fun add_for_f fname simps =
note_theorem
((NameSpace.qualified fname label, Attrib.internal (K Simplifier.simp_add) :: moreatts),
simps) #> snd
in
(saved_simps,
fold2 add_for_f fnames simps_by_f lthy)
end
fun fundef_afterqed config fixes spec defname cont sort_cont [[proof]] lthy =
let
val FundefResult {f, R, psimps, trsimps, subset_pinducts, simple_pinducts, termination, domintros, cases, ...} =
cont (Goal.close_result proof)
val qualify = NameSpace.qualified defname
val addsmps = add_simps fixes spec 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 (InductAttrib.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', f=f, R=R }
in
lthy (* FIXME proper handling of morphism *)
|> LocalTheory.declaration (fn phi => add_fundef_data defname cdata) (* save in target *)
|> Context.proof_map (add_fundef_data defname cdata) (* also save in local context *)
end (* FIXME: Add cases for induct and cases thm *)
fun prep_with_flags prep fixspec eqnss_flags global_flag lthy =
let
val eqnss = map (map (apsnd (map fst))) eqnss_flags
val flags = map (map (map (fn (_, f) => global_flag orelse f) o snd)) eqnss_flags
val ((fixes, _), ctxt') = prep fixspec [] lthy
val spec = map (fn eqns => snd (fst (prep [] eqns ctxt'))) eqnss
|> map (map (apsnd (map (fn t => fold_rev (mk_forall o Free) (frees_in_term ctxt' t) t)))) (* Add quantifiers *)
|> map2 (map2 (fn fs => fn (r, thms) => (r, fs ~~ thms))) flags
|> (burrow o burrow_snd o burrow)
(FundefSplit.split_some_equations lthy)
|> map (map (apsnd flat))
in
((fixes, spec), ctxt')
end
fun gen_add_fundef prep_spec fixspec eqnss_flags config lthy =
let
val FundefConfig {sequential, default, tailrec, ...} = config
val ((fixes, spec), ctxt') = prep_with_flags prep_spec fixspec eqnss_flags sequential lthy
val defname = mk_defname fixes
val t_eqns = spec
|> flat |> map snd |> flat (* flatten external structure *)
val ((goalstate, cont, sort_cont), lthy) =
FundefMutual.prepare_fundef_mutual config defname fixes t_eqns default lthy
val afterqed = fundef_afterqed config fixes spec defname cont sort_cont
in
(defname, 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 defname data [[totality]] lthy =
let
val FundefCtxData { add_simps, psimps, pinducts, ... } = 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
(* FIXME: How to generate code from (possibly) local contexts*)
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 NONE))]
val qualify = NameSpace.qualified defname;
in
lthy
|> add_simps "simps" allatts tsimps |> snd
|> note_theorem ((qualify "induct", []), tinduct) |> snd
end
fun setup_termination_proof name_opt lthy =
let
val defname = the_default (get_last_fundef (Context.Proof lthy)) name_opt
val data = the (get_fundef_data defname (Context.Proof lthy))
handle Option.Option => raise ERROR ("No such function definition: " ^ defname)
val FundefCtxData {termination, R, ...} = data
val goal = FundefTermination.mk_total_termination_goal R
in
lthy
|> ProofContext.note_thmss_i ""
[(("termination", [ContextRules.intro_query NONE]),
[([Goal.norm_result termination], [])])] |> snd
|> set_termination_rule termination
|> Proof.theorem_i NONE (total_termination_afterqed defname data) [[(goal, [])]]
end
val add_fundef = gen_add_fundef Specification.read_specification
val add_fundef_i = gen_add_fundef Specification.cert_specification
(* congruence rules *)
val cong_add = Thm.declaration_attribute (map_fundef_congs o Drule.add_rule o safe_mk_meta_eq);
val cong_del = Thm.declaration_attribute (map_fundef_congs o Drule.del_rule o safe_mk_meta_eq);
(* Datatype hook to declare datatype congs as "fundef_congs" *)
fun add_case_cong n thy =
Context.theory_map (map_fundef_congs (Drule.add_rule
(DatatypePackage.get_datatype thy n |> the
|> #case_cong
|> safe_mk_meta_eq)))
thy
val case_cong_hook = fold add_case_cong
val setup_case_cong_hook =
DatatypeHooks.add case_cong_hook
#> (fn thy => case_cong_hook (Symtab.keys (DatatypePackage.get_datatypes thy)) thy)
(* setup *)
val setup =
FundefData.init
#> FundefCongs.init
#> TerminationRule.init
#> Attrib.add_attributes
[("fundef_cong", Attrib.add_del_args cong_add cong_del, "declaration of congruence rule for function definitions")]
#> setup_case_cong_hook
#> FundefRelation.setup
val get_congs = FundefCommon.get_fundef_congs o Context.Theory
(* outer syntax *)
local structure P = OuterParse and K = OuterKeyword in
fun or_list1 s = P.enum1 "|" s
val opt_sequential = Scan.optional ((P.$$$ "(" |-- P.$$$ "sequential" --| P.$$$ ")") >> K true) false
val otherwise = P.$$$ "(" |-- P.$$$ "otherwise" --| P.$$$ ")"
val statement_ow = P.and_list1 (SpecParse.opt_thm_name ":" -- Scan.repeat1 (P.prop -- Scan.optional (otherwise >> K true) false))
val statements_ow = or_list1 statement_ow
val functionP =
OuterSyntax.command "function" "define general recursive functions" K.thy_goal
((config_parser default_config -- P.opt_target -- P.fixes --| P.$$$ "where" -- statements_ow)
>> (fn (((config, target), fixes), statements) =>
Toplevel.local_theory_to_proof target (add_fundef fixes statements config #> snd)
#> Toplevel.print));
val terminationP =
OuterSyntax.command "termination" "prove termination of a recursive function" K.thy_goal
(P.opt_target -- Scan.option P.name
>> (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