(* Title: Provers/classical.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1992 University of Cambridge
Theorem prover for classical reasoning, including predicate calculus, set
theory, etc.
Rules must be classified as intr, elim, safe, hazardous (unsafe).
A rule is unsafe unless it can be applied blindly without harmful results.
For a rule to be safe, its premises and conclusion should be logically
equivalent. There should be no variables in the premises that are not in
the conclusion.
*)
(*higher precedence than := facilitates use of references*)
infix 4 addSIs addSEs addSDs addIs addEs addDs delrules
setSWrapper compSWrapper setWrapper compWrapper
addSbefore addSaltern addbefore addaltern;
(*should be a type abbreviation in signature CLASSICAL*)
type netpair = (int * (bool * thm)) Net.net * (int * (bool * thm)) Net.net;
signature CLASET_THY_DATA =
sig
val clasetK: string
exception ClasetData of object ref
val thy_data: string * (object * (object -> object) *
(object * object -> object) * (Sign.sg -> object -> unit))
val fix_methods: object * (object -> object) *
(object * object -> object) * (Sign.sg -> object -> unit) -> unit
end;
signature CLASSICAL_DATA =
sig
val mp : thm (* [| P-->Q; P |] ==> Q *)
val not_elim : thm (* [| ~P; P |] ==> R *)
val classical : thm (* (~P ==> P) ==> P *)
val sizef : thm -> int (* size function for BEST_FIRST *)
val hyp_subst_tacs: (int -> tactic) list
end;
signature CLASSICAL =
sig
type claset
val empty_cs: claset
val print_cs: claset -> unit
val print_claset: theory -> unit
val rep_claset:
claset -> {safeIs: thm list, safeEs: thm list,
hazIs: thm list, hazEs: thm list,
uwrapper: (int -> tactic) -> (int -> tactic),
swrapper: (int -> tactic) -> (int -> tactic),
safe0_netpair: netpair, safep_netpair: netpair,
haz_netpair: netpair, dup_netpair: netpair}
val merge_cs : claset * claset -> claset
val addDs : claset * thm list -> claset
val addEs : claset * thm list -> claset
val addIs : claset * thm list -> claset
val addSDs : claset * thm list -> claset
val addSEs : claset * thm list -> claset
val addSIs : claset * thm list -> claset
val delrules : claset * thm list -> claset
val setSWrapper : claset * ((int -> tactic) -> (int -> tactic)) ->claset
val compSWrapper : claset * ((int -> tactic) -> (int -> tactic)) ->claset
val setWrapper : claset * ((int -> tactic) -> (int -> tactic)) ->claset
val compWrapper : claset * ((int -> tactic) -> (int -> tactic)) ->claset
val addSbefore : claset * (int -> tactic) -> claset
val addSaltern : claset * (int -> tactic) -> claset
val addbefore : claset * (int -> tactic) -> claset
val addaltern : claset * (int -> tactic) -> claset
val getWrapper : claset -> (int -> tactic) -> (int -> tactic)
val getSWrapper : claset -> (int -> tactic) -> (int -> tactic)
val claset_ref_of_sg: Sign.sg -> claset ref
val claset_ref_of: theory -> claset ref
val claset_of_sg: Sign.sg -> claset
val claset_of: theory -> claset
val CLASET: (claset -> tactic) -> tactic
val CLASET': (claset -> 'a -> tactic) -> 'a -> tactic
val claset: unit -> claset
val claset_ref: unit -> claset ref
val fast_tac : claset -> int -> tactic
val slow_tac : claset -> int -> tactic
val weight_ASTAR : int ref
val astar_tac : claset -> int -> tactic
val slow_astar_tac : claset -> int -> tactic
val best_tac : claset -> int -> tactic
val slow_best_tac : claset -> int -> tactic
val depth_tac : claset -> int -> int -> tactic
val deepen_tac : claset -> int -> int -> tactic
val contr_tac : int -> tactic
val dup_elim : thm -> thm
val dup_intr : thm -> thm
val dup_step_tac : claset -> int -> tactic
val eq_mp_tac : int -> tactic
val haz_step_tac : claset -> int -> tactic
val joinrules : thm list * thm list -> (bool * thm) list
val mp_tac : int -> tactic
val safe_tac : claset -> tactic
val safe_step_tac : claset -> int -> tactic
val clarify_tac : claset -> int -> tactic
val clarify_step_tac : claset -> int -> tactic
val step_tac : claset -> int -> tactic
val slow_step_tac : claset -> int -> tactic
val swap : thm (* ~P ==> (~Q ==> P) ==> Q *)
val swapify : thm list -> thm list
val swap_res_tac : thm list -> int -> tactic
val inst_step_tac : claset -> int -> tactic
val inst0_step_tac : claset -> int -> tactic
val instp_step_tac : claset -> int -> tactic
val AddDs : thm list -> unit
val AddEs : thm list -> unit
val AddIs : thm list -> unit
val AddSDs : thm list -> unit
val AddSEs : thm list -> unit
val AddSIs : thm list -> unit
val Delrules : thm list -> unit
val Safe_tac : tactic
val Safe_step_tac : int -> tactic
val Clarify_tac : int -> tactic
val Clarify_step_tac : int -> tactic
val Step_tac : int -> tactic
val Fast_tac : int -> tactic
val Best_tac : int -> tactic
val Slow_tac : int -> tactic
val Slow_best_tac : int -> tactic
val Deepen_tac : int -> int -> tactic
end;
structure ClasetThyData: CLASET_THY_DATA =
struct
(* data kind claset -- forward declaration *)
val clasetK = "claset";
exception ClasetData of object ref;
local
fun undef _ = raise Match;
val empty_ref = ref ERROR;
val prep_ext_fn = ref (undef: object -> object);
val merge_fn = ref (undef: object * object -> object);
val print_fn = ref (undef: Sign.sg -> object -> unit);
val empty = ClasetData empty_ref;
fun prep_ext exn = ! prep_ext_fn exn;
fun merge exn = ! merge_fn exn;
fun print sg exn = ! print_fn sg exn;
in
val thy_data = (clasetK, (empty, prep_ext, merge, print));
fun fix_methods (e, ext, mrg, prt) =
(empty_ref := e; prep_ext_fn := ext; merge_fn := mrg; print_fn := prt);
end;
end;
functor ClassicalFun(Data: CLASSICAL_DATA): CLASSICAL =
struct
local open ClasetThyData Data in
(*** Useful tactics for classical reasoning ***)
val imp_elim = (*cannot use bind_thm within a structure!*)
store_thm ("imp_elim", make_elim mp);
(*Prove goal that assumes both P and ~P.
No backtracking if it finds an equal assumption. Perhaps should call
ematch_tac instead of eresolve_tac, but then cannot prove ZF/cantor.*)
val contr_tac = eresolve_tac [not_elim] THEN'
(eq_assume_tac ORELSE' assume_tac);
(*Finds P-->Q and P in the assumptions, replaces implication by Q.
Could do the same thing for P<->Q and P... *)
fun mp_tac i = eresolve_tac [not_elim, imp_elim] i THEN assume_tac i;
(*Like mp_tac but instantiates no variables*)
fun eq_mp_tac i = ematch_tac [not_elim, imp_elim] i THEN eq_assume_tac i;
val swap =
store_thm ("swap", rule_by_tactic (etac thin_rl 1) (not_elim RS classical));
(*Creates rules to eliminate ~A, from rules to introduce A*)
fun swapify intrs = intrs RLN (2, [swap]);
(*Uses introduction rules in the normal way, or on negated assumptions,
trying rules in order. *)
fun swap_res_tac rls =
let fun addrl (rl,brls) = (false, rl) :: (true, rl RSN (2,swap)) :: brls
in assume_tac ORELSE'
contr_tac ORELSE'
biresolve_tac (foldr addrl (rls,[]))
end;
(*Duplication of hazardous rules, for complete provers*)
fun dup_intr th = zero_var_indexes (th RS classical);
fun dup_elim th = th RSN (2, revcut_rl) |> assumption 2 |> Seq.hd |>
rule_by_tactic (TRYALL (etac revcut_rl));
(**** Classical rule sets ****)
datatype claset =
CS of {safeIs : thm list, (*safe introduction rules*)
safeEs : thm list, (*safe elimination rules*)
hazIs : thm list, (*unsafe introduction rules*)
hazEs : thm list, (*unsafe elimination rules*)
uwrapper : (int -> tactic) ->
(int -> tactic), (*for transforming step_tac*)
swrapper : (int -> tactic) ->
(int -> tactic), (*for transform. safe_step_tac*)
safe0_netpair : netpair, (*nets for trivial cases*)
safep_netpair : netpair, (*nets for >0 subgoals*)
haz_netpair : netpair, (*nets for unsafe rules*)
dup_netpair : netpair}; (*nets for duplication*)
(*Desired invariants are
safe0_netpair = build safe0_brls,
safep_netpair = build safep_brls,
haz_netpair = build (joinrules(hazIs, hazEs)),
dup_netpair = build (joinrules(map dup_intr hazIs,
map dup_elim hazEs))}
where build = build_netpair(Net.empty,Net.empty),
safe0_brls contains all brules that solve the subgoal, and
safep_brls contains all brules that generate 1 or more new subgoals.
The theorem lists are largely comments, though they are used in merge_cs and print_cs.
Nets must be built incrementally, to save space and time.
*)
val empty_cs =
CS{safeIs = [],
safeEs = [],
hazIs = [],
hazEs = [],
uwrapper = I,
swrapper = I,
safe0_netpair = (Net.empty,Net.empty),
safep_netpair = (Net.empty,Net.empty),
haz_netpair = (Net.empty,Net.empty),
dup_netpair = (Net.empty,Net.empty)};
fun print_cs (CS {safeIs, safeEs, hazIs, hazEs, ...}) =
let val pretty_thms = map Display.pretty_thm in
Pretty.writeln (Pretty.big_list "introduction rules:" (pretty_thms hazIs));
Pretty.writeln (Pretty.big_list "safe introduction rules:" (pretty_thms safeIs));
Pretty.writeln (Pretty.big_list "elimination rules:" (pretty_thms hazEs));
Pretty.writeln (Pretty.big_list "safe elimination rules:" (pretty_thms safeEs))
end;
fun rep_claset (CS args) = args;
fun getWrapper (CS{uwrapper,...}) = uwrapper;
fun getSWrapper (CS{swrapper,...}) = swrapper;
(*** Adding (un)safe introduction or elimination rules.
In case of overlap, new rules are tried BEFORE old ones!!
***)
(*For use with biresolve_tac. Combines intr rules with swap to handle negated
assumptions. Pairs elim rules with true. *)
fun joinrules (intrs,elims) =
(map (pair true) (elims @ swapify intrs) @
map (pair false) intrs);
(*Priority: prefer rules with fewest subgoals,
then rules added most recently (preferring the head of the list).*)
fun tag_brls k [] = []
| tag_brls k (brl::brls) =
(1000000*subgoals_of_brl brl + k, brl) ::
tag_brls (k+1) brls;
fun insert_tagged_list kbrls netpr = foldr insert_tagged_brl (kbrls, netpr);
(*Insert into netpair that already has nI intr rules and nE elim rules.
Count the intr rules double (to account for swapify). Negate to give the
new insertions the lowest priority.*)
fun insert (nI,nE) = insert_tagged_list o (tag_brls (~(2*nI+nE))) o joinrules;
fun delete_tagged_list brls netpr = foldr delete_tagged_brl (brls, netpr);
val delete = delete_tagged_list o joinrules;
val mem_thm = gen_mem eq_thm
and rem_thm = gen_rem eq_thm;
(*Warn if the rule is already present ELSEWHERE in the claset. The addition
is still allowed.*)
fun warn_dup th (CS{safeIs, safeEs, hazIs, hazEs, ...}) =
if mem_thm (th, safeIs) then
warning ("Rule already in claset as Safe Intr\n" ^ string_of_thm th)
else if mem_thm (th, safeEs) then
warning ("Rule already in claset as Safe Elim\n" ^ string_of_thm th)
else if mem_thm (th, hazIs) then
warning ("Rule already in claset as unsafe Intr\n" ^ string_of_thm th)
else if mem_thm (th, hazEs) then
warning ("Rule already in claset as unsafe Elim\n" ^ string_of_thm th)
else ();
(*** Safe rules ***)
fun addSI (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair},
th) =
if mem_thm (th, safeIs) then
(warning ("Ignoring duplicate Safe Intr\n" ^ string_of_thm th);
cs)
else
let val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*)
partition (fn rl => nprems_of rl=0) [th]
val nI = length safeIs + 1
and nE = length safeEs
in warn_dup th cs;
CS{safeIs = th::safeIs,
safe0_netpair = insert (nI,nE) (safe0_rls, []) safe0_netpair,
safep_netpair = insert (nI,nE) (safep_rls, []) safep_netpair,
safeEs = safeEs,
hazIs = hazIs,
hazEs = hazEs,
uwrapper = uwrapper,
swrapper = swrapper,
haz_netpair = haz_netpair,
dup_netpair = dup_netpair}
end;
fun addSE (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair},
th) =
if mem_thm (th, safeEs) then
(warning ("Ignoring duplicate Safe Elim\n" ^ string_of_thm th);
cs)
else
let val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*)
partition (fn rl => nprems_of rl=1) [th]
val nI = length safeIs
and nE = length safeEs + 1
in warn_dup th cs;
CS{safeEs = th::safeEs,
safe0_netpair = insert (nI,nE) ([], safe0_rls) safe0_netpair,
safep_netpair = insert (nI,nE) ([], safep_rls) safep_netpair,
safeIs = safeIs,
hazIs = hazIs,
hazEs = hazEs,
uwrapper = uwrapper,
swrapper = swrapper,
haz_netpair = haz_netpair,
dup_netpair = dup_netpair}
end;
fun rev_foldl f (e, l) = foldl f (e, rev l);
val op addSIs = rev_foldl addSI;
val op addSEs = rev_foldl addSE;
fun cs addSDs ths = cs addSEs (map make_elim ths);
(*** Hazardous (unsafe) rules ***)
fun addI (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair},
th)=
if mem_thm (th, hazIs) then
(warning ("Ignoring duplicate unsafe Intr\n" ^ string_of_thm th);
cs)
else
let val nI = length hazIs + 1
and nE = length hazEs
in warn_dup th cs;
CS{hazIs = th::hazIs,
haz_netpair = insert (nI,nE) ([th], []) haz_netpair,
dup_netpair = insert (nI,nE) (map dup_intr [th], []) dup_netpair,
safeIs = safeIs,
safeEs = safeEs,
hazEs = hazEs,
uwrapper = uwrapper,
swrapper = swrapper,
safe0_netpair = safe0_netpair,
safep_netpair = safep_netpair}
end;
fun addE (cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair},
th) =
if mem_thm (th, hazEs) then
(warning ("Ignoring duplicate unsafe Elim\n" ^ string_of_thm th);
cs)
else
let val nI = length hazIs
and nE = length hazEs + 1
in warn_dup th cs;
CS{hazEs = th::hazEs,
haz_netpair = insert (nI,nE) ([], [th]) haz_netpair,
dup_netpair = insert (nI,nE) ([], map dup_elim [th]) dup_netpair,
safeIs = safeIs,
safeEs = safeEs,
hazIs = hazIs,
uwrapper = uwrapper,
swrapper = swrapper,
safe0_netpair = safe0_netpair,
safep_netpair = safep_netpair}
end;
val op addIs = rev_foldl addI;
val op addEs = rev_foldl addE;
fun cs addDs ths = cs addEs (map make_elim ths);
(*** Deletion of rules
Working out what to delete, requires repeating much of the code used
to insert.
Separate functions delSI, etc., are not exported; instead delrules
searches in all the lists and chooses the relevant delXX functions.
***)
fun delSI th
(cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}) =
if mem_thm (th, safeIs) then
let val (safe0_rls, safep_rls) = partition (fn rl => nprems_of rl=0) [th]
in CS{safe0_netpair = delete (safe0_rls, []) safe0_netpair,
safep_netpair = delete (safep_rls, []) safep_netpair,
safeIs = rem_thm (safeIs,th),
safeEs = safeEs,
hazIs = hazIs,
hazEs = hazEs,
uwrapper = uwrapper,
swrapper = swrapper,
haz_netpair = haz_netpair,
dup_netpair = dup_netpair}
end
else cs;
fun delSE th
(cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}) =
if mem_thm (th, safeEs) then
let val (safe0_rls, safep_rls) = partition (fn rl => nprems_of rl=1) [th]
in CS{safe0_netpair = delete ([], safe0_rls) safe0_netpair,
safep_netpair = delete ([], safep_rls) safep_netpair,
safeIs = safeIs,
safeEs = rem_thm (safeEs,th),
hazIs = hazIs,
hazEs = hazEs,
uwrapper = uwrapper,
swrapper = swrapper,
haz_netpair = haz_netpair,
dup_netpair = dup_netpair}
end
else cs;
fun delI th
(cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}) =
if mem_thm (th, hazIs) then
CS{haz_netpair = delete ([th], []) haz_netpair,
dup_netpair = delete ([dup_intr th], []) dup_netpair,
safeIs = safeIs,
safeEs = safeEs,
hazIs = rem_thm (hazIs,th),
hazEs = hazEs,
uwrapper = uwrapper,
swrapper = swrapper,
safe0_netpair = safe0_netpair,
safep_netpair = safep_netpair}
else cs;
fun delE th
(cs as CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair}) =
if mem_thm (th, hazEs) then
CS{haz_netpair = delete ([], [th]) haz_netpair,
dup_netpair = delete ([], [dup_elim th]) dup_netpair,
safeIs = safeIs,
safeEs = safeEs,
hazIs = hazIs,
hazEs = rem_thm (hazEs,th),
uwrapper = uwrapper,
swrapper = swrapper,
safe0_netpair = safe0_netpair,
safep_netpair = safep_netpair}
else cs;
(*Delete ALL occurrences of "th" in the claset (perhaps from several lists)*)
fun delrule (cs as CS{safeIs, safeEs, hazIs, hazEs, ...}, th) =
if mem_thm (th, safeIs) orelse mem_thm (th, safeEs) orelse
mem_thm (th, hazIs) orelse mem_thm (th, hazEs)
then delSI th (delSE th (delI th (delE th cs)))
else (warning ("Rule not in claset\n" ^ (string_of_thm th));
cs);
val op delrules = foldl delrule;
(*** Setting or modifying the wrapper tacticals ***)
(*Set a new uwrapper*)
fun (CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair, ...})
setWrapper new_uwrapper =
CS{safeIs = safeIs,
safeEs = safeEs,
hazIs = hazIs,
hazEs = hazEs,
uwrapper = new_uwrapper,
swrapper = swrapper,
safe0_netpair = safe0_netpair,
safep_netpair = safep_netpair,
haz_netpair = haz_netpair,
dup_netpair = dup_netpair};
(*Set a new swrapper*)
fun (CS{safeIs, safeEs, hazIs, hazEs, uwrapper, swrapper,
safe0_netpair, safep_netpair, haz_netpair, dup_netpair, ...})
setSWrapper new_swrapper =
CS{safeIs = safeIs,
safeEs = safeEs,
hazIs = hazIs,
hazEs = hazEs,
uwrapper = uwrapper,
swrapper = new_swrapper,
safe0_netpair = safe0_netpair,
safep_netpair = safep_netpair,
haz_netpair = haz_netpair,
dup_netpair = dup_netpair};
(*Compose a tactical with the existing uwrapper*)
fun cs compWrapper uwrapper' = cs setWrapper (uwrapper' o getWrapper cs);
(*Compose a tactical with the existing swrapper*)
fun cs compSWrapper swrapper' = cs setSWrapper (swrapper' o getSWrapper cs);
(*compose a safe tactic sequentially before/alternatively after safe_step_tac*)
fun cs addSbefore tac1 = cs compSWrapper (fn tac2 => tac1 THEN_MAYBE' tac2);
fun cs addSaltern tac2 = cs compSWrapper (fn tac1 => tac1 ORELSE' tac2);
(*compose a tactic sequentially before/alternatively after the step tactic*)
fun cs addbefore tac1 = cs compWrapper (fn tac2 => tac1 THEN_MAYBE' tac2);
fun cs addaltern tac2 = cs compWrapper (fn tac1 => tac1 APPEND' tac2);
(*Merge works by adding all new rules of the 2nd claset into the 1st claset.
Merging the term nets may look more efficient, but the rather delicate
treatment of priority might get muddled up.*)
fun merge_cs
(cs as CS{safeIs, safeEs, hazIs, hazEs, ...},
CS{safeIs=safeIs2, safeEs=safeEs2, hazIs=hazIs2, hazEs=hazEs2,...}) =
let val safeIs' = gen_rems eq_thm (safeIs2,safeIs)
val safeEs' = gen_rems eq_thm (safeEs2,safeEs)
val hazIs' = gen_rems eq_thm ( hazIs2, hazIs)
val hazEs' = gen_rems eq_thm ( hazEs2, hazEs)
in cs addSIs safeIs'
addSEs safeEs'
addIs hazIs'
addEs hazEs'
end;
(**** Simple tactics for theorem proving ****)
(*Attack subgoals using safe inferences -- matching, not resolution*)
fun safe_step_tac (cs as CS{safe0_netpair,safep_netpair,...}) =
getSWrapper cs (FIRST' [
eq_assume_tac,
eq_mp_tac,
bimatch_from_nets_tac safe0_netpair,
FIRST' hyp_subst_tacs,
bimatch_from_nets_tac safep_netpair]);
(*Repeatedly attack subgoals using safe inferences -- it's deterministic!*)
fun safe_tac cs = REPEAT_DETERM_FIRST
(fn i => COND (has_fewer_prems i) no_tac (safe_step_tac cs i));
(*** Clarify_tac: do safe steps without causing branching ***)
fun nsubgoalsP n (k,brl) = (subgoals_of_brl brl = n);
(*version of bimatch_from_nets_tac that only applies rules that
create precisely n subgoals.*)
fun n_bimatch_from_nets_tac n =
biresolution_from_nets_tac (orderlist o filter (nsubgoalsP n)) true;
fun eq_contr_tac i = ematch_tac [not_elim] i THEN eq_assume_tac i;
val eq_assume_contr_tac = eq_assume_tac ORELSE' eq_contr_tac;
(*Two-way branching is allowed only if one of the branches immediately closes*)
fun bimatch2_tac netpair i =
n_bimatch_from_nets_tac 2 netpair i THEN
(eq_assume_contr_tac i ORELSE eq_assume_contr_tac (i+1));
(*Attack subgoals using safe inferences -- matching, not resolution*)
fun clarify_step_tac (cs as CS{safe0_netpair,safep_netpair,...}) =
getSWrapper cs (FIRST' [
eq_assume_contr_tac,
bimatch_from_nets_tac safe0_netpair,
FIRST' hyp_subst_tacs,
n_bimatch_from_nets_tac 1 safep_netpair,
bimatch2_tac safep_netpair]);
fun clarify_tac cs = SELECT_GOAL (REPEAT_DETERM (clarify_step_tac cs 1));
(*** Unsafe steps instantiate variables or lose information ***)
(*Backtracking is allowed among the various these unsafe ways of
proving a subgoal. *)
fun inst0_step_tac (CS{safe0_netpair,safep_netpair,...}) =
assume_tac APPEND'
contr_tac APPEND'
biresolve_from_nets_tac safe0_netpair;
(*These unsafe steps could generate more subgoals.*)
fun instp_step_tac (CS{safep_netpair,...}) =
biresolve_from_nets_tac safep_netpair;
(*These steps could instantiate variables and are therefore unsafe.*)
fun inst_step_tac cs = inst0_step_tac cs APPEND' instp_step_tac cs;
fun haz_step_tac (CS{haz_netpair,...}) =
biresolve_from_nets_tac haz_netpair;
(*Single step for the prover. FAILS unless it makes progress. *)
fun step_tac cs i = getWrapper cs
(K (safe_tac cs) ORELSE' (inst_step_tac cs ORELSE' haz_step_tac cs)) i;
(*Using a "safe" rule to instantiate variables is unsafe. This tactic
allows backtracking from "safe" rules to "unsafe" rules here.*)
fun slow_step_tac cs i = getWrapper cs
(K (safe_tac cs) ORELSE' (inst_step_tac cs APPEND' haz_step_tac cs)) i;
(**** The following tactics all fail unless they solve one goal ****)
(*Dumb but fast*)
fun fast_tac cs = SELECT_GOAL (DEPTH_SOLVE (step_tac cs 1));
(*Slower but smarter than fast_tac*)
fun best_tac cs =
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (step_tac cs 1));
fun slow_tac cs = SELECT_GOAL (DEPTH_SOLVE (slow_step_tac cs 1));
fun slow_best_tac cs =
SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, sizef) (slow_step_tac cs 1));
(***ASTAR with weight weight_ASTAR, by Norbert Voelker*)
val weight_ASTAR = ref 5;
fun astar_tac cs =
SELECT_GOAL ( ASTAR (has_fewer_prems 1
, fn level =>(fn thm =>size_of_thm thm + !weight_ASTAR *level))
(step_tac cs 1));
fun slow_astar_tac cs =
SELECT_GOAL ( ASTAR (has_fewer_prems 1
, fn level =>(fn thm =>size_of_thm thm + !weight_ASTAR *level))
(slow_step_tac cs 1));
(**** Complete tactic, loosely based upon LeanTaP. This tactic is the outcome
of much experimentation! Changing APPEND to ORELSE below would prove
easy theorems faster, but loses completeness -- and many of the harder
theorems such as 43. ****)
(*Non-deterministic! Could always expand the first unsafe connective.
That's hard to implement and did not perform better in experiments, due to
greater search depth required.*)
fun dup_step_tac (cs as (CS{dup_netpair,...})) =
biresolve_from_nets_tac dup_netpair;
(*Searching to depth m.*)
fun depth_tac cs m i state =
SELECT_GOAL
(getWrapper cs
(fn i => REPEAT_DETERM1 (COND (has_fewer_prems i) no_tac
(safe_step_tac cs i)) THEN_ELSE
(DEPTH_SOLVE (depth_tac cs m i),
inst0_step_tac cs i APPEND
COND (K(m=0)) no_tac
((instp_step_tac cs i APPEND dup_step_tac cs i)
THEN DEPTH_SOLVE (depth_tac cs (m-1) i)))) 1)
i state;
(*Search, with depth bound m.
This is the "entry point", which does safe inferences first.*)
fun safe_depth_tac cs m =
SUBGOAL
(fn (prem,i) =>
let val deti =
(*No Vars in the goal? No need to backtrack between goals.*)
case term_vars prem of
[] => DETERM
| _::_ => I
in SELECT_GOAL (TRY (safe_tac cs) THEN
DEPTH_SOLVE (deti (depth_tac cs m 1))) i
end);
fun deepen_tac cs = DEEPEN (2,10) (safe_depth_tac cs);
(** claset theory data **)
(* init data kind claset *)
exception CSData of claset ref;
local
val empty = CSData (ref empty_cs);
(*create new references*)
fun prep_ext (ClasetData (ref (CSData (ref cs)))) =
ClasetData (ref (CSData (ref cs)));
fun merge (ClasetData (ref (CSData (ref cs1))), ClasetData (ref (CSData (ref cs2)))) =
ClasetData (ref (CSData (ref (merge_cs (cs1, cs2)))));
fun print (_: Sign.sg) (ClasetData (ref (CSData (ref cs)))) = print_cs cs;
in
val _ = fix_methods (empty, prep_ext, merge, print);
end;
(* access claset *)
fun print_claset thy = Display.print_data thy clasetK;
fun claset_ref_of_sg sg =
(case Sign.get_data sg clasetK of
ClasetData (ref (CSData r)) => r
| _ => sys_error "claset_ref_of_sg");
val claset_ref_of = claset_ref_of_sg o sign_of;
val claset_of_sg = ! o claset_ref_of_sg;
val claset_of = claset_of_sg o sign_of;
fun CLASET tacf state = tacf (claset_of_sg (sign_of_thm state)) state;
fun CLASET' tacf i state = tacf (claset_of_sg (sign_of_thm state)) i state;
val claset = claset_of o Context.get_context;
val claset_ref = claset_ref_of_sg o sign_of o Context.get_context;
(* change claset *)
fun change_claset f x = claset_ref () := (f (claset (), x));
val AddDs = change_claset (op addDs);
val AddEs = change_claset (op addEs);
val AddIs = change_claset (op addIs);
val AddSDs = change_claset (op addSDs);
val AddSEs = change_claset (op addSEs);
val AddSIs = change_claset (op addSIs);
val Delrules = change_claset (op delrules);
(* tactics referring to the implicit claset *)
(*the abstraction over the proof state delays the dereferencing*)
fun Safe_tac st = safe_tac (claset()) st;
fun Safe_step_tac i st = safe_step_tac (claset()) i st;
fun Clarify_step_tac i st = clarify_step_tac (claset()) i st;
fun Clarify_tac i st = clarify_tac (claset()) i st;
fun Step_tac i st = step_tac (claset()) i st;
fun Fast_tac i st = fast_tac (claset()) i st;
fun Best_tac i st = best_tac (claset()) i st;
fun Slow_tac i st = slow_tac (claset()) i st;
fun Slow_best_tac i st = slow_best_tac (claset()) i st;
fun Deepen_tac m = deepen_tac (claset()) m;
end;
end;