(* Title: Pure/Isar/method.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
License: GPL (GNU GENERAL PUBLIC LICENSE)
Proof methods.
*)
signature BASIC_METHOD =
sig
val print_methods: theory -> unit
val Method: bstring -> (Args.src -> Proof.context -> Proof.method) -> string -> unit
end;
signature METHOD =
sig
include BASIC_METHOD
val print_global_rules: theory -> unit
val print_local_rules: Proof.context -> unit
val dest_global: theory attribute
val elim_global: theory attribute
val intro_global: theory attribute
val delrule_global: theory attribute
val dest_local: Proof.context attribute
val elim_local: Proof.context attribute
val intro_local: Proof.context attribute
val delrule_local: Proof.context attribute
val METHOD: (thm list -> tactic) -> Proof.method
val METHOD_CASES:
(thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq) -> Proof.method
val METHOD0: tactic -> Proof.method
val fail: Proof.method
val succeed: Proof.method
val defer: int option -> Proof.method
val prefer: int -> Proof.method
val insert_tac: thm list -> int -> tactic
val insert: thm list -> Proof.method
val insert_facts: Proof.method
val unfold: thm list -> Proof.method
val fold: thm list -> Proof.method
val multi_resolve: thm list -> thm -> thm Seq.seq
val multi_resolves: thm list -> thm list -> thm Seq.seq
val resolveq_tac: thm Seq.seq -> int -> tactic
val resolveq_cases_tac: bool -> (thm * string list) Seq.seq
-> int -> thm -> (thm * (string * RuleCases.T) list) Seq.seq
val rule_tac: thm list -> thm list -> int -> tactic
val rule: thm list -> Proof.method
val erule: thm list -> Proof.method
val drule: thm list -> Proof.method
val frule: thm list -> Proof.method
val this: Proof.method
val assumption: Proof.context -> Proof.method
val set_tactic: (Proof.context -> thm list -> tactic) -> unit
val tactic: string -> Proof.context -> Proof.method
exception METHOD_FAIL of (string * Position.T) * exn
val method: theory -> Args.src -> Proof.context -> Proof.method
val add_method: bstring * (Args.src -> Proof.context -> Proof.method) * string -> theory -> theory
val add_methods: (bstring * (Args.src -> Proof.context -> Proof.method) * string) list
-> theory -> theory
val syntax: (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list)) ->
Args.src -> Proof.context -> Proof.context * 'a
val simple_args: (Args.T list -> 'a * Args.T list)
-> ('a -> Proof.context -> Proof.method) -> Args.src -> Proof.context -> Proof.method
val ctxt_args: (Proof.context -> Proof.method) -> Args.src -> Proof.context -> Proof.method
val no_args: Proof.method -> Args.src -> Proof.context -> Proof.method
type modifier
val sectioned_args: (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list)) ->
(Args.T list -> modifier * Args.T list) list ->
('a -> Proof.context -> Proof.method) -> Args.src -> Proof.context -> Proof.method
val bang_sectioned_args:
(Args.T list -> modifier * Args.T list) list ->
(thm list -> Proof.context -> Proof.method) -> Args.src -> Proof.context -> Proof.method
val only_sectioned_args:
(Args.T list -> modifier * Args.T list) list ->
(Proof.context -> Proof.method) -> Args.src -> Proof.context -> Proof.method
val thms_ctxt_args: (thm list -> Proof.context -> Proof.method)
-> Args.src -> Proof.context -> Proof.method
val thms_args: (thm list -> Proof.method) -> Args.src -> Proof.context -> Proof.method
datatype text =
Basic of (Proof.context -> Proof.method) |
Source of Args.src |
Then of text list |
Orelse of text list |
Try of text |
Repeat1 of text
val refine: text -> Proof.state -> Proof.state Seq.seq
val refine_end: text -> Proof.state -> Proof.state Seq.seq
val proof: text option -> Proof.state -> Proof.state Seq.seq
val local_qed: bool -> text option
-> ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)
-> Proof.state -> Proof.state Seq.seq
val local_terminal_proof: text * text option
-> ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)
-> Proof.state -> Proof.state Seq.seq
val local_default_proof: ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)
-> Proof.state -> Proof.state Seq.seq
val local_immediate_proof: ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)
-> Proof.state -> Proof.state Seq.seq
val local_done_proof: ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)
-> Proof.state -> Proof.state Seq.seq
val global_qed: bool -> text option
-> Proof.state -> theory * {kind: string, name: string, thm: thm}
val global_terminal_proof: text * text option
-> Proof.state -> theory * {kind: string, name: string, thm: thm}
val global_default_proof: Proof.state -> theory * {kind: string, name: string, thm: thm}
val global_immediate_proof: Proof.state -> theory * {kind: string, name: string, thm: thm}
val global_done_proof: Proof.state -> theory * {kind: string, name: string, thm: thm}
val setup: (theory -> theory) list
end;
structure Method: METHOD =
struct
(** global and local rule data **)
fun prt_rules kind ths =
Pretty.writeln (Pretty.big_list ("standard " ^ kind ^ " rules:") (map Display.pretty_thm ths));
fun print_rules (intro, elim) =
(prt_rules "introduction" intro; prt_rules "elimination" elim);
fun merge_rules (ths1, ths2) = Library.generic_merge Thm.eq_thm I I ths1 ths2;
(* theory data kind 'Isar/rules' *)
structure GlobalRulesArgs =
struct
val name = "Isar/rules";
type T = thm list * thm list;
val empty = ([], []);
val copy = I;
val prep_ext = I;
fun merge ((intro1, elim1), (intro2, elim2)) =
(merge_rules (intro1, intro2), merge_rules (elim1, elim2));
fun print _ = print_rules;
end;
structure GlobalRules = TheoryDataFun(GlobalRulesArgs);
val print_global_rules = GlobalRules.print;
(* proof data kind 'Isar/rules' *)
structure LocalRulesArgs =
struct
val name = "Isar/rules";
type T = thm list * thm list;
val init = GlobalRules.get;
fun print _ = print_rules;
end;
structure LocalRules = ProofDataFun(LocalRulesArgs);
val print_local_rules = LocalRules.print;
(** attributes **)
(* add rules *)
local
fun add_rule thm rules = Library.gen_ins Thm.eq_thm (thm, rules);
fun del_rule thm rules = Library.gen_rem Thm.eq_thm (rules, thm);
fun add_dest thm (intro, elim) = (intro, add_rule (Tactic.make_elim thm) elim);
fun add_elim thm (intro, elim) = (intro, add_rule thm elim);
fun add_intro thm (intro, elim) = (add_rule thm intro, elim);
fun delrule thm (intro, elim) = (del_rule thm intro, del_rule thm elim);
fun mk_att f g (x, thm) = (f (g thm) x, thm);
in
val dest_global = mk_att GlobalRules.map add_dest;
val elim_global = mk_att GlobalRules.map add_elim;
val intro_global = mk_att GlobalRules.map add_intro;
val delrule_global = mk_att GlobalRules.map delrule;
val dest_local = mk_att LocalRules.map add_dest;
val elim_local = mk_att LocalRules.map add_elim;
val intro_local = mk_att LocalRules.map add_intro;
val delrule_local = mk_att LocalRules.map delrule;
end;
(* concrete syntax *)
val rule_atts =
[("dest", (Attrib.no_args dest_global, Attrib.no_args dest_local), "declare destruction rule"),
("elim", (Attrib.no_args elim_global, Attrib.no_args elim_local), "declare elimination rule"),
("intro", (Attrib.no_args intro_global, Attrib.no_args intro_local), "declare introduction rule"),
("delrule", (Attrib.no_args delrule_global, Attrib.no_args delrule_local), "undeclare rule")];
(** proof methods **)
(* make methods *)
val METHOD = Proof.method;
val METHOD_CASES = Proof.method_cases;
fun METHOD0 tac = METHOD (fn [] => tac | _ => error "Cannot handle current facts");
(* primitive *)
val fail = METHOD (K no_tac);
val succeed = METHOD (K all_tac);
(* shuffle *)
fun prefer i = METHOD (K (Tactic.defer_tac i THEN PRIMITIVE (Thm.permute_prems 0 ~1)));
fun defer opt_i = METHOD (K (Tactic.defer_tac (if_none opt_i 1)));
(* insert *)
local
fun cut_rule_tac raw_rule =
let
val rule = Drule.forall_intr_vars raw_rule;
val revcut_rl = Drule.incr_indexes_wrt [] [] [] [rule] Drule.revcut_rl;
in Tactic.rtac (rule COMP revcut_rl) end;
in
fun insert_tac [] i = all_tac
| insert_tac facts i = EVERY (map (fn th => cut_rule_tac th i) facts);
val insert_facts = METHOD (ALLGOALS o insert_tac);
fun insert thms = METHOD (fn _ => ALLGOALS (insert_tac thms));
end;
(* unfold / fold definitions *)
fun unfold thms = METHOD (fn facts => ALLGOALS (insert_tac facts) THEN rewrite_goals_tac thms);
fun fold thms = METHOD (fn facts => ALLGOALS (insert_tac facts) THEN fold_goals_tac thms);
(* multi_resolve *)
local
fun res th i rule =
Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;
fun multi_res _ [] rule = Seq.single rule
| multi_res i (th :: ths) rule = Seq.flat (Seq.map (res th i) (multi_res (i + 1) ths rule));
in
val multi_resolve = multi_res 1;
fun multi_resolves facts rules = Seq.flat (Seq.map (multi_resolve facts) (Seq.of_list rules));
end;
(* general rule *)
fun gen_resolveq_tac tac rules i st =
Seq.flat (Seq.map (fn rule => tac rule i st) rules);
val resolveq_tac = gen_resolveq_tac Tactic.rtac;
fun resolveq_cases_tac opaq = gen_resolveq_tac (fn (rule, cases) => fn i => fn st =>
Seq.map (rpair (RuleCases.make opaq rule cases)) (Tactic.rtac rule i st));
(* simple rule *)
local
fun gen_rule_tac tac rules [] = tac rules
| gen_rule_tac tac erules facts = gen_resolveq_tac (tac o single) (multi_resolves facts erules);
fun gen_rule tac rules = METHOD (HEADGOAL o tac rules);
fun gen_rule' tac arg_rules ctxt = METHOD (fn facts =>
let val rules =
if not (null arg_rules) then arg_rules
else if null facts then #1 (LocalRules.get ctxt)
else op @ (LocalRules.get ctxt);
in HEADGOAL (tac rules facts) end);
fun setup raw_tac =
let val tac = gen_rule_tac raw_tac
in (tac, gen_rule tac, gen_rule' tac) end;
in
val (rule_tac, rule, some_rule) = setup Tactic.resolve_tac;
val (erule_tac, erule, some_erule) = setup Tactic.eresolve_tac;
val (drule_tac, drule, some_drule) = setup Tactic.dresolve_tac;
val (frule_tac, frule, some_frule) = setup Tactic.forward_tac;
end;
(* this *)
val this = METHOD (EVERY o map (HEADGOAL o Tactic.rtac));
(* assumption *)
fun assm_tac ctxt =
assume_tac APPEND' resolve_tac (filter Thm.no_prems (ProofContext.prems_of ctxt));
fun assumption_tac ctxt [] = assm_tac ctxt
| assumption_tac _ [fact] = resolve_tac [fact]
| assumption_tac _ _ = K no_tac;
fun assumption ctxt = METHOD (HEADGOAL o assumption_tac ctxt);
(* res_inst_tac emulations *)
(*Note: insts refer to the implicit (!) goal context; use at your own risk*)
fun gen_res_inst tac (quant, (insts, thm)) =
METHOD (fn facts => (quant (insert_tac facts THEN' tac insts thm)));
val res_inst = gen_res_inst Tactic.res_inst_tac;
val eres_inst = gen_res_inst Tactic.eres_inst_tac;
val dres_inst = gen_res_inst Tactic.dres_inst_tac;
val forw_inst = gen_res_inst Tactic.forw_inst_tac;
(* simple Prolog interpreter *)
fun prolog_tac rules facts =
DEPTH_SOLVE_1 (HEADGOAL (Tactic.assume_tac APPEND' Tactic.resolve_tac (facts @ rules)));
val prolog = METHOD o prolog_tac;
(* ML tactics *)
val tactic_ref = ref ((fn _ => raise Match): Proof.context -> thm list -> tactic);
fun set_tactic f = tactic_ref := f;
fun tactic txt ctxt = METHOD (fn facts =>
(Context.use_mltext
("let fun tactic (ctxt: PureIsar.Proof.context) (facts: thm list) : tactic = \
\let val thm = PureIsar.ProofContext.get_thm ctxt and thms = PureIsar.ProofContext.get_thms ctxt in\n"
^ txt ^
"\nend in PureIsar.Method.set_tactic tactic end")
false (Some (ProofContext.theory_of ctxt)); ! tactic_ref ctxt facts));
(** methods theory data **)
(* data kind 'Isar/methods' *)
structure MethodsDataArgs =
struct
val name = "Isar/methods";
type T =
{space: NameSpace.T,
meths: (((Args.src -> Proof.context -> Proof.method) * string) * stamp) Symtab.table};
val empty = {space = NameSpace.empty, meths = Symtab.empty};
val copy = I;
val prep_ext = I;
fun merge ({space = space1, meths = meths1}, {space = space2, meths = meths2}) =
{space = NameSpace.merge (space1, space2),
meths = Symtab.merge eq_snd (meths1, meths2) handle Symtab.DUPS dups =>
error ("Attempt to merge different versions of methods " ^ commas_quote dups)};
fun print _ {space, meths} =
let
fun prt_meth (name, ((_, comment), _)) = Pretty.block
[Pretty.str (name ^ ":"), Pretty.brk 2, Pretty.str comment];
in
[Pretty.big_list "methods:" (map prt_meth (NameSpace.cond_extern_table space meths))]
|> Pretty.chunks |> Pretty.writeln
end;
end;
structure MethodsData = TheoryDataFun(MethodsDataArgs);
val print_methods = MethodsData.print;
(* get methods *)
exception METHOD_FAIL of (string * Position.T) * exn;
fun method thy =
let
val {space, meths} = MethodsData.get thy;
fun meth src =
let
val ((raw_name, _), pos) = Args.dest_src src;
val name = NameSpace.intern space raw_name;
in
(case Symtab.lookup (meths, name) of
None => error ("Unknown proof method: " ^ quote name ^ Position.str_of pos)
| Some ((mth, _), _) => transform_failure (curry METHOD_FAIL (name, pos)) (mth src))
end;
in meth end;
(* add_method(s) *)
fun add_methods raw_meths thy =
let
val full = Sign.full_name (Theory.sign_of thy);
val new_meths =
map (fn (name, f, comment) => (full name, ((f, comment), stamp ()))) raw_meths;
val {space, meths} = MethodsData.get thy;
val space' = NameSpace.extend (space, map fst new_meths);
val meths' = Symtab.extend (meths, new_meths) handle Symtab.DUPS dups =>
error ("Duplicate declaration of method(s) " ^ commas_quote dups);
in
thy |> MethodsData.put {space = space', meths = meths'}
end;
val add_method = add_methods o Library.single;
(*implicit version*)
fun Method name meth cmt = Context.>> (add_methods [(name, meth, cmt)]);
(** method syntax **)
(* basic *)
fun syntax (scan: (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list))) =
Args.syntax "method" scan;
fun simple_args scan f src ctxt : Proof.method =
#2 (syntax (Scan.lift (scan >> (fn x => f x ctxt))) src ctxt);
fun ctxt_args (f: Proof.context -> Proof.method) src ctxt =
#2 (syntax (Scan.succeed (f ctxt)) src ctxt);
fun no_args m = ctxt_args (K m);
(* sections *)
type modifier = (Proof.context -> Proof.context) * Proof.context attribute;
local
fun sect ss = Scan.first (map Scan.lift ss);
fun thms ss = Scan.unless (sect ss) Attrib.local_thms;
fun thmss ss = Scan.repeat (thms ss) >> flat;
fun apply (f, att) (ctxt, ths) = Thm.applys_attributes ((f ctxt, ths), [att]);
fun section ss = (sect ss -- thmss ss) :-- (fn (m, ths) => Scan.depend (fn ctxt =>
Scan.succeed (apply m (ctxt, ths)))) >> #2;
fun sectioned args ss = args -- Scan.repeat (section ss);
in
fun sectioned_args args ss f src ctxt =
let val (ctxt', (x, _)) = syntax (sectioned args ss) src ctxt
in f x ctxt' end;
fun bang_sectioned_args ss f = sectioned_args Args.bang_facts ss f;
fun only_sectioned_args ss f = sectioned_args (Scan.succeed ()) ss (fn () => f);
fun thms_ctxt_args f = sectioned_args (thmss []) [] f;
fun thms_args f = thms_ctxt_args (K o f);
end;
(* insts *)
val insts =
Args.enum1 "and" (Scan.lift (Args.name -- Args.!!! (Args.$$$ "=" |-- Args.name))) --
(Scan.lift (Args.$$$ "in") |-- Attrib.local_thm);
fun inst_args f = f oo (#2 oo syntax (Args.goal_spec HEADGOAL -- insts));
(* subgoal *)
fun subgoal x = (Args.goal_spec HEADGOAL -- Scan.lift Args.name >>
(fn (quant, s) => METHOD (fn facts => quant (insert_tac facts THEN' Tactic.subgoal_tac s)))) x;
val subgoal_meth = #2 oo syntax subgoal;
(** method text **)
(* datatype text *)
datatype text =
Basic of (Proof.context -> Proof.method) |
Source of Args.src |
Then of text list |
Orelse of text list |
Try of text |
Repeat1 of text;
(* refine *)
fun gen_refine f text state =
let
val thy = Proof.theory_of state;
fun eval (Basic mth) = f mth
| eval (Source src) = f (method thy src)
| eval (Then txts) = Seq.EVERY (map eval txts)
| eval (Orelse txts) = Seq.FIRST (map eval txts)
| eval (Try txt) = Seq.TRY (eval txt)
| eval (Repeat1 txt) = Seq.REPEAT1 (eval txt);
in eval text state end;
val refine = gen_refine Proof.refine;
val refine_end = gen_refine Proof.refine_end;
(* structured proof steps *)
val default_text = Source (Args.src (("default", []), Position.none));
val this_text = Basic (K this);
val done_text = Basic (K (METHOD0 all_tac));
fun close_text asm = Basic (fn ctxt => METHOD (K
(FILTER Thm.no_prems ((if asm then ALLGOALS (assm_tac ctxt) else all_tac) THEN flexflex_tac))));
fun finish_text asm None = close_text asm
| finish_text asm (Some txt) = Then [txt, close_text asm];
fun proof opt_text state =
state
|> Proof.assert_backward
|> refine (if_none opt_text default_text)
|> Seq.map (Proof.goal_facts (K []))
|> Seq.map Proof.enter_forward;
fun local_qed asm opt_text = Proof.local_qed (refine (finish_text asm opt_text));
fun local_terminal_proof (text, opt_text) pr =
Seq.THEN (proof (Some text), local_qed true opt_text pr);
val local_default_proof = local_terminal_proof (default_text, None);
val local_immediate_proof = local_terminal_proof (this_text, None);
fun local_done_proof pr = Seq.THEN (proof (Some done_text), local_qed false None pr);
fun global_qeds asm opt_text = Proof.global_qed (refine (finish_text asm opt_text));
fun global_qed asm opt_text state =
state
|> global_qeds asm opt_text
|> Proof.check_result "Failed to finish proof" state
|> Seq.hd;
fun global_term_proof asm (text, opt_text) state =
state
|> proof (Some text)
|> Proof.check_result "Terminal proof method failed" state
|> (Seq.flat o Seq.map (global_qeds asm opt_text))
|> Proof.check_result "Failed to finish proof (after successful terminal method)" state
|> Seq.hd;
val global_terminal_proof = global_term_proof true;
val global_default_proof = global_terminal_proof (default_text, None);
val global_immediate_proof = global_terminal_proof (this_text, None);
val global_done_proof = global_term_proof false (done_text, None);
(** theory setup **)
(* pure_methods *)
val pure_methods =
[("fail", no_args fail, "force failure"),
("succeed", no_args succeed, "succeed"),
("-", no_args insert_facts, "do nothing, inserting current facts only"),
("insert", thms_args insert, "insert theorems, ignoring facts (improper!)"),
("unfold", thms_args unfold, "unfold definitions"),
("fold", thms_args fold, "fold definitions"),
("default", thms_ctxt_args some_rule, "apply some rule"),
("rule", thms_ctxt_args some_rule, "apply some rule"),
("erule", thms_ctxt_args some_erule, "apply some rule in elimination manner (improper!)"),
("drule", thms_ctxt_args some_drule, "apply some rule in destruct manner (improper!)"),
("frule", thms_ctxt_args some_frule, "apply some rule in forward manner (improper!)"),
("this", no_args this, "apply current facts as rules"),
("assumption", ctxt_args assumption, "proof by assumption, preferring facts"),
("res_inst_tac", inst_args res_inst, "res_inst_tac emulation (dynamic instantiation!)"),
("eres_inst_tac", inst_args eres_inst, "eres_inst_tac emulation (dynamic instantiation!)"),
("dres_inst_tac", inst_args dres_inst, "dres_inst_tac emulation (dynamic instantiation!)"),
("forw_inst_tac", inst_args forw_inst, "forw_inst_tac emulation (dynamic instantiation!)"),
("subgoal_tac", subgoal_meth, "subgoal_tac emulation (dynamic instantiation!)"),
("prolog", thms_args prolog, "simple prolog interpreter"),
("tactic", simple_args Args.name tactic, "ML tactic as proof method")];
(* setup *)
val setup =
[GlobalRules.init, LocalRules.init, Attrib.add_attributes rule_atts,
MethodsData.init, add_methods pure_methods];
end;
structure BasicMethod: BASIC_METHOD = Method;
open BasicMethod;