File function.ML


(*  Title:      HOL/Tools/Function/fundef.ML
Author: Alexander Krauss, TU Muenchen

A package for general recursive function definitions.
Isar commands.
*)

signature FUNCTION =
sig
include FUNCTION_DATA

val add_function: (binding * typ option * mixfix) list ->
(Attrib.binding * term) list -> Function_Common.function_config ->
(Proof.context -> tactic) -> local_theory -> info * local_theory

val add_function_cmd: (binding * string option * mixfix) list ->
(Attrib.binding * string) list -> Function_Common.function_config ->
(Proof.context -> tactic) -> local_theory -> info * local_theory

val function: (binding * typ option * mixfix) list ->
(Attrib.binding * term) list -> Function_Common.function_config ->
local_theory -> Proof.state

val function_cmd: (binding * string option * mixfix) list ->
(Attrib.binding * string) list -> Function_Common.function_config ->
local_theory -> Proof.state

val prove_termination: term option -> tactic -> local_theory ->
info * local_theory
val prove_termination_cmd: string option -> tactic -> local_theory ->
info * local_theory

val termination : term option -> local_theory -> Proof.state
val termination_cmd : string option -> local_theory -> Proof.state

val setup : theory -> theory
val get_congs : Proof.context -> thm list

val get_info : Proof.context -> term -> info
end


structure Function : FUNCTION =
struct

open Function_Lib
open Function_Common

val simp_attribs = map (Attrib.internal o K)
[Simplifier.simp_add,
Code.add_default_eqn_attribute,
Nitpick_Simps.add]

val psimp_attribs = map (Attrib.internal o K)
[Simplifier.simp_add,
Nitpick_Psimps.add]

fun mk_defname fixes = fixes |> map (fst o fst) |> space_implode "_"

fun add_simps fnames post sort extra_qualify label mod_binding moreatts
simps lthy =
let
val spec = post simps
|> map (apfst (apsnd (fn ats => moreatts @ ats)))
|> map (apfst (apfst extra_qualify))

val (saved_spec_simps, lthy) =
fold_map Local_Theory.note spec lthy

val saved_simps = maps snd saved_spec_simps
val simps_by_f = sort saved_simps

fun add_for_f fname simps =
Local_Theory.note
((mod_binding (Binding.qualify true fname (Binding.name label)), []), simps)
#> snd
in
(saved_simps, fold2 add_for_f fnames simps_by_f lthy)
end

fun prepare_function is_external prep default_constraint fixspec eqns config lthy =
let
val constrn_fxs = map (fn (b, T, mx) => (b, SOME (the_default default_constraint T), mx))
val ((fixes0, spec0), ctxt') = prep (constrn_fxs fixspec) eqns lthy
val fixes = map (apfst (apfst Binding.name_of)) fixes0;
val spec = map (fn (bnd, prop) => (bnd, [prop])) spec0;
val (eqs, post, sort_cont, cnames) = get_preproc lthy config ctxt' fixes spec

val defname = mk_defname fixes
val FunctionConfig {partials, ...} = config

val ((goal_state, cont), lthy') =
Function_Mutual.prepare_function_mutual config defname fixes eqs lthy

fun afterqed [[proof]] lthy =
let
val FunctionResult {fs, R, psimps, trsimps, simple_pinducts,
termination, domintros, cases, ...} =
cont (Thm.close_derivation proof)

val fnames = map (fst o fst) fixes
fun qualify n = Binding.name n
|> Binding.qualify true defname
val conceal_partial = if partials then I else Binding.conceal

val addsmps = add_simps fnames post sort_cont

val (((psimps', pinducts'), (_, [termination'])), lthy) =
lthy
|> addsmps (conceal_partial o Binding.qualify false "partial")
"psimps" conceal_partial psimp_attribs psimps
||> fold_option (snd oo addsmps I "simps" I simp_attribs) trsimps
||> fold_option (Spec_Rules.add Spec_Rules.Equational o pair fs) trsimps
||>> Local_Theory.note ((conceal_partial (qualify "pinduct"),
[Attrib.internal (K (Rule_Cases.case_names cnames)),
Attrib.internal (K (Rule_Cases.consumes 1)),
Attrib.internal (K (Induct.induct_pred ""))]), simple_pinducts)
||>> Local_Theory.note ((Binding.conceal (qualify "termination"), []), [termination])
||> (snd o Local_Theory.note ((qualify "cases",
[Attrib.internal (K (Rule_Cases.case_names cnames))]), [cases]))
||> fold_option (snd oo curry Local_Theory.note (qualify "domintros", [])) domintros

val info = { add_simps=addsmps, case_names=cnames, psimps=psimps',
pinducts=snd pinducts', simps=NONE, inducts=NONE, termination=termination',
fs=fs, R=R, defname=defname, is_partial=true }

val _ =
if not is_external then ()
else Specification.print_consts lthy (K false) (map fst fixes)
in
(info,
lthy |> Local_Theory.declaration false (add_function_data o morph_function_data info))
end
in
((goal_state, afterqed), lthy')
end

fun gen_add_function is_external prep default_constraint fixspec eqns config tac lthy =
let
val ((goal_state, afterqed), lthy') =
prepare_function is_external prep default_constraint fixspec eqns config lthy
val pattern_thm =
case SINGLE (tac lthy') goal_state of
NONE => error "pattern completeness and compatibility proof failed"
| SOME st => Goal.finish lthy' st
in
lthy'
|> afterqed [[pattern_thm]]
end

val add_function =
gen_add_function false Specification.check_spec (Type_Infer.anyT HOLogic.typeS)
val add_function_cmd = gen_add_function true Specification.read_spec "_::type"

fun gen_function is_external prep default_constraint fixspec eqns config lthy =
let
val ((goal_state, afterqed), lthy') =
prepare_function is_external prep default_constraint fixspec eqns config lthy
in
lthy'
|> Proof.theorem NONE (snd oo afterqed) [[(Logic.unprotect (concl_of goal_state), [])]]
|> Proof.refine (Method.primitive_text (K goal_state)) |> Seq.hd
end

val function =
gen_function false Specification.check_spec (Type_Infer.anyT HOLogic.typeS)
val function_cmd = gen_function true Specification.read_spec "_::type"

fun prepare_termination_proof prep_term raw_term_opt lthy =
let
val term_opt = Option.map (prep_term lthy) raw_term_opt
val info = the (case term_opt of
SOME t => (import_function_data t lthy
handle Option.Option =>
error ("Not a function: " ^ quote (Syntax.string_of_term lthy t)))
| NONE => (import_last_function lthy handle Option.Option => error "Not a function"))

val { termination, fs, R, add_simps, case_names, psimps,
pinducts, defname, ...} = info
val domT = domain_type (fastype_of R)
val goal = HOLogic.mk_Trueprop
(HOLogic.mk_all ("x", domT, mk_acc domT R $ Free ("x", domT)))
fun afterqed [[totality]] lthy =
let
val totality = Thm.close_derivation totality
val remove_domain_condition =
full_simplify (HOL_basic_ss addsimps [totality, @{thm True_implies_equals}])
val tsimps = map remove_domain_condition psimps
val tinduct = map remove_domain_condition pinducts

fun qualify n = Binding.name n
|> Binding.qualify true defname
in
lthy
|> add_simps I "simps" I simp_attribs tsimps
||>> Local_Theory.note
((qualify "induct",
[Attrib.internal (K (Rule_Cases.case_names case_names))]),
tinduct)
|-> (fn (simps, (_, inducts)) => fn lthy =>
let val info' = { is_partial=false, defname=defname, add_simps=add_simps,
case_names=case_names, fs=fs, R=R, psimps=psimps, pinducts=pinducts,
simps=SOME simps, inducts=SOME inducts, termination=termination }
in
(info',
lthy
|> Local_Theory.declaration false (add_function_data o morph_function_data info')
|> Spec_Rules.add Spec_Rules.Equational (fs, tsimps))
end)
end
in
(goal, afterqed, termination)
end

fun gen_prove_termination prep_term raw_term_opt tac lthy =
let
val (goal, afterqed, termination) =
prepare_termination_proof prep_term raw_term_opt lthy

val totality = Goal.prove lthy [] [] goal (K tac)
in
afterqed [[totality]] lthy
end

val prove_termination = gen_prove_termination Syntax.check_term
val prove_termination_cmd = gen_prove_termination Syntax.read_term

fun gen_termination prep_term raw_term_opt lthy =
let
val (goal, afterqed, termination) = prepare_termination_proof prep_term raw_term_opt lthy
in
lthy
|> ProofContext.note_thmss ""
[((Binding.empty, [Context_Rules.rule_del]), [([allI], [])])] |> snd
|> ProofContext.note_thmss ""
[((Binding.empty, [Context_Rules.intro_bang (SOME 1)]), [([allI], [])])] |> snd
|> ProofContext.note_thmss ""
[((Binding.name "termination", [Context_Rules.intro_bang (SOME 0)]),
[([Goal.norm_result termination], [])])] |> snd
|> Proof.theorem NONE (snd oo afterqed) [[(goal, [])]]
end

val termination = gen_termination Syntax.check_term
val termination_cmd = gen_termination Syntax.read_term


(* Datatype hook to declare datatype congs as "function_congs" *)


fun add_case_cong n thy =
let
val cong = #case_cong (Datatype.the_info thy n)
|> safe_mk_meta_eq
in
Context.theory_map
(Function_Ctx_Tree.map_function_congs (Thm.add_thm cong)) thy
end

val setup_case_cong = Datatype.interpretation (K (fold add_case_cong))


(* setup *)

val setup =
Attrib.setup @{binding fundef_cong}
(Attrib.add_del Function_Ctx_Tree.cong_add Function_Ctx_Tree.cong_del)
"declaration of congruence rule for function definitions"
#> setup_case_cong
#> Function_Relation.setup
#> Function_Common.Termination_Simps.setup

val get_congs = Function_Ctx_Tree.get_function_congs

fun get_info ctxt t = Item_Net.retrieve (get_function ctxt) t
|> the_single |> snd


(* outer syntax *)

val _ =
Outer_Syntax.local_theory_to_proof "function" "define general recursive functions"
Keyword.thy_goal
(function_parser default_config
>> (fn ((config, fixes), statements) => function_cmd fixes statements config))

val _ =
Outer_Syntax.local_theory_to_proof "termination" "prove termination of a recursive function"
Keyword.thy_goal
(Scan.option Parse.term >> termination_cmd)


end