(* Title: Pure/Isar/method.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
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 METHOD: (thm list -> tactic) -> Proof.method
val METHOD0: tactic -> Proof.method
val fail: Proof.method
val succeed: 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 rule_tac: thm list -> thm list -> int -> tactic
val erule_tac: thm list -> thm list -> int -> tactic
val rule: thm list -> Proof.method
val erule: thm list -> Proof.method
val assumption: Proof.context -> Proof.method
exception METHOD_FAIL of (string * Position.T) * exn
val help_methods: theory option -> unit
val method: theory -> Args.src -> Proof.context -> Proof.method
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)) ->
Proof.context -> Args.src -> Proof.context * 'a
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_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_no_facts: text -> Proof.state -> Proof.state Seq.seq
val proof: text option -> Proof.state -> Proof.state Seq.seq
val local_qed: 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_immediate_proof: ({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 global_qed: 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_immediate_proof: Proof.state -> theory * {kind: string, name: string, thm: thm}
val global_default_proof: Proof.state -> theory * {kind: string, name: string, thm: thm}
val setup: (theory -> theory) list
end;
structure Method: METHOD =
struct
(** proof methods **)
(* method from tactic *)
val METHOD = Proof.method;
fun METHOD0 tac = METHOD (fn [] => tac | _ => error "Method may not be used with facts");
(* primitive *)
val fail = METHOD (K no_tac);
val succeed = METHOD (K all_tac);
(* 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;
(* rule *)
local
fun gen_rule_tac tac rules [] = tac rules
| gen_rule_tac tac erules facts =
let
val rules = multi_resolves facts erules;
fun tactic i state = Seq.flat (Seq.map (fn rule => tac [rule] i state) rules);
in tactic end;
in
val rule_tac = gen_rule_tac Tactic.resolve_tac;
val erule_tac = gen_rule_tac Tactic.eresolve_tac;
fun rule rules = METHOD (FIRSTGOAL o rule_tac rules);
fun erule rules = METHOD (FIRSTGOAL o erule_tac rules);
end;
(* assumption / finish *)
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 (FIRSTGOAL o assumption_tac ctxt);
fun finish ctxt = METHOD (K (FILTER Thm.no_prems (ALLGOALS (assm_tac ctxt))));
(** 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_meths verbose {space, meths} =
let
fun prt_meth (name, ((_, comment), _)) = Pretty.block
[Pretty.str (name ^ ":"), Pretty.brk 2, Pretty.str comment];
in
if not verbose then ()
else Pretty.writeln (Display.pretty_name_space ("method name space", space));
Pretty.writeln (Pretty.big_list "methods:"
(map prt_meth (NameSpace.cond_extern_table space meths)))
end;
fun print _ = print_meths true;
end;
structure MethodsData = TheoryDataFun(MethodsDataArgs);
val print_methods = MethodsData.print;
fun help_methods None = writeln "methods: (unkown theory context)"
| help_methods (Some thy) = MethodsDataArgs.print_meths false (MethodsData.get thy);
(* 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_methods *)
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;
(*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 ctxt_args (f: Proof.context -> Proof.method) src ctxt =
#2 (syntax (Scan.succeed (f ctxt)) ctxt src);
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 (fn s => Scan.lift (s --| Args.$$$ ":")) 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) ctxt src
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_args f = sectioned_args (thmss []) [] (fn ths => fn _ => f ths);
end;
(** 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 refine text state =
let
val thy = Proof.theory_of state;
fun eval (Basic mth) = Proof.refine mth
| eval (Source src) = Proof.refine (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;
fun refine_no_facts text state =
state
|> Proof.goal_facts (K [])
|> refine text;
(* structured proof steps *)
val default_text = Source (Args.src (("default", []), Position.none));
fun finish_text None = Basic finish
| finish_text (Some txt) = Then [txt, Basic finish];
fun proof opt_text state =
state
|> Proof.assert_backward
|> refine (if_none opt_text default_text)
|> Seq.map Proof.enter_forward;
fun local_qed opt_text = Proof.local_qed (refine (finish_text opt_text));
fun local_terminal_proof (text, opt_text) pr = Seq.THEN (proof (Some text), local_qed opt_text pr);
val local_immediate_proof = local_terminal_proof (Basic assumption, None);
val local_default_proof = local_terminal_proof (default_text, None);
fun global_qeds opt_text = Proof.global_qed (refine (finish_text opt_text));
fun global_qed opt_text state =
state
|> global_qeds opt_text
|> Proof.check_result "Failed to finish proof" state
|> Seq.hd;
fun global_terminal_proof (text, opt_text) state =
state
|> proof (Some text)
|> Proof.check_result "Terminal proof method failed" state
|> (Seq.flat o Seq.map (global_qeds opt_text))
|> Proof.check_result "Failed to finish proof (after successful terminal method)" state
|> Seq.hd;
val global_immediate_proof = global_terminal_proof (Basic assumption, None);
val global_default_proof = global_terminal_proof (default_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"),
("rule", thms_args rule, "apply some rule"),
("erule", thms_args erule, "apply some erule (improper!)"),
("assumption", ctxt_args assumption, "proof by assumption, preferring facts")];
(* setup *)
val setup = [MethodsData.init, add_methods pure_methods];
end;
structure BasicMethod: BASIC_METHOD = Method;
open BasicMethod;