(* Title: Pure/Isar/method.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
Proof methods.
*)
signature BASIC_METHOD =
sig
val trace_rules: bool ref
val print_methods: theory -> unit
val Method: bstring -> (Args.src -> Proof.context -> Proof.method) -> string -> unit
end;
signature METHOD =
sig
include BASIC_METHOD
type src
val trace: Proof.context -> thm list -> unit
val RAW_METHOD: (thm list -> tactic) -> Proof.method
val RAW_METHOD_CASES:
(thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq) -> Proof.method
val METHOD: (thm list -> tactic) -> Proof.method
val METHOD_CASES:
(thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq) -> Proof.method
val SIMPLE_METHOD: tactic -> Proof.method
val SIMPLE_METHOD': ((int -> tactic) -> tactic) -> (int -> 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 rules_tac: Proof.context -> int option -> int -> tactic
val rule_tac: thm list -> thm list -> int -> tactic
val some_rule_tac: thm list -> Proof.context -> thm list -> int -> tactic
val rule: thm list -> Proof.method
val erule: int -> thm list -> Proof.method
val drule: int -> thm list -> Proof.method
val frule: int -> thm list -> Proof.method
val this: Proof.method
val assumption: Proof.context -> Proof.method
val bires_inst_tac: bool -> Proof.context -> (indexname * string) list -> thm -> int -> tactic
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 -> src -> Proof.context -> Proof.method
val add_method: bstring * (src -> Proof.context -> Proof.method) * string
-> theory -> theory
val add_methods: (bstring * (src -> Proof.context -> Proof.method) * string) list
-> theory -> theory
val syntax: (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list)) ->
src -> Proof.context -> Proof.context * 'a
val simple_args: (Args.T list -> 'a * Args.T list)
-> ('a -> Proof.context -> Proof.method) -> src -> Proof.context -> Proof.method
val ctxt_args: (Proof.context -> Proof.method) -> src -> Proof.context -> Proof.method
val no_args: Proof.method -> 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 -> 'b) -> src -> Proof.context -> 'b
val bang_sectioned_args:
(Args.T list -> modifier * Args.T list) list ->
(thm list -> Proof.context -> 'a) -> src -> Proof.context -> 'a
val bang_sectioned_args':
(Args.T list -> modifier * Args.T list) list ->
(Proof.context * Args.T list -> 'a * (Proof.context * Args.T list)) ->
('a -> thm list -> Proof.context -> 'b) -> src -> Proof.context -> 'b
val only_sectioned_args:
(Args.T list -> modifier * Args.T list) list ->
(Proof.context -> 'a) -> src -> Proof.context -> 'a
val thms_ctxt_args: (thm list -> Proof.context -> 'a) -> src -> Proof.context -> 'a
val thms_args: (thm list -> 'a) -> src -> Proof.context -> 'a
val thm_args: (thm -> 'a) -> src -> Proof.context -> 'a
datatype text =
Basic of (Proof.context -> Proof.method) |
Source of 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
-> (Proof.context -> string * (string * thm list) list -> unit) *
(Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq
val local_terminal_proof: text * text option
-> (Proof.context -> string * (string * thm list) list -> unit) *
(Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq
val local_default_proof: (Proof.context -> string * (string * thm list) list -> unit) *
(Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq
val local_immediate_proof: (Proof.context -> string * (string * thm list) list -> unit) *
(Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq
val local_done_proof: (Proof.context -> string * (string * thm list) list -> unit) *
(Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq
val global_qed: bool -> text option
-> Proof.state -> theory * ((string * string) * (string * thm list) list)
val global_terminal_proof: text * text option
-> Proof.state -> theory * ((string * string) * (string * thm list) list)
val global_default_proof: Proof.state -> theory * ((string * string) * (string * thm list) list)
val global_immediate_proof: Proof.state ->
theory * ((string * string) * (string * thm list) list)
val global_done_proof: Proof.state -> theory * ((string * string) * (string * thm list) list)
val goal_args: (Args.T list -> 'a * Args.T list) -> ('a -> int -> tactic)
-> src -> Proof.context -> Proof.method
val goal_args': (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list))
-> ('a -> int -> tactic) -> src -> Proof.context -> Proof.method
val goal_args_ctxt: (Args.T list -> 'a * Args.T list) -> (Proof.context -> 'a -> int -> tactic)
-> src -> Proof.context -> Proof.method
val goal_args_ctxt': (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list))
-> (Proof.context -> 'a -> int -> tactic) -> src -> Proof.context -> Proof.method
end;
structure Method: METHOD =
struct
type src = Args.src;
(** proof methods **)
(* tracing *)
val trace_rules = ref false;
fun trace ctxt rules =
conditional (! trace_rules andalso not (null rules)) (fn () =>
Pretty.big_list "rules:" (map (ProofContext.pretty_thm ctxt) rules)
|> Pretty.string_of |> tracing);
(* make methods *)
val RAW_METHOD = Proof.method;
val RAW_METHOD_CASES = Proof.method_cases;
fun METHOD m = Proof.method (fn facts => TRY Tactic.conjunction_tac THEN m facts);
fun METHOD_CASES m =
Proof.method_cases (fn facts => Seq.THEN (TRY Tactic.conjunction_tac, m 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));
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));
end;
(* unfold/fold definitions *)
fun unfold ths = SIMPLE_METHOD (CHANGED_PROP (rewrite_goals_tac ths));
fun fold ths = SIMPLE_METHOD (CHANGED_PROP (fold_goals_tac ths));
(* atomize rule statements *)
fun atomize false = SIMPLE_METHOD' HEADGOAL (CHANGED_PROP o ObjectLogic.atomize_tac)
| atomize true = RAW_METHOD (K (HEADGOAL (CHANGED_PROP o ObjectLogic.full_atomize_tac)));
(* unfold intro/elim rules *)
fun intro ths = SIMPLE_METHOD' HEADGOAL (CHANGED_PROP o REPEAT_ALL_NEW (Tactic.match_tac ths));
fun elim ths = SIMPLE_METHOD' HEADGOAL (CHANGED_PROP o REPEAT_ALL_NEW (Tactic.ematch_tac ths));
(* 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;
(* rules_tac *)
local
val remdups_tac = SUBGOAL (fn (g, i) =>
let val prems = Logic.strip_assums_hyp g in
REPEAT_DETERM_N (length prems - length (gen_distinct op aconv prems))
(Tactic.ematch_tac [Drule.remdups_rl] i THEN Tactic.eq_assume_tac i)
end);
fun REMDUPS tac = tac THEN_ALL_NEW remdups_tac;
fun gen_eq_set e s1 s2 =
length s1 = length s2 andalso
gen_subset e (s1, s2) andalso gen_subset e (s2, s1);
val bires_tac = Tactic.biresolution_from_nets_tac ContextRules.orderlist;
fun safe_step_tac ctxt =
ContextRules.Swrap ctxt
(eq_assume_tac ORELSE'
bires_tac true (ContextRules.netpair_bang ctxt));
fun unsafe_step_tac ctxt =
ContextRules.wrap ctxt
(assume_tac APPEND'
bires_tac false (ContextRules.netpair_bang ctxt) APPEND'
bires_tac false (ContextRules.netpair ctxt));
fun step_tac ctxt i =
REPEAT_DETERM1 (REMDUPS (safe_step_tac ctxt) i) ORELSE
REMDUPS (unsafe_step_tac ctxt) i;
fun intpr_tac ctxt gs d lim = SUBGOAL (fn (g, i) => if d > lim then no_tac else
let
val ps = Logic.strip_assums_hyp g;
val c = Logic.strip_assums_concl g;
in
if gen_mem (fn ((ps1, c1), (ps2, c2)) =>
c1 aconv c2 andalso gen_eq_set op aconv ps1 ps2) ((ps, c), gs) then no_tac
else (step_tac ctxt THEN_ALL_NEW intpr_tac ctxt ((ps, c) :: gs) (d + 1) lim) i
end);
in
fun rules_tac ctxt opt_lim =
SELECT_GOAL (DEEPEN (2, if_none opt_lim 20) (intpr_tac ctxt [] 0) 4 1);
end;
(* rule_tac etc. *)
local
fun gen_rule_tac tac rules [] i st = tac rules i st
| gen_rule_tac tac rules facts i st =
Seq.flat (Seq.map (fn rule => (tac o single) rule i st) (multi_resolves facts rules));
fun gen_arule_tac tac j rules facts =
EVERY' (gen_rule_tac tac rules facts :: replicate j Tactic.assume_tac);
fun gen_some_rule_tac tac arg_rules ctxt facts = SUBGOAL (fn (goal, i) =>
let
val rules =
if not (null arg_rules) then arg_rules
else List.concat (ContextRules.find_rules false facts goal ctxt)
in trace ctxt rules; tac rules facts i end);
fun meth tac x = METHOD (HEADGOAL o tac x);
fun meth' tac x y = METHOD (HEADGOAL o tac x y);
in
val rule_tac = gen_rule_tac Tactic.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 Tactic.eresolve_tac);
val drule = meth' (gen_arule_tac Tactic.dresolve_tac);
val frule = meth' (gen_arule_tac Tactic.forward_tac);
end;
(* this *)
val this = METHOD (EVERY o map (HEADGOAL o Tactic.rtac));
(* assumption *)
fun asm_tac ths =
foldr (op APPEND') (K no_tac) (map (fn th => Tactic.rtac th THEN_ALL_NEW assume_tac) ths);
fun assm_tac ctxt =
assume_tac APPEND'
asm_tac (ProofContext.prems_of ctxt) APPEND'
Tactic.rtac Drule.reflexive_thm;
fun assumption_tac ctxt [] = assm_tac ctxt
| assumption_tac _ [fact] = asm_tac [fact]
| assumption_tac _ _ = K no_tac;
fun assumption ctxt = METHOD (HEADGOAL o assumption_tac ctxt);
(* res_inst_tac etc. *)
(*Reimplemented to support both static (Isar) and dynamic (proof state)
context. By Clemens Ballarin.*)
fun bires_inst_tac bires_flag ctxt insts thm =
let
val sign = ProofContext.sign_of ctxt;
(* Separate type and term insts *)
fun has_type_var ((x, _), _) = (case Symbol.explode x of
"'"::cs => true | cs => false);
val Tinsts = List.filter has_type_var insts;
val tinsts = filter_out has_type_var insts;
(* Tactic *)
fun tac i st =
let
(* Preprocess state: extract environment information:
- variables and their types
- type variables and their sorts
- parameters and their types *)
val (types, sorts) = types_sorts st;
(* Process type insts: Tinsts_env *)
fun absent xi = error
("No such variable in theorem: " ^ Syntax.string_of_vname xi);
val (rtypes, rsorts) = types_sorts thm;
fun readT (xi, s) =
let val S = case rsorts xi of SOME S => S | NONE => absent xi;
val T = Sign.read_typ (sign, sorts) s;
val U = TVar (xi, S);
in if Sign.typ_instance sign (T, U) then (U, T)
else error
("Instantiation of " ^ Syntax.string_of_vname xi ^ " fails")
end;
val Tinsts_env = map readT Tinsts;
(* Preprocess rule: extract vars and their types, apply Tinsts *)
fun get_typ xi =
(case rtypes xi of
SOME T => typ_subst_atomic Tinsts_env T
| NONE => absent xi);
val (xis, ss) = Library.split_list tinsts;
val Ts = map get_typ xis;
val (_, _, Bi, _) = dest_state(st,i)
val params = Logic.strip_params Bi
(* params of subgoal i as string typ pairs *)
val params = rev(Term.rename_wrt_term Bi params)
(* as they are printed: bound variables with *)
(* the same name are renamed during printing *)
fun types' (a, ~1) = (case assoc (params, a) of
NONE => types (a, ~1)
| some => some)
| types' xi = types xi;
fun internal x = is_some (types' (x, ~1));
val used = Drule.add_used thm (Drule.add_used st []);
val (ts, envT) =
ProofContext.read_termTs_schematic ctxt internal types' sorts used (ss ~~ Ts);
val envT' = map (fn (ixn, T) =>
(TVar (ixn, the (rsorts ixn)), T)) envT @ Tinsts_env;
val cenv =
map
(fn (xi, t) =>
pairself (Thm.cterm_of sign) (Var (xi, fastype_of t), t))
(gen_distinct
(fn ((x1, t1), (x2, t2)) => x1 = x2 andalso t1 aconv t2)
(xis ~~ ts));
(* Lift and instantiate rule *)
val {maxidx, ...} = rep_thm st;
val paramTs = map #2 params
and inc = maxidx+1
fun liftvar (Var ((a,j), T)) =
Var((a, j+inc), paramTs ---> incr_tvar inc T)
| liftvar t = raise TERM("Variable expected", [t]);
fun liftterm t = list_abs_free
(params, Logic.incr_indexes(paramTs,inc) t)
fun liftpair (cv,ct) =
(cterm_fun liftvar cv, cterm_fun liftterm ct)
val lifttvar = pairself (ctyp_of sign o incr_tvar inc);
val rule = Drule.instantiate
(map lifttvar envT', map liftpair cenv)
(lift_rule (st, i) thm)
in
if i > nprems_of st then no_tac st
else st |>
compose_tac (bires_flag, rule, nprems_of thm) i
end
handle TERM (msg,_) => (warning msg; no_tac st)
| THM (msg,_,_) => (warning msg; no_tac st);
in
tac
end;
fun gen_inst _ tac _ (quant, ([], thms)) =
METHOD (fn facts => quant (insert_tac facts THEN' tac thms))
| gen_inst inst_tac _ ctxt (quant, (insts, [thm])) =
METHOD (fn facts =>
quant (insert_tac facts THEN' inst_tac ctxt insts thm))
| gen_inst _ _ _ _ = error "Cannot have instantiations with multiple rules";
val res_inst_meth = gen_inst (bires_inst_tac false) Tactic.resolve_tac;
val eres_inst_meth = gen_inst (bires_inst_tac true) Tactic.eresolve_tac;
(* Preserve Var indexes of rl; increment revcut_rl instead.
Copied from tactic.ML *)
fun make_elim_preserve rl =
let val {maxidx,...} = rep_thm rl
fun cvar xi = cterm_of (Theory.sign_of ProtoPure.thy) (Var(xi,propT));
val revcut_rl' =
instantiate ([], [(cvar("V",0), cvar("V",maxidx+1)),
(cvar("W",0), cvar("W",maxidx+1))]) revcut_rl
val arg = (false, rl, nprems_of rl)
val [th] = Seq.list_of (bicompose false arg 1 revcut_rl')
in th end
handle Bind => raise THM("make_elim_preserve", 1, [rl]);
val cut_inst_meth =
gen_inst
(fn ctxt => fn insts => fn thm =>
bires_inst_tac false ctxt insts (make_elim_preserve thm))
Tactic.cut_rules_tac;
val dres_inst_meth =
gen_inst
(fn ctxt => fn insts => fn rule =>
bires_inst_tac true ctxt insts (make_elim_preserve rule))
Tactic.dresolve_tac;
val forw_inst_meth =
gen_inst
(fn ctxt => fn insts => fn rule =>
bires_inst_tac false ctxt insts (make_elim_preserve rule) THEN'
assume_tac)
Tactic.forward_tac;
fun subgoal_tac ctxt sprop =
DETERM o bires_inst_tac false ctxt [(("psi", 0), sprop)] cut_rl THEN'
SUBGOAL (fn (prop, _) =>
let val concl' = Logic.strip_assums_concl prop in
if null (term_tvars concl') then ()
else warning "Type variables in new subgoal: add a type constraint?";
all_tac
end);
fun subgoals_tac ctxt sprops = EVERY' (map (subgoal_tac ctxt) sprops);
fun thin_tac ctxt s =
bires_inst_tac true ctxt [(("V", 0), s)] thin_rl;
(* 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: Proof.context) (facts: thm list) : tactic = \
\let val thm = ProofContext.get_thm_closure ctxt o rpair NONE\n\
\ and thms = ProofContext.get_thms_closure ctxt o rpair NONE in\n"
^ txt ^
"\nend in Method.set_tactic tactic end")
false NONE;
Context.setmp (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: (((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 _ = Context.add_setup [MethodsData.init];
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) >> List.concat;
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 bang_sectioned_args' ss scan f =
sectioned_args (Args.bang_facts -- scan >> swap) ss (uncurry 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);
fun thm_args f = thms_args (fn [thm] => f thm | _ => error "Single theorem expected");
end;
(* rules syntax *)
local
val introN = "intro";
val elimN = "elim";
val destN = "dest";
val ruleN = "rule";
fun modifier name kind kind' att =
Args.$$$ name |-- (kind >> K NONE || kind' |-- Args.nat --| Args.colon >> SOME)
>> (pair (I: Proof.context -> Proof.context) o att);
val rules_modifiers =
[modifier destN Args.bang_colon Args.bang ContextRules.dest_bang_local,
modifier destN Args.colon (Scan.succeed ()) ContextRules.dest_local,
modifier elimN Args.bang_colon Args.bang ContextRules.elim_bang_local,
modifier elimN Args.colon (Scan.succeed ()) ContextRules.elim_local,
modifier introN Args.bang_colon Args.bang ContextRules.intro_bang_local,
modifier introN Args.colon (Scan.succeed ()) ContextRules.intro_local,
Args.del -- Args.colon >> K (I, ContextRules.rule_del_local)];
in
fun rules_args m = bang_sectioned_args' rules_modifiers (Scan.lift (Scan.option Args.nat)) m;
fun rules_meth n prems ctxt = METHOD (fn facts =>
HEADGOAL (insert_tac (prems @ facts) THEN' ObjectLogic.atomize_tac THEN' rules_tac ctxt n));
end;
(* tactic syntax *)
fun nat_thms_args f = uncurry f oo
(#2 oo syntax (Scan.lift (Scan.optional (Args.parens Args.nat) 0) -- Attrib.local_thmss));
val insts =
Scan.optional
(Args.enum1 "and" (Scan.lift (Args.name -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|
Scan.lift (Args.$$$ "in")) [] -- Attrib.local_thmss;
fun inst_args f src ctxt = f ctxt (#2 (syntax (Args.goal_spec HEADGOAL -- insts) src ctxt));
val insts_var =
Scan.optional
(Args.enum1 "and" (Scan.lift (Args.var -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|
Scan.lift (Args.$$$ "in")) [] -- Attrib.local_thmss;
fun inst_args_var f src ctxt = f ctxt (#2 (syntax (Args.goal_spec HEADGOAL -- insts_var) src ctxt));
fun goal_args' args tac src ctxt = #2 (syntax (Args.goal_spec HEADGOAL -- args >>
(fn (quant, s) => SIMPLE_METHOD' quant (tac s))) src ctxt);
fun goal_args args tac = goal_args' (Scan.lift args) tac;
fun goal_args_ctxt' args tac src ctxt =
#2 (syntax (Args.goal_spec HEADGOAL -- args >>
(fn (quant, s) => SIMPLE_METHOD' quant (tac ctxt s))) src ctxt);
fun goal_args_ctxt args tac = goal_args_ctxt' (Scan.lift args) tac;
(** method text **)
(* datatype text *)
datatype text =
Basic of (Proof.context -> Proof.method) |
Source of 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 (SIMPLE_METHOD 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);
(* misc tactic emulations *)
val subgoal_meth = goal_args_ctxt (Scan.repeat1 Args.name) subgoals_tac;
val thin_meth = goal_args_ctxt Args.name thin_tac;
val rename_meth = goal_args (Scan.repeat1 Args.name) Tactic.rename_params_tac;
val rotate_meth = goal_args (Scan.optional Args.int 1) Tactic.rotate_tac;
(* pure_methods *)
val pure_methods =
[("fail", no_args fail, "force failure"),
("succeed", no_args succeed, "succeed"),
("-", no_args insert_facts, "do nothing (insert current facts only)"),
("insert", thms_args insert, "insert theorems, ignoring facts (improper)"),
("unfold", thms_args unfold, "unfold definitions"),
("intro", thms_args intro, "repeatedly apply introduction rules"),
("elim", thms_args elim, "repeatedly apply elimination rules"),
("fold", thms_args fold, "fold definitions"),
("atomize", (atomize o #2) oo syntax (Args.mode "full"),
"present local premises as object-level statements"),
("rules", rules_args rules_meth, "apply many rules, including proof search"),
("rule", thms_ctxt_args some_rule, "apply some intro/elim rule"),
("erule", nat_thms_args erule, "apply rule in elimination manner (improper)"),
("drule", nat_thms_args drule, "apply rule in destruct manner (improper)"),
("frule", nat_thms_args frule, "apply rule in forward manner (improper)"),
("this", no_args this, "apply current facts as rules"),
("assumption", ctxt_args assumption, "proof by assumption, preferring facts"),
("rule_tac", inst_args_var res_inst_meth, "apply rule (dynamic instantiation)"),
("erule_tac", inst_args_var eres_inst_meth, "apply rule in elimination manner (dynamic instantiation)"),
("drule_tac", inst_args_var dres_inst_meth, "apply rule in destruct manner (dynamic instantiation)"),
("frule_tac", inst_args_var forw_inst_meth, "apply rule in forward manner (dynamic instantiation)"),
("cut_tac", inst_args_var cut_inst_meth, "cut rule (dynamic instantiation)"),
("subgoal_tac", subgoal_meth, "insert subgoal (dynamic instantiation)"),
("thin_tac", thin_meth, "remove premise (dynamic instantiation)"),
("rename_tac", rename_meth, "rename parameters of goal (dynamic instantiation)"),
("rotate_tac", rotate_meth, "rotate assumptions of goal"),
("prolog", thms_args prolog, "simple prolog interpreter"),
("tactic", simple_args Args.name tactic, "ML tactic as proof method")];
val _ = Context.add_setup [add_methods pure_methods];
end;
structure BasicMethod: BASIC_METHOD = Method;
open BasicMethod;