(* Title: Pure/Isar/method.ML
Author: Markus Wenzel, TU Muenchen
Isar proof methods.
*)
signature METHOD =
sig
type method = thm list -> cases_tactic
val METHOD_CASES: (thm list -> cases_tactic) -> method
val METHOD: (thm list -> tactic) -> method
val fail: method
val succeed: method
val insert_tac: thm list -> int -> tactic
val insert: thm list -> method
val insert_facts: method
val SIMPLE_METHOD: tactic -> method
val SIMPLE_METHOD': (int -> tactic) -> method
val SIMPLE_METHOD'': ((int -> tactic) -> tactic) -> (int -> tactic) -> method
val cheating: Proof.context -> bool -> method
val intro: thm list -> method
val elim: thm list -> method
val unfold: thm list -> Proof.context -> method
val fold: thm list -> Proof.context -> method
val atomize: bool -> Proof.context -> method
val this: method
val fact: thm list -> Proof.context -> method
val assm_tac: Proof.context -> int -> tactic
val all_assm_tac: Proof.context -> tactic
val assumption: Proof.context -> method
val rule_trace: bool Config.T
val trace: Proof.context -> thm list -> unit
val rule_tac: Proof.context -> thm list -> thm list -> int -> tactic
val some_rule_tac: Proof.context -> thm list -> thm list -> int -> tactic
val intros_tac: thm list -> thm list -> tactic
val try_intros_tac: thm list -> thm list -> tactic
val rule: Proof.context -> thm list -> method
val erule: Proof.context -> int -> thm list -> method
val drule: Proof.context -> int -> thm list -> method
val frule: Proof.context -> int -> thm list -> method
val set_tactic: (thm list -> tactic) -> Proof.context -> Proof.context
val tactic: Symbol_Pos.source -> Proof.context -> method
val raw_tactic: Symbol_Pos.source -> Proof.context -> method
type src = Args.src
type combinator_info
val no_combinator_info: combinator_info
datatype combinator = Then | Orelse | Try | Repeat1 | Select_Goals of int
datatype text =
Source of src |
Basic of Proof.context -> method |
Combinator of combinator_info * combinator * text list
val map_source: (src -> src) -> text -> text
val primitive_text: (Proof.context -> thm -> thm) -> text
val succeed_text: text
val default_text: text
val this_text: text
val done_text: text
val sorry_text: bool -> text
val finish_text: text option * bool -> text
val print_methods: Proof.context -> unit
val check_name: Proof.context -> xstring * Position.T -> string
val method_syntax: (Proof.context -> method) context_parser -> Args.src -> Proof.context -> method
val setup: binding -> (Proof.context -> method) context_parser -> string -> theory -> theory
val local_setup: binding -> (Proof.context -> method) context_parser -> string ->
local_theory -> local_theory
val method_setup: bstring * Position.T -> Symbol_Pos.source -> string ->
local_theory -> local_theory
val method: Proof.context -> src -> Proof.context -> method
val method_closure: Proof.context -> src -> src
val method_cmd: Proof.context -> src -> Proof.context -> method
val evaluate: text -> Proof.context -> Proof.context -> method
type modifier = (Proof.context -> Proof.context) * attribute
val section: modifier parser list -> thm list context_parser
val sections: modifier parser list -> thm list list context_parser
type text_range = text * Position.range
val text: text_range option -> text option
val position: text_range option -> Position.T
val reports_of: text_range -> Position.report list
val report: text_range -> unit
val parse: text_range parser
end;
structure Method: METHOD =
struct
(** proof methods **)
(* method *)
type method = thm list -> cases_tactic;
fun METHOD_CASES tac facts = Seq.THEN (ALLGOALS Goal.conjunction_tac, tac facts);
fun METHOD tac facts = NO_CASES (ALLGOALS Goal.conjunction_tac THEN tac facts);
val fail = METHOD (K no_tac);
val succeed = METHOD (K all_tac);
(* insert facts *)
local
fun cut_rule_tac rule =
rtac (Drule.forall_intr_vars rule COMP_INCR revcut_rl);
in
fun insert_tac [] _ = 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));
fun SIMPLE_METHOD tac = METHOD (fn facts => ALLGOALS (insert_tac facts) THEN tac);
fun SIMPLE_METHOD'' quant tac = METHOD (fn facts => quant (insert_tac facts THEN' tac));
val SIMPLE_METHOD' = SIMPLE_METHOD'' HEADGOAL;
end;
(* cheating *)
fun cheating ctxt int = METHOD (fn _ => fn st =>
if int orelse Config.get ctxt quick_and_dirty then
ALLGOALS Skip_Proof.cheat_tac st
else error "Cheating requires quick_and_dirty mode!");
(* unfold intro/elim rules *)
fun intro ths = SIMPLE_METHOD' (CHANGED_PROP o REPEAT_ALL_NEW (match_tac ths));
fun elim ths = SIMPLE_METHOD' (CHANGED_PROP o REPEAT_ALL_NEW (ematch_tac ths));
(* unfold/fold definitions *)
fun unfold_meth ths ctxt = SIMPLE_METHOD (CHANGED_PROP (Local_Defs.unfold_tac ctxt ths));
fun fold_meth ths ctxt = SIMPLE_METHOD (CHANGED_PROP (Local_Defs.fold_tac ctxt ths));
(* atomize rule statements *)
fun atomize false ctxt =
SIMPLE_METHOD' (CHANGED_PROP o Object_Logic.atomize_prems_tac ctxt)
| atomize true ctxt =
NO_CASES o K (HEADGOAL (CHANGED_PROP o Object_Logic.full_atomize_tac ctxt));
(* this -- resolve facts directly *)
val this = METHOD (EVERY o map (HEADGOAL o rtac));
(* fact -- composition by facts from context *)
fun fact [] ctxt = SIMPLE_METHOD' (Proof_Context.some_fact_tac ctxt)
| fact rules ctxt = SIMPLE_METHOD' (Proof_Context.fact_tac ctxt rules);
(* assumption *)
local
fun cond_rtac cond rule = SUBGOAL (fn (prop, i) =>
if cond (Logic.strip_assums_concl prop)
then rtac rule i else no_tac);
in
fun assm_tac ctxt =
assume_tac APPEND'
Goal.assume_rule_tac ctxt APPEND'
cond_rtac (can Logic.dest_equals) Drule.reflexive_thm APPEND'
cond_rtac (can Logic.dest_term) Drule.termI;
fun all_assm_tac ctxt =
let
fun tac i st =
if i > Thm.nprems_of st then all_tac st
else ((assm_tac ctxt i THEN tac i) ORELSE tac (i + 1)) st;
in tac 1 end;
fun assumption ctxt = METHOD (HEADGOAL o
(fn [] => assm_tac ctxt
| [fact] => solve_tac [fact]
| _ => K no_tac));
fun finish immed ctxt =
METHOD (K ((if immed then all_assm_tac ctxt else all_tac) THEN flexflex_tac));
end;
(* rule etc. -- single-step refinements *)
val rule_trace = Attrib.setup_config_bool @{binding rule_trace} (fn _ => false);
fun trace ctxt rules =
if Config.get ctxt rule_trace andalso not (null rules) then
Pretty.big_list "rules:" (map (Display.pretty_thm_item ctxt) rules)
|> Pretty.string_of |> tracing
else ();
local
fun gen_rule_tac tac ctxt rules facts =
(fn i => fn st =>
if null facts then tac rules i st
else Seq.maps (fn rule => (tac o single) rule i st) (Drule.multi_resolves facts rules))
THEN_ALL_NEW Goal.norm_hhf_tac ctxt;
fun gen_arule_tac tac ctxt j rules facts =
EVERY' (gen_rule_tac tac ctxt rules facts :: replicate j assume_tac);
fun gen_some_rule_tac tac ctxt arg_rules facts = SUBGOAL (fn (goal, i) =>
let
val rules =
if not (null arg_rules) then arg_rules
else flat (Context_Rules.find_rules false facts goal ctxt)
in trace ctxt rules; tac ctxt rules facts i end);
fun meth tac x y = METHOD (HEADGOAL o tac x y);
fun meth' tac x y z = METHOD (HEADGOAL o tac x y z);
in
val rule_tac = gen_rule_tac resolve_tac;
val rule = meth rule_tac;
val some_rule_tac = gen_some_rule_tac rule_tac;
val some_rule = meth some_rule_tac;
val erule = meth' (gen_arule_tac eresolve_tac);
val drule = meth' (gen_arule_tac dresolve_tac);
val frule = meth' (gen_arule_tac forward_tac);
end;
(* intros_tac -- pervasive search spanned by intro rules *)
fun gen_intros_tac goals intros facts =
goals (insert_tac facts THEN'
REPEAT_ALL_NEW (resolve_tac intros))
THEN Tactic.distinct_subgoals_tac;
val intros_tac = gen_intros_tac ALLGOALS;
val try_intros_tac = gen_intros_tac TRYALL;
(* ML tactics *)
structure ML_Tactic = Proof_Data
(
type T = thm list -> tactic;
fun init _ = undefined;
);
val set_tactic = ML_Tactic.put;
fun ml_tactic source ctxt =
let
val ctxt' = ctxt |> Context.proof_map
(ML_Context.expression (#pos source)
"fun tactic (facts: thm list) : tactic"
"Context.map_proof (Method.set_tactic tactic)" (ML_Lex.read_source false source));
in Context.setmp_thread_data (SOME (Context.Proof ctxt)) (ML_Tactic.get ctxt') end;
fun tactic source ctxt = METHOD (ml_tactic source ctxt);
fun raw_tactic source ctxt = NO_CASES o ml_tactic source ctxt;
(** method syntax **)
(* method text *)
type src = Args.src;
datatype combinator_info = Combinator_Info of {keywords: Position.T list};
fun combinator_info keywords = Combinator_Info {keywords = keywords};
val no_combinator_info = combinator_info [];
datatype combinator = Then | Orelse | Try | Repeat1 | Select_Goals of int;
datatype text =
Source of src |
Basic of Proof.context -> method |
Combinator of combinator_info * combinator * text list;
fun map_source f (Source src) = Source (f src)
| map_source _ (Basic meth) = Basic meth
| map_source f (Combinator (info, comb, txts)) = Combinator (info, comb, map (map_source f) txts);
fun primitive_text r = Basic (SIMPLE_METHOD o PRIMITIVE o r);
val succeed_text = Basic (K succeed);
val default_text = Source (Args.src ("default", Position.none) []);
val this_text = Basic (K this);
val done_text = Basic (K (SIMPLE_METHOD all_tac));
fun sorry_text int = Basic (fn ctxt => cheating ctxt int);
fun finish_text (NONE, immed) = Basic (finish immed)
| finish_text (SOME txt, immed) =
Combinator (no_combinator_info, Then, [txt, Basic (finish immed)]);
(* method definitions *)
structure Methods = Generic_Data
(
type T = ((src -> Proof.context -> method) * string) Name_Space.table;
val empty : T = Name_Space.empty_table "method";
val extend = I;
fun merge data : T = Name_Space.merge_tables data;
);
val get_methods = Methods.get o Context.Proof;
fun transfer_methods ctxt =
let
val meths0 = Methods.get (Context.Theory (Proof_Context.theory_of ctxt));
val meths' = Name_Space.merge_tables (meths0, get_methods ctxt);
in Context.proof_map (Methods.put meths') ctxt end;
fun print_methods ctxt =
let
val meths = get_methods ctxt;
fun prt_meth (name, (_, "")) = Pretty.mark_str name
| prt_meth (name, (_, comment)) =
Pretty.block
(Pretty.mark_str name :: Pretty.str ":" :: Pretty.brk 2 :: Pretty.text comment);
in
[Pretty.big_list "methods:" (map prt_meth (Name_Space.markup_table ctxt meths))]
|> Pretty.writeln_chunks
end;
(* define *)
fun define_global binding meth comment thy =
let
val context = Context.Theory thy;
val (name, meths') =
Name_Space.define context true (binding, (meth, comment)) (Methods.get context);
in (name, Context.the_theory (Methods.put meths' context)) end;
fun define binding meth comment =
Local_Theory.background_theory_result (define_global binding meth comment)
#-> (fn name =>
Local_Theory.map_contexts (K transfer_methods)
#> Local_Theory.generic_alias Methods.map binding name
#> pair name);
(* check *)
fun check_name ctxt = #1 o Name_Space.check (Context.Proof ctxt) (get_methods ctxt);
fun check_src ctxt src = Args.check_src ctxt (get_methods ctxt) src;
(* method setup *)
fun method_syntax scan src ctxt : method =
let val (m, ctxt') = Args.syntax scan src ctxt in m ctxt' end;
fun setup binding scan comment = define_global binding (method_syntax scan) comment #> snd;
fun local_setup binding scan comment = define binding (method_syntax scan) comment #> snd;
fun method_setup name source cmt =
(ML_Lex.read Position.none ("(" ^ ML_Syntax.make_binding name ^ ", ") @
ML_Lex.read_source false source @
ML_Lex.read Position.none (", " ^ ML_Syntax.print_string cmt ^ ")"))
|> ML_Context.expression (#pos source)
"val (name, scan, comment): binding * (Proof.context -> Proof.method) context_parser * string"
"Context.map_proof (Method.local_setup name scan comment)"
|> Context.proof_map;
(* prepare methods *)
fun method ctxt =
let val table = get_methods ctxt
in fn src => #1 (Name_Space.get table (#1 (Args.name_of_src src))) src end;
fun method_closure ctxt0 src0 =
let
val (src1, meth) = check_src ctxt0 src0;
val src2 = Args.init_assignable src1;
val ctxt = Context_Position.not_really ctxt0;
val _ = Seq.pull (method ctxt src2 ctxt [] (Goal.protect 0 Drule.dummy_thm));
in Args.closure src2 end;
fun method_cmd ctxt = method ctxt o method_closure ctxt;
(* evaluate method text *)
local
fun APPEND_CASES (meth: cases_tactic) (cases, st) =
meth st |> Seq.map (fn (cases', st') => (cases @ cases', st'));
fun BYPASS_CASES (tac: tactic) (cases, st) =
tac st |> Seq.map (pair cases);
val op THEN = Seq.THEN;
fun SELECT_GOALS n method =
BYPASS_CASES
(ALLGOALS Goal.conjunction_tac THEN PRIMITIVE (Goal.restrict 1 n) THEN Goal.conjunction_tac 1)
THEN method
THEN BYPASS_CASES (PRIMITIVE (Goal.unrestrict 1));
fun COMBINATOR1 comb [meth] = comb meth
| COMBINATOR1 _ _ = raise Fail "Method combinator requires exactly one argument";
fun combinator Then = Seq.EVERY
| combinator Orelse = Seq.FIRST
| combinator Try = COMBINATOR1 Seq.TRY
| combinator Repeat1 = COMBINATOR1 Seq.REPEAT1
| combinator (Select_Goals n) = COMBINATOR1 (SELECT_GOALS n);
in
fun evaluate text static_ctxt =
let
fun eval (Basic meth) = APPEND_CASES oo meth
| eval (Source src) = APPEND_CASES oo method_cmd static_ctxt src
| eval (Combinator (_, c, txts)) =
let
val comb = combinator c;
val meths = map eval txts
in fn ctxt => fn facts => comb (map (fn meth => meth ctxt facts) meths) end;
val meth = eval text;
in fn ctxt => fn facts => fn st => meth ctxt facts ([], st) end;
end;
(** concrete syntax **)
(* sections *)
type modifier = (Proof.context -> Proof.context) * attribute;
local
fun thms ss = Scan.repeat (Scan.unless (Scan.lift (Scan.first ss)) Attrib.multi_thm) >> flat;
fun app (f, att) ths context = fold_map (Thm.apply_attribute att) ths (Context.map_proof f context);
in
fun section ss = Scan.depend (fn context => (Scan.first ss -- Scan.pass context (thms ss)) :|--
(fn (m, ths) => Scan.succeed (swap (app m ths context))));
fun sections ss = Scan.repeat (section ss);
end;
(* extra rule methods *)
fun xrule_meth meth =
Scan.lift (Scan.optional (Args.parens Parse.nat) 0) -- Attrib.thms >>
(fn (n, ths) => fn ctxt => meth ctxt n ths);
(* text range *)
type text_range = text * Position.range;
fun text NONE = NONE
| text (SOME (txt, _)) = SOME txt;
fun position NONE = Position.none
| position (SOME (_, (pos, _))) = pos;
(* reports *)
local
fun keyword_positions (Source _) = []
| keyword_positions (Basic _) = []
| keyword_positions (Combinator (Combinator_Info {keywords}, _, texts)) =
keywords @ maps keyword_positions texts;
in
fun reports_of ((text, (pos, _)): text_range) =
(pos, Markup.language_method) ::
maps (fn p => map (pair p) (Markup.keyword3 :: Completion.suppress_abbrevs ""))
(keyword_positions text);
val report = Position.reports o reports_of;
end;
(* outer parser *)
fun is_symid_meth s =
s <> "|" andalso s <> "?" andalso s <> "+" andalso Token.ident_or_symbolic s;
local
fun meth4 x =
(Parse.position Parse.xname >> (fn name => Source (Args.src name [])) ||
Scan.ahead Parse.cartouche |-- Parse.not_eof >> (fn tok =>
Source (Args.src ("cartouche", Token.pos_of tok) [tok])) ||
Parse.$$$ "(" |-- Parse.!!! (meth0 --| Parse.$$$ ")")) x
and meth3 x =
(meth4 -- Parse.position (Parse.$$$ "?")
>> (fn (m, (_, pos)) => Combinator (combinator_info [pos], Try, [m])) ||
meth4 -- Parse.position (Parse.$$$ "+")
>> (fn (m, (_, pos)) => Combinator (combinator_info [pos], Repeat1, [m])) ||
meth4 --
(Parse.position (Parse.$$$ "[") -- Scan.optional Parse.nat 1 -- Parse.position (Parse.$$$ "]"))
>> (fn (m, (((_, pos1), n), (_, pos2))) =>
Combinator (combinator_info [pos1, pos2], Select_Goals n, [m])) ||
meth4) x
and meth2 x =
(Parse.position Parse.xname -- Parse.args1 is_symid_meth >> (Source o uncurry Args.src) ||
meth3) x
and meth1 x =
(Parse.enum1_positions "," meth2
>> (fn ([m], _) => m | (ms, ps) => Combinator (combinator_info ps, Then, ms))) x
and meth0 x =
(Parse.enum1_positions "|" meth1
>> (fn ([m], _) => m | (ms, ps) => Combinator (combinator_info ps, Orelse, ms))) x;
in
val parse =
Scan.trace meth3 >> (fn (m, toks) => (m, Token.range_of toks));
end;
(* theory setup *)
val _ = Theory.setup
(setup @{binding fail} (Scan.succeed (K fail)) "force failure" #>
setup @{binding succeed} (Scan.succeed (K succeed)) "succeed" #>
setup @{binding "-"} (Scan.succeed (K insert_facts))
"do nothing (insert current facts only)" #>
setup @{binding insert} (Attrib.thms >> (K o insert))
"insert theorems, ignoring facts (improper)" #>
setup @{binding intro} (Attrib.thms >> (K o intro))
"repeatedly apply introduction rules" #>
setup @{binding elim} (Attrib.thms >> (K o elim))
"repeatedly apply elimination rules" #>
setup @{binding unfold} (Attrib.thms >> unfold_meth) "unfold definitions" #>
setup @{binding fold} (Attrib.thms >> fold_meth) "fold definitions" #>
setup @{binding atomize} (Scan.lift (Args.mode "full") >> atomize)
"present local premises as object-level statements" #>
setup @{binding rule} (Attrib.thms >> (fn ths => fn ctxt => some_rule ctxt ths))
"apply some intro/elim rule" #>
setup @{binding erule} (xrule_meth erule) "apply rule in elimination manner (improper)" #>
setup @{binding drule} (xrule_meth drule) "apply rule in destruct manner (improper)" #>
setup @{binding frule} (xrule_meth frule) "apply rule in forward manner (improper)" #>
setup @{binding this} (Scan.succeed (K this)) "apply current facts as rules" #>
setup @{binding fact} (Attrib.thms >> fact) "composition by facts from context" #>
setup @{binding assumption} (Scan.succeed assumption)
"proof by assumption, preferring facts" #>
setup @{binding rename_tac} (Args.goal_spec -- Scan.lift (Scan.repeat1 Args.name) >>
(fn (quant, xs) => K (SIMPLE_METHOD'' quant (rename_tac xs))))
"rename parameters of goal" #>
setup @{binding rotate_tac} (Args.goal_spec -- Scan.lift (Scan.optional Parse.int 1) >>
(fn (quant, i) => K (SIMPLE_METHOD'' quant (rotate_tac i))))
"rotate assumptions of goal" #>
setup @{binding tactic} (Scan.lift Args.text_source_position >> tactic)
"ML tactic as proof method" #>
setup @{binding raw_tactic} (Scan.lift Args.text_source_position >> raw_tactic)
"ML tactic as raw proof method");
(*final declarations of this structure!*)
val unfold = unfold_meth;
val fold = fold_meth;
end;
val METHOD_CASES = Method.METHOD_CASES;
val METHOD = Method.METHOD;
val SIMPLE_METHOD = Method.SIMPLE_METHOD;
val SIMPLE_METHOD' = Method.SIMPLE_METHOD';
val SIMPLE_METHOD'' = Method.SIMPLE_METHOD'';