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prove.pl
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prove.pl
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:- [basic].
term_poseq_term(Var, _) :- var(Var), !.
term_poseq_term(_, Var) :- var(Var), !.
term_poseq_term((FUN $ TERMS_A), (FUN $ TERMS_B)) :-
length(TERMS_A, LTH),
length(TERMS_B, LTH).
term_poseq_term(_, TERM_A, TERM_B) :-
term_poseq_term(TERM_A, TERM_B).
term_poseq_term(OPQEs, TERM_A, TERM_B) :-
member((_, QE), OPQEs),
inst_with_lvs(QE, ("=" $ [TERM_L, TERM_R])),
(
term_poseq_term(TERM_A, TERM_L) ;
term_poseq_term(TERM_A, TERM_R) ;
term_poseq_term(TERM_B, TERM_R) ;
term_poseq_term(TERM_B, TERM_L)
).
%%%%%%% Decomposition to Equational goals %%%%%%%
intro_eqs(MONO, [], [], GOAL, MONO, [], GOAL).
intro_eqs(MONO, [TERM_A | TERMS_A], [TERM_B | TERMS_B], GOAL, Iff, [(ONE, SubGOAL) | HGS], GOAL_N) :-
apply_c(MONO, TERM_A, GOAL, MONOA, GOAL_A),
apply_c(MONOA, TERM_B, GOAL_A, MONOAB, GOAL_AB),
apply_b(MONOAB, GOAL_AB, ONE, TempMONO, SubGOAL, GOAL_T),
intro_eqs(TempMONO, TERMS_A, TERMS_B, GOAL_T, Iff, HGS, GOAL_N).
break_eq_fun(OPEs, ONE, GOAL, HGS) :-
ONE = (_, ~ (("=" $ [TERM_A, TERM_B]))),
\+ var(TERM_A),
\+ var(TERM_B),
TERM_A = (FUN $ TERMS_A),
TERM_B = (FUN $ TERMS_B),
length(TERMS_A, LTH),
length(TERMS_B, LTH),
cmap(term_poseq_term(OPEs), TERMS_A, TERMS_B),
mk_mono_fun(LTH, FUN, MONOForm),
apply_t(MONOForm, GOAL, MONO, GOAL0),
intro_eqs(MONO, TERMS_A, TERMS_B, GOAL0, OPE, HGS, GOAL1),
apply_x(ONE, OPE, GOAL1).
break_eq_rel(OPEs, OPA, ONA, GOAL, HGS) :-
OPA = (_, (REL $ TERMS_A)),
ONA = (_, ~ ((REL $ TERMS_B))),
length(TERMS_A, LTH),
length(TERMS_B, LTH),
cmap(term_poseq_term(OPEs), TERMS_A, TERMS_B),
mk_mono_rel(LTH, REL, MONOForm),
apply_t(MONOForm, GOAL, MONO, GOAL0),
intro_eqs(MONO, TERMS_A, TERMS_B, GOAL0, IMP, HGS, GOAL1),
apply_b(IMP, GOAL1, HYP_L, HYP_R, GOAL_L, GOAL_R),
apply_x(HYP_L, OPA, GOAL_L),
apply_x(ONA, HYP_R, GOAL_R).
subst_fun_mul(OPEs, ONE, GOAL, NewOPEs) :-
ONE = (_, ~ (("=" $ [TERM_A, TERM_B]))),
(
TERM_A == TERM_B ->
(eq_refl(ONE, GOAL), NewOPEs = OPEs) ;
subst_fun_mul_0(OPEs, ONE, GOAL, NewOPEs)
).
subst_fun_mul_0(OPEs, ONF, GOAL, OPEs) :-
ONF = (_, ~ (("=" $ [TERM_A, TERM_B]))),
unify_with_occurs_check(TERM_A, TERM_B),
eq_refl(ONF, GOAL).
subst_fun_mul_0(OPEs, ONE, GOAL, NewOPEs) :-
break_eq_fun(OPEs, ONE, GOAL, HGS),
subst_fun_mul_aux(OPEs, HGS, NewOPEs).
subst_fun_mul_0(OPQEs, ONE, GOAL, NewOPQEs) :-
ONE = (_, ~ (("=" $ [TERM_A0, TERM_C]))),
pluck_uniq(OPQEs, OPQE, REST),
rp([c], [OPQE], GOAL, [PRE_OPE], GOAL_T),
PRE_OPE = (_, (("=" $ [_, _]))),
orient_hyp(PRE_OPE, GOAL_T, OPE, GOAL0),
OPE = (_, (("=" $ [TERM_A1, TERM_B]))),
unify_with_occurs_check(TERM_A0, TERM_A1),
apply_s(("=" $ [TERM_B, TERM_C]), GOAL0, NewONE, NewOPE, GOAL1, GOAL2),
subst_fun_mul(REST, NewONE, GOAL1, NewOPQEs),
eq_trans(OPE, NewOPE, ONE, GOAL2).
subst_fun_mul_aux(OPEs, [], OPEs).
subst_fun_mul_aux(OPEs, [(ONE, GOAL) | HGS], NewOPEs) :-
subst_fun_mul(OPEs, ONE, GOAL, TempOPEs),
subst_fun_mul_aux(TempOPEs, HGS, NewOPEs).
subst_rel_mul(HYP_L, OPEs, HYP_R, GOAL, NewOPEs) :-
orient_literal_hyps(HYP_L, HYP_R, PreOPA, ONA),
orient_hyp(PreOPA, GOAL, OPA, GOAL_T),
break_eq_rel(OPEs, OPA, ONA, GOAL_T, HGS),
subst_fun_mul_aux(OPEs, HGS, NewOPEs).
subst_fun_add(EQNS, (HYP, GOAL)) :-
subst_fun_add(EQNS, HYP, GOAL).
subst_fun_add(EQNS, ONE, GOAL) :-
ONE = (_, ~ (("=" $ [TERM_A, TERM_B]))),
(
TERM_A == TERM_B ->
eq_refl(ONE, GOAL) ;
subst_fun_add_0(EQNS, ONE, GOAL)
).
subst_fun_add_0(_, ONF, GOAL) :-
ONF = (_, ~ (("=" $ [TERM_A, TERM_B]))),
unify_with_occurs_check(TERM_A, TERM_B),
eq_refl(ONF, GOAL).
subst_fun_add_0(EQNS, ONE, GOAL) :-
break_eq_fun(EQNS, ONE, GOAL, HGS),
maplist(subst_fun_add(EQNS), HGS).
subst_fun_add_0(OPQEs, ONE, GOAL) :-
ONE = (_, ~ (("=" $ [TERM_A0, TERM_C]))),
pluck_uniq(OPQEs, OPQE, REST),
rp([c], [OPQE], GOAL, [PRE_OPE], GOAL_T),
PRE_OPE = (_, (("=" $ [_, _]))),
orient_hyp(PRE_OPE, GOAL_T, OPE, GOAL0),
OPE = (_, (("=" $ [TERM_A1, TERM_B]))),
unify_with_occurs_check(TERM_A0, TERM_A1),
apply_s(("=" $ [TERM_B, TERM_C]), GOAL0, NewONE, NewOPE, GOAL1, GOAL2),
subst_fun_add(REST, NewONE, GOAL1),
eq_trans(OPE, NewOPE, ONE, GOAL2).
subst_rel_add(EQNS, HYP_L, HYP_R, GOAL) :-
orient_literal_hyps(HYP_L, HYP_R, PreOPA, ONA),
orient_hyp(PreOPA, GOAL, OPA, GOAL_T),
break_eq_rel(EQNS, OPA, ONA, GOAL_T, HGS),
maplist(subst_fun_add(EQNS), HGS).
pick_pivot(HYPS, HYP, GOAL, HYP_N, GOAL_N) :-
rp([b, c, n], [HYP], GOAL, HGS),
pluck(HGS, ([HYP_N], GOAL_N), REST),
maplist(pick_mate(HYPS), REST).
pick_pivot_prop(HYPS, HYP, GOAL, HYP_N, GOAL_N) :-
rp([b, n], [HYP], GOAL, HGS),
pluck(HGS, ([HYP_N], GOAL_N), REST),
maplist(pick_mate(HYPS), REST).
apply_aocs(ANTE, [AOC | AOCS], GOAL_I, CONS, GOAL_O) :-
rp([c], [AOC], GOAL_I, [IMP], GOAL_T),
apply_b(IMP, GOAL_T, HYP_L, HYP_R, GOAL_L, GOAL_R),
mate(ANTE, HYP_L, GOAL_L),
apply_aocs(HYP_R, AOCS, GOAL_R, CONS, GOAL_O).
apply_aocs(HYP, [], GOAL, HYP, GOAL).
vcnf(PREM, HYPS, GOAL) :-
apply_n(PREM, GOAL, PREM_N, GOAL_N), !,
vcnf(PREM_N, HYPS, GOAL_N).
vcnf(PREM, HYPS, GOAL) :-
apply_b(PREM, GOAL, PREM_A, PREM_B, GOAL_A, GOAL_B), !,
vcnf(PREM_A, HYPS, GOAL_A),
vcnf(PREM_B, HYPS, GOAL_B).
vcnf(PREM, HYPS, GOAL) :-
apply_c(PREM, _, GOAL, PREM_N, GOAL_N), !,
vcnf(PREM_N, HYPS, GOAL_N).
vcnf(PREM, HYPS, GOAL) :-
member(DIR, [lft, rgt]),
apply_a(PREM, DIR, GOAL, PREM_N, GOAL_N),
vcnf(PREM_N, HYPS, GOAL_N).
vcnf(PREM, HYPS, GOAL) :-
member(HYP, HYPS),
mate(PREM, HYP, GOAL).
vacc_aux(TRP) :-
para__n(TRP, TRP_N) ->
mate(TRP_N) ;
mate(TRP).
vacc_aux((PREM, CONC, GOAL)) :-
pmt_cla(PREM, CONC, GOAL).
vacc(PREM, CONC, GOAL) :-
rp([d], [CONC], GOAL, [CONC_N], GOAL1),
rp([c], [PREM], GOAL1, [PREM_T], GOAL2),
member(DIR, [lft, rgt]),
apply_a(PREM_T, DIR, GOAL2, PREM_N, GOAL3),
paraab_choice((PREM_N, CONC_N, GOAL3), TRP_A, TRP_B),
vacc_aux(TRP_A),
vacc_aux(TRP_B).
pmt_cla(PREM, CONC, GOAL) :-
rp([a, d, n], [CONC], GOAL, HYPS, GOAL_T),
rp([b, c, n], [PREM], GOAL_T, HGS),
maplist(pick_mate(HYPS), HGS).
res(PYP0, PYP1, NYP, GOAL) :-
rp([a, d, n], [NYP], GOAL, HYPS, GOAL_T),
(
res_core(PYP0, PYP1, HYPS, GOAL_T) ;
res_core(PYP1, PYP0, HYPS, GOAL_T)
), !.
res_core(PYP0, PYP1, HYPS, GOAL) :-
apply_s(_, GOAL, NPVT, PPVT, GOAL_N, GOAL_P),
rp([b, c, n], [PYP0], GOAL_N, HGS0),
rp([b, c, n], [PYP1], GOAL_P, HGS1), !,
pluck(HGS0, ([HYP0], GOAL0), REST0),
mate_pn(HYP0, NPVT, GOAL0),
pluck(HGS1, ([HYP1], GOAL1), REST1),
mate_pn(PPVT, HYP1, GOAL1),
maplist(pick_mate([NPVT | HYPS]), REST0),
maplist(pick_mate([PPVT | HYPS]), REST1).
dfu(DEFS, PREM, CONC, GOAL) :-
rp([a, d, n], [CONC], GOAL, HYPS, GOAL_T),
rp([b, c, n], [PREM], GOAL_T, HGS),
dfu_many(DEFS, HYPS, HGS).
dfu_many(_, [], []).
dfu_many(EQNS, HYPS, [([HYP], GOAL) | HGS]) :-
pluck(HYPS, CMP, REST),
subst_rel_add(EQNS, HYP, CMP, GOAL),
dfu_many(EQNS, REST, HGS).
dff(_, HYP0, HYP1, DFP) :-
mate(HYP0, HYP1, DFP).
dff(Defs, HYP0, HYP1, DFP) :-
(
paran((HYP0, HYP1, DFP), (NewHYP0, NewHYP1, NewDFP)) ;
paracd((HYP0, HYP1, DFP), (NewHYP0, NewHYP1, NewDFP))
), !,
dff(Defs, NewHYP0, NewHYP1, NewDFP).
dff(Defs, HYP0, HYP1, GOAL) :-
paraab((HYP0, HYP1, GOAL), (HYP0L, HYP1L, GOAL_L), (HYP0R, HYP1R, GOAL_R)),
dff(Defs, HYP0L, HYP1L, GOAL_L),
dff(Defs, HYP0R, HYP1R, GOAL_R).
dff(Defs, HYP0, HYP1, DFP) :-
HYP1 = (_, Atom),
atomic_form(Atom),
member(Def, Defs),
rp([c], [Def], DFP, [IFF], DFP0),
IFF = (_, ((Atom <> _))), !,
apply_a(IFF, lft, DFP0, IMP, DFP1),
apply_b(IMP, DFP1, Ante, Cons, DFP2, DFP3),
mate(HYP1, Ante, DFP2),
dff(Defs, HYP0, Cons, DFP3).
dff(Defs, HYP0, HYP1, DFP) :-
HYP1 = (_, ~ Atom),
atomic_form(Atom),
member(Def, Defs),
rp([c], [Def], DFP, [IFF], DFP0),
IFF = (_, (Atom <> _)), !,
apply_a(IFF, rgt, DFP0, IMP, DFP1),
apply_b(IMP, DFP1, Ante, Cons, DFP2, DFP3),
mate(HYP1, Cons, DFP3),
dff(Defs, HYP0, Ante, DFP2).
%%%%%%%%%%%%%%%% SAT SOLVER %%%%%%%%%%%%%%%%
lit_num(ANA, ~ ATOM, NEG) :- !,
get_assoc(ATOM, ANA, NUM),
NEG is - NUM.
lit_num(ANA, ATOM, NUM) :- !,
get_assoc(ATOM, ANA, NUM).
cla_hyp_nums(ANA, (_, CLA), NUMS) :-
cla_lits(CLA, LITS),
cmap(lit_num(ANA), LITS, NUMS).
% cla_lits((_, CF), LITS) :-
% cf_lits(CF, LITS).
cla_hyp_atoms((_, CLA), ATOMS) :-
cla_lits(CLA, LITS),
cmap(lit_atom, LITS, ATOMS).
add_to_sat_table(CH, TBL_I, TBL_O) :-
cla_hyp_atoms(CH, ATOMS),
foldl(atom_table, ATOMS, TBL_I, TBL_O).
atom_table(ATOM, (NUM_I, ANA_I, NAA_I), TBL_O) :-
get_assoc(ATOM, ANA_I, _) ->
TBL_O = (NUM_I, ANA_I, NAA_I)
;
num_succ(NUM_I, NUM_O),
put_assoc(ATOM, ANA_I, NUM_I, ANA_O),
put_assoc(NUM_I, NAA_I, ATOM, NAA_O),
TBL_O = (NUM_O, ANA_O, NAA_O).
mk_sat_tables(CHS, ANA, NAA) :-
empty_assoc(EMP),
foldl(add_to_sat_table, CHS, (1, EMP, EMP), (_, ANA, NAA)).
add_cla_hyp_to_ctx(CH, (NUM_I, CTX_I), (NUM_O, CTX_O)) :-
num_succ(NUM_I, NUM_O),
put_assoc(NUM_I, CTX_I, CH, CTX_O).
mk_sat_ctx(CHS, CTX) :-
empty_assoc(EMP),
foldl(add_cla_hyp_to_ctx, CHS, (1, EMP), (_, CTX)).
string_numbers(STR, NUMS) :-
split_string(STR, " ", "", STRS),
cmap(string_number, STRS, NUMS).
nums_dimacs(NUMS, Str) :-
maplist(number_string, NUMS, Strs),
strings_concat_with(" ", Strs, TempStr),
string_concat(TempStr, " 0", Str).
num_lit(NAA, NUM, LIT) :-
NUM < 0 ->
NEG is - NUM,
get_assoc(NEG, NAA, ATOM),
LIT = ~ ATOM
;
get_assoc(NUM, NAA, LIT).
lits_cla([], ff).
lits_cla(Lits, Cla) :- lits_cla_core(Lits, Cla).
lits_cla_core([Lit], Lit).
lits_cla_core([Lit | Lits], (Lit \/ Cla)) :- lits_cla_core(Lits, Cla).
nums_cla(NAA, NUMS, CLA) :-
cmap(num_lit(NAA), NUMS, LITS),
lits_cla(LITS, CLA).
line_sat_insts(_, LINE, SIS, SIS) :-
split_string(LINE, " ", "", [_, "d" | _]), !.
line_sat_insts(NAA, LINE, [rup(SIDS, SID, CLA) | SIS], SIS) :-
string_numbers(LINE, [SID | NUMS]),
append(CLA_NUMS, [0 | REST], NUMS),
nums_cla(NAA, CLA_NUMS, CLA),
append(SIDS, [0], REST).
file_sat_insts(NAA, FILE, SIS) :-
read_file_strings(FILE, LINES),
foldl(line_sat_insts(NAA), LINES, SIS, []).
nums_maxvar(NUMS, MaxVar) :-
cmap(abs, NUMS, Nats),
max_list(Nats, MaxVar).
numss_maxvar(NUMSs, MaxVar) :-
maplist(nums_maxvar, NUMSs, MaxVars),
max_list(MaxVars, MaxVar).
numss_dimacs(NUMSs, DIMACS) :-
numss_maxvar(NUMSs, MaxVar),
number_string(MaxVar, MaxVarStr),
length(NUMSs, NumCla),
number_string(NumCla, NumClaStr),
strings_concat(["p cnf ", MaxVarStr, " ", NumClaStr], Str),
maplist(nums_dimacs, NUMSs, Strs),
strings_concat_with("\n", [Str | Strs], DIMACS).
find_new_unit_core([LIT], _, LIT) :- !.
find_new_unit_core([LIT_A | LITS_A], LITS_B, LIT) :-
member(LIT_B, LITS_B),
complements(LIT_A, LIT_B), !,
find_new_unit_core(LITS_A, LITS_B, LIT).
find_new_unit_core([LIT | _], _, LIT).
find_new_unit((_, FORM), HYPS, LIT) :-
cla_lits(FORM, LITS_A),
cmap(hyp_form, HYPS, LITS_B),
find_new_unit_core(LITS_A, LITS_B, LIT).
unit_propagate(PREM, (HYPS_I, GOAL_I), ([HYP_O | HYPS_I], GOAL_O)) :-
find_new_unit(PREM, HYPS_I, LIT),
apply_s(LIT, GOAL_I, HYP_T, HYP_O, GOAL_T, GOAL_O),
rp([n], [HYP_T], GOAL_T, [HYP_C], GOAL_C),
rp([b, n], [PREM], GOAL_C, HGS),
cmap(pick_mate([HYP_C | HYPS_I]), HGS).
get_sat_cla(CTX, SID, CLA) :-
get_assoc(SID, CTX, CLA).
put_sat_cla(CTX_I, SID, CLA, CTX_O) :-
put_assoc(SID, CTX_I, CLA, CTX_O).
use_sat_inst(CTX, del(_), GOAL, CTX, GOAL).
use_sat_inst(CTX, rup(SIDS, SID, CLA), GOAL, CTX_N, GOAL_N) :-
apply_s(CLA, GOAL, NYP, PYP, GOAL_T, GOAL_N),
put_sat_cla(CTX, SID, PYP, CTX_N),
rp([a, n], [NYP], GOAL_T, HYPS_I, GOAL_I),
cmap(get_sat_cla(CTX), SIDS, PREMS), !,
foldl_cut(unit_propagate, PREMS, (HYPS_I, GOAL_I), ([HYP | HYPS_O], GOAL_O)), !,
member(CMP, HYPS_O),
mate(HYP, CMP, GOAL_O), !.
use_sat_insts(CTX, [SI | SIS], GOAL) :-
use_sat_inst(CTX, SI, GOAL, CTX_N, GOAL_N),
(
SIS = [] ->
SI = rup(_, SID, _),
get_sat_cla(CTX_N, SID, CLA),
use_pf(CLA, GOAL_N)
;
use_sat_insts(CTX_N, SIS, GOAL_N)
).
sat(CHS, GOAL) :-
mk_sat_tables(CHS, ANA, NAA),
cmap(cla_hyp_nums(ANA), CHS, NUMSS),
numss_dimacs(NUMSS, DIMACS),
write_file("temp.cnf", DIMACS), !,
shell("cadical -q temp.cnf temp.drat", _), !,
shell("drat-trim temp.cnf temp.drat -L temp.lrat", _), !,
write("Reading LRAT file...\n\n"),
file_sat_insts(NAA, "temp.lrat", SIS),
write("Constructing SAT context...\n\n"),
mk_sat_ctx(CHS, CTX),
write("Using SAT instructions...\n\n"),
use_sat_insts(CTX, SIS, GOAL),
delete_file("temp.cnf"),
delete_file("temp.drat"),
delete_file("temp.lrat"),
true.
eskm(AOCS, H2G) :-
para_mate(H2G) -> true
;
paraab(H2G, H2G_L, H2G_R) ->
skm(AOCS, H2G_L),
skm(AOCS, H2G_R)
;
para__d(H2G, H2G_N) ->
eskm(AOCS, H2G_N)
;
para_c_(H2G, H2G_N) ->
eskm(AOCS, H2G_N)
;
H2G = (PREM, CONC, GOAL),
pluck(AOCS, AOC, REST),
rp([c], [AOC], GOAL, [HYP], GOAL_T),
apply_b(HYP, GOAL_T, HYP_L, HYP_R, GOAL_L, GOAL_R),
apply_x(HYP_L, PREM, GOAL_L),
eskm(REST, (HYP_R, CONC, GOAL_R)).
skm(AOCS, H2G) :-
para_mate(H2G) -> true
;
para_c_(H2G, H2G_N),
skm(AOCS, H2G_N)
;
para_cd_lax(H2G, H2G_N),
skm(AOCS, H2G_N)
;
paraab(H2G, H2G_L, H2G_R),
skm(AOCS, H2G_L),
skm(AOCS, H2G_R)
;
H2G = (PREM, CONC, GOAL),
pluck(AOCS, AOC, REST),
rp([c], [AOC], GOAL, [HYP], GOAL_T),
apply_b(HYP, GOAL_T, HYP_L, HYP_R, GOAL_L, GOAL_R),
apply_x(HYP_L, PREM, GOAL_L),
skm(REST, (HYP_R, CONC, GOAL_R)).
spl_exp([], [], GOAL, [], GOAL).
spl_exp([PREM | PREMS], HYPS_I, GOAL_I, [HYP | HYPS_O], GOAL_O) :-
pluck(HYPS_I, HYP_I, REST),
(
apply_a(PREM, lft, GOAL_I, HYP_T, GOAL_T) ;
apply_a(PREM, rgt, GOAL_I, HYP_T, GOAL_T)
),
(
apply_b(HYP_T, GOAL_T, HYP_A, HYP_B, GOAL_A, GOAL_B) ;
apply_b(HYP_T, GOAL_T, HYP_B, HYP_A, GOAL_B, GOAL_A)
),
mate(HYP_A, HYP_I, GOAL_A),
rp([d, n], [HYP_B], GOAL_B, [HYP], GOAL),
spl_exp(PREMS, REST, GOAL, HYPS_O, GOAL_O).
eqf(HYPS, EQN, ([HYP], GOAL)) :-
member(CMP, HYPS),
subst_rel_add([EQN], CMP, HYP, GOAL).
rwa(AYP, TRP) :-
TRP = (PREM, _, GOAL),
(
para_mate(TRP) -> true ;
paran(TRP, TRP_N) -> rwa(AYP, TRP_N) ;
paraab(TRP, TRP_L, TRP_R),
rwa(AYP, TRP_L),
rwa(AYP, TRP_R)
;
mate(AYP, PREM, GOAL)
).
pmt((PREM, CONC, GOAL)) :-
rp([a, n], [CONC], GOAL, HYPS, GOAL_T),
rp([b, n], [PREM], GOAL_T, HGS),
maplist(pick_mate(HYPS), HGS).
speq(TRP) :-
para_cd(TRP, TEMP) -> speq(TEMP) ;
a_para(TRP, TEMP),
para_mate(TEMP).
scj(H2G) :-
pmt(H2G) -> true ;
paran(H2G, H2G_N) -> scj(H2G_N) ;
a_para(H2G, H2G_N),
scj(H2G_N).
/*
esimp_fork_not(TRP, TRP_A, TRP_B) :-
TRP = ((_, ~ FORM), _, _),
bool_simp(FORM, NORM),
para_s_(~ NORM, TRP, TRP_A, TRP_B).
esimp_not(X) :-
para_falsehood(X) -> true ;
para_mate(X) -> true ;
paran(X, Y),
esimp_not(Y).
esimp_bct(X) :- para_falsehood(X).
esimp_bct(X) :-
para_b_(X, Y, Z),
para_mlc(Y),
para_mlc(Z).
esimp_bct(X) :-
paraab(X, Y, Z),
para_mate(Y),
para_mate(Z).
esimp_bct((PREM, CONC, GOAL)) :-
apply_aa(PREM, GOAL, HYP_L, HYP_R, GOAL_T),
(
use_falsehood(HYP_L, GOAL_T) ;
use_falsehood(HYP_R, GOAL_T) ;
mate(HYP_L, CONC, GOAL_T) ;
mate(HYP_R, CONC, GOAL_T) ;
mate(HYP_L, HYP_R, GOAL_T) ;
(
(HYP = HYP_L ; HYP = HYP_R),
TRP = (HYP, CONC, GOAL_T),
(para_b_(TRP, TRP_A, TRP_B) ; para_b_(TRP, TRP_B, TRP_A)),
para_falsehood(TRP_A),
(para__n(TRP_B, TRP_C) ; true),
para_mate(TRP_C)
)
).
esimp_bct((PREM, _, GOAL)) :-
apply_b(PREM, GOAL, PREM_L, PREM_R, GOAL_L, GOAL_R),
apply_aa(PREM_L, GOAL_L, PREM_LL, PREM_LR, GOAL_LT),
mate(PREM_LL, PREM_LR, GOAL_LT),
apply_aa(PREM_R, GOAL_R, PREM_RL, PREM_RR, GOAL_RT),
mate(PREM_RL, PREM_RR, GOAL_RT).
esimp_fork_bct((HYP_A, HYP_B, GOAL), (HYP_A, HYP_L, GOAL_L), (HYP_R, HYP_B, GOAL_R)) :-
hyp_sign_form(HYP_A, SIGN, FORM),
break_bct(FORM, BCT, FORM_A, FORM_B),
bool_simp(FORM_A, NORM_A),
bool_simp(FORM_B, NORM_B),
apply_bct(BCT, NORM_A, NORM_B, NORM),
apply_uct(SIGN, NORM, SF),
fps(SF, GOAL, HYP_L, HYP_R, GOAL_L, GOAL_R).
esimp_fork_qtf((HYP_A, HYP_B, GOAL), (HYP_A, HYP_L, GOAL_L), (HYP_R, HYP_B, GOAL_R)) :-
hyp_sign_form(HYP_A, SIGN, FORM),
break_qtf(FORM, QTF, SUB_FORM),
bool_simp(SUB_FORM, SUB_NORM),
apply_uct(QTF, SUB_NORM, NORM),
apply_uct(SIGN, NORM, SF),
fps(SF, GOAL, HYP_L, HYP_R, GOAL_L, GOAL_R).
esimp_qtf(X) :-
para_falsehood(X) -> true ;
para_mate(X) -> true ;
para_c_(X, Y) ->
esimp_qtf(Y) ;
para_d_(X, Y) ->
esimp_qtf(Y).
*/
% para_simp_e(X) :- para_falsehood(X), !.
% para_simp_e(X) :- para_mate(X), !.
% para_simp_e(X) :- paran(X, Y), !, para_simp_e(Y).
% para_simp_e(TRP) :-
% TRP = ((_, FORM), _, _),
% break_a(lft, FORM, FORM_A), !,
% break_a(rgt, FORM, FORM_B),
% bool_simp(FORM_A, NORM_A),
% bool_simp(FORM_B, NORM_B),
% para_simp_e(X) :-
% para_falsehood(X) -> true ;
% para_mate(X) -> true ;
% esimp_fork_not(X, Y, Z) ->
% para_n_(Y, Y1),
% para__n(Y1, Y2),
% para_simp_e(Y2),
% esimp_not(Z)
% ;
% esimp_fork_bct(X, Y, Z) ->
% paraab(Y, Y1, Y2),
% para_simp_e(Y1),
% para_simp_e(Y2),
% esimp_bct(Z)
% ;
% esimp_fork_qtf(X, Y, Z) ->
% paracd(Y, Y1),
% para_simp_e(Y1),
% esimp_qtf(Z).
%
% mscj(H2G) :-
% para_mate(H2G) -> true ;
% paran(H2G, H2G_N) -> mscj(H2G_N) ;
% para__d(H2G, H2G_N) -> mscj(H2G_N) ;
% para_c_(H2G, H2G_N) -> mscj(H2G_N) ;
% a_para(H2G, H2G_N),
% mscj(H2G_N).
%
orig_aux(PREM, GOAL, CONC) :-
mate(PREM, CONC, GOAL) ;
pmt_cla(PREM, CONC, GOAL) ;
para_clausal((PREM, CONC, GOAL)).
sup_aux(HYPS, _, ([HYP], GOAL)) :- member_rev(CMP, HYPS), mate(HYP, CMP, GOAL).
sup_aux(HYPS, EQN, ([HYP], GOAL)) :-
member_rev(CMP, HYPS),
subst_rel_add([EQN], HYP, CMP, GOAL).
/*
gs_aux(HYP, CMP, GOAL, HYP_N, GOAL_N) :-
(
apply_b(CMP, GOAL, HYP_A, HYP_B, GOAL_A, GOAL_B) ;
apply_b(CMP, GOAL, HYP_B, HYP_A, GOAL_B, GOAL_A)
),
rp([n], [HYP, HYP_A], GOAL_A, [HYP_0, HYP_1], GOAL_C),
mate(HYP_0, HYP_1, GOAL_C),
rp([n], [HYP_B], GOAL_B, [HYP_N], GOAL_N).
urr_aux(SRC, AUX, TGT, GOAL) :-
(
apply_b(AUX, GOAL, HYP_A, HYP_B, GOAL_A, GOAL_B) ;
apply_b(AUX, GOAL, HYP_B, HYP_A, GOAL_B, GOAL_A)
),
rp([n], [SRC], GOAL_A, [SRC_BODY], GOAL_C),
rp([n], [HYP_A], GOAL_C, [HYP_NA], GOAL_D),
mate(SRC_BODY, HYP_NA, GOAL_D),
rp([n], [TGT], GOAL_B, [TGT_BODY], GOAL_E),
rp([n], [HYP_B], GOAL_E, [HYP_NB], GOAL_F),
mate(TGT_BODY, HYP_NB, GOAL_F).
urr(PREMS, CONCS, ([PREM], GOAL)) :-
ground(PREM),
(member(CMP, CONCS) ; member(CMP, PREMS)),
ground(CMP),
mate(PREM, CMP, GOAL), !.
urr(PREMS, CONCS, ([PREM], GOAL)) :-
(member(CMP, CONCS) ; member(CMP, PREMS)),
mate(PREM, CMP, GOAL).
urr(PREMS, CONCS, ([PREM], GOAL)) :-
member(CONC, CONCS),
member(AUX, PREMS),
urr_aux(PREM, AUX, CONC, GOAL).
gs(PREMS, CONCS, ([PREM], GOAL)) :-
ground(PREM),
(member(CMP, CONCS) ; member(CMP, PREMS)),
ground(CMP),
mate(PREM, CMP, GOAL), !.
gs(PREMS, CONCS, ([PREM], GOAL)) :-
(member(CMP, CONCS) ; member(CMP, PREMS)),
mate(PREM, CMP, GOAL).
gs(PREMS, CONCS, ([PREM], GOAL)) :-
pluck(PREMS, AUX, REST),
gs_aux(PREM, AUX, GOAL, PREM_N, GOAL_N),
gs(REST, CONCS, ([PREM_N], GOAL_N)).
*/
inrw(EQ, ([PREM], GOAL), CONC) :-
subst_rel_add([EQ], PREM, CONC, GOAL).
%%%%%%%%%%%%%%%% MAIN PROOF COMPILATION %%%%%%%%%%%%%%%%
infer(v, ig, [PREM], CONC, GOAL) :-
rp([d], [CONC], GOAL, [CONC_N], GOAL_A),
rp([c], [PREM], GOAL_A, [PREM_N], GOAL_B),
para_clausal((PREM_N, CONC_N, GOAL_B)).
infer(e, para_dist, [PREM], CONC, GOAL) :-
para_dist((PREM, CONC, GOAL)).
infer(_, para_pull, [PREM], CONC, GOAL) :-
rp([d], [CONC], GOAL, [HYP], GOAL_T),
para_pull((PREM, HYP, GOAL_T)).
infer(e, para_e1, [PREM], CONC, GOAL) :-
para_e1((PREM, CONC, GOAL)).
infer(e, para_push, [PREM], CONC, GOAL) :-
para_push((PREM, CONC, GOAL)).
infer(_, rnm, [PREM | _], CONC, GOAL) :-
mate(PREM, CONC, GOAL).
infer(e, simp, [PREM | _], CONC, GOAL) :-
para_simp(e, (PREM, CONC, GOAL)).
infer(PRVR, skm, [PREM | AOCS], CONC, GOAL) :-
PRVR = e ->
eskm(AOCS, (PREM, CONC, GOAL))
;
rp([d], [CONC], GOAL, [CONC_N], GOAL1),
% rp([c], [PREM], GOAL1, [PREM_N], GOAL2),
skm(AOCS, (PREM, CONC_N, GOAL1)).
infer(_, ngt, [PREM], CONC, GOAL) :-
apply_n(CONC, GOAL, TEMP, GOAL_T),
mate(PREM, TEMP, GOAL_T).
infer(_, dff, [PREM | PREMS], CONC, GOAL) :-
sort(PREMS, DEFS),
dff(DEFS, PREM, CONC, GOAL).
infer(_, dfu, [PREM | PREMS], CONC, GOAL) :-
dfu(PREMS, PREM, CONC, GOAL).
infer(v, sat, PREMS, _, GOAL) :-
sat(PREMS, GOAL).
infer(v, gs, PREMS, CONC, GOAL) :-
rp([a,d,n], [CONC], GOAL, HYPS_TEMP, GOAL_TEMP),
append(HYPS_TEMP, PREMS, HYPS),
pblx(q, HYPS, GOAL_TEMP).
% infer(v, gs, PREMS, CONC, GOAL) :-
% rp([a,d,n], [CONC], GOAL, CONCS_N, GOAL_A),
% rp([c,n], PREMS, GOAL_A, PREMS_BODY, GOAL_B),
% pluck(PREMS_BODY, PREM, PREMS_AUX),
% rp([b,c,n], [PREM], GOAL_B, HGS),
% maplist(gs(PREMS_AUX, CONCS_N), HGS).
% infer(v, urr, PREMS, CONC, GOAL) :-
% rp([a, d, n], [CONC], GOAL, CONCS_N, GOAL_A),
% rp([c, n], PREMS, GOAL_A, PREMS_BODY, GOAL_B),
% pluck(PREMS_BODY, PREM, PREMS_AUX),
% rp([b, n], [PREM], GOAL_B, HGS),
% urr(HGS, PREMS_AUX, CONCS_N).
/*
infer(v, urr, PREMS, CONC, GOAL) :-
% list_head_last(PREMS, ORS, PREM),
(
reverse(PREMS, [PREM | ORS]) ;
PREMS = [PREM | ORS]
),
rp([d], [CONC], GOAL, [CONC_TEMP], GOAL_A),
cp_rop([PREM | ORS], GOAL_A, [PREM_TEMP | ORS_TEMP], GOAL_B),
% ap_rop(CONC_TEMP, GOAL_B, [TGT | TGTS], GOAL_C),
% rp([b], PREM_TEMP, GOAL_C, [([SRC], GOAL_D) | HGS]),
ap_rop(CONC_TEMP, GOAL_B, TGTS, GOAL_C),
rp([b], PREM_TEMP, GOAL_C, HGS),
(
TGTS = [TGT | TGTS_TAIL],
HGS = [([SRC], GOAL_D) | HGS_TAIL],
mate(TGT, SRC, GOAL_D)
;
TGTS_TAIL = TGTS,
HGS_TAIL = HGS
),
zip(TGTS_TAIL, ORS_TEMP, HGS_TAIL, H3GS),
cmap(urr_aux, H3GS).
*/
infer(_, rwa, [PREM_A, PREM_B], CONC, GOAL) :-
rp([d], [CONC], GOAL, [HYP_C], GOAL_C),
rp([c], [PREM_B], GOAL_C, [HYP_B], GOAL_B),
rp([c], [PREM_A], GOAL_B, [HYP_A], GOAL_A),
rwa(HYP_B, (HYP_A, HYP_C, GOAL_A)).
infer(v, gaoc, AOCS, GAOC, GOAL) :-
rp([d], [GAOC], GOAL, [IMP], GOAL0),
IMP = (_, ~ ((_ => _))),
apply_aa(IMP, GOAL0, ANTE, CONS, GOAL1),
apply_aocs(ANTE, AOCS, GOAL1, TEMP, GOAL2),
para_lax((TEMP, CONS, GOAL2)).
infer(PRVR, res, [PYP0, PYP1], NYP, GOAL) :-
member(PRVR, [v, e]),
res(PYP0, PYP1, NYP, GOAL).
infer(e, orig, PREMS, CONC, GOAL) :-
member(PREM, PREMS),
orig_aux(PREM, GOAL, CONC).
infer(v, orig, [PREM], CONC, GOAL) :-
mate(PREM, CONC, GOAL) ;
pmt_cla(PREM, CONC, GOAL) ;
infer(v, para_clausal, [PREM], CONC, GOAL).
infer(v, inrw, [PREM], CONC, GOAL) :-
rp([n,a,d], [CONC], GOAL, [CONC_EQ | CONCS], GOAL_A),
rp([n,c,b], [PREM], GOAL_A, [([PREM_EQ], GOAL_B) | HSGS]),
mate(PREM_EQ, CONC_EQ, GOAL_B),
maplist(inrw(CONC_EQ), HSGS, CONCS).
infer(v, ttsc, [], CONC, GOAL) :-
rp([a, d, n], [CONC], GOAL, HYPS, TEMP),
pluck(HYPS, HYP_A, [HYP_B, HYP_C]),
HYP_A = (_, (("=" $ [_, _]))),
subst_rel_add([HYP_A], HYP_B, HYP_C, TEMP).
infer(_, eqf, [PREM], CONC, GOAL) :-
rp([a, d, n], [CONC], GOAL, HYPS, GOAL_T),
pluck(HYPS, HYP, REST),
HYP = (_, (("=" $ [_, _]))),
rp([b, c, n], [PREM], GOAL_T, HGS),
maplist(eqf(REST, HYP), HGS).
infer(_, eqr, [PREM], CONC, GOAL) :- eqr(PREM, CONC, GOAL).
infer(v, updr, [PREM], CONC, GOAL) :-
rp([d], [CONC], GOAL, [CONC_N], GOAL0),
rp([c], [PREM], GOAL0, [PREM_N], GOAL1),
(
apply_a(PREM_N, lft, GOAL1, PREM_D, GOAL2) ;
apply_a(PREM_N, rgt, GOAL1, PREM_D, GOAL2)
),
mate(PREM_D, CONC_N, GOAL2).
infer(e, fnnf, [PREM], CONC, GOAL) :-
fnnf((PREM, CONC, GOAL)).
infer(_, rwe, [PREM_L, PREM_R], CONC, GOAL) :-
rp([d], [CONC], GOAL, [TEMP_C], GOAL0),
rp([c], [PREM_L], GOAL0, [TEMP_L], GOAL1),
rp([d], [TEMP_L], GOAL1, [BODY_L], GOAL2),
rp([c], [TEMP_C], GOAL2, [BODY_C], GOAL3),
rp([c], [PREM_R], GOAL3, [BODY_R], GOAL4),
rp([a, n], [BODY_C], GOAL4, HYPS, GOAL5),
pick_pivot_prop(HYPS, BODY_L, GOAL5, SRC, GOAL6),
pick_pivot_prop(HYPS, BODY_R, GOAL6, PRE_EQN, GOAL7),
PRE_EQN = (_, (("=" $ [_, _]))),
orient_hyp(PRE_EQN, GOAL7, EQN, GOAL8),
member_rev(TGT, HYPS),
subst_rel_add([EQN], SRC, TGT, GOAL8).
infer(_, (sup,DIR), [PREM_A, PREM_B], CONC, GOAL) :-
orient_dir(PREM_A, PREM_B, DIR, PREM_L, PREM_R),
rp([a, d, n], [CONC], GOAL, HYPS, GOAL0),
pick_pivot(HYPS, PREM_L, GOAL0, SRC, GOAL1),
pick_pivot(HYPS, PREM_R, GOAL1, PRE_EQN, GOAL2),
PRE_EQN = (_, (("=" $ [_, _]))),
orient_hyp(PRE_EQN, GOAL2, EQN, GOAL3),
member_rev(TGT, HYPS),
subst_rel_add([EQN], SRC, TGT, GOAL3).
infer(_, sup, [PREM_A, PREM_B], CONC, GOAL) :-
orient_dir(PREM_A, PREM_B, _, PREM_L, PREM_R),
rp([a, d, n], [CONC], GOAL, HYPS, GOAL_A),
% pick_pivot(HYPS, PREM_L, GOAL0, SRC, GOAL1),
pick_pivot(HYPS, PREM_R, GOAL_A, PRE_EQN, GOAL_B),
PRE_EQN = (_, (("=" $ [_, _]))),
orient_hyp(PRE_EQN, GOAL_B, EQN, GOAL_C),
rp([b, c, n], [PREM_L], GOAL_C, HGS),
maplist(sup_aux(HYPS, EQN), HGS).
% member_rev(TGT, HYPS),
% subst_rel_add([EQN], SRC, TGT, GOAL3).
infer(v, spl, [PREM | PREMS], CONC, GOAL) :-
rp([a, d, n], [CONC], GOAL, HYPS0, GOAL0),
spl_exp(PREMS, HYPS0, GOAL0, HYPS1, GOAL1),
append(HYPS0, HYPS1, HYPS),
pblx(q, [PREM | HYPS], GOAL1).
infer(_, para, PREMS, CONC, GOAL) :-
member(PREM, PREMS),
para((PREM, CONC, GOAL)).
infer(_, sbsm, [PREM], CONC, GOAL) :-
sbsm(PREM, CONC, GOAL).
infer(v, cnf, [PREM], CONC, GOAL) :-
rp([a, d, n], [CONC], GOAL, HYPS, TEMP),
vcnf(PREM, HYPS, TEMP).
infer(v, acc, [PREM], CONC, GOAL) :-
vacc(PREM, CONC, GOAL).
infer(v, ppr, [PREM], CONC, GOAL) :-
ppr(PREM, CONC, GOAL) ;
ppr((PREM, CONC, GOAL)).
infer(v, paras, PREMS, CONC, GOAL) :-
member(PREM, PREMS),
para_choice((PREM, CONC, GOAL)).
infer(v, paral, PREMS, CONC, GOAL) :-
member(PREM, PREMS),
para_lax((PREM, CONC, GOAL)).
infer(v, para_vac, PREMS, CONC, GOAL) :-
member(PREM, PREMS),
para_vac((PREM, CONC, GOAL)).
% infer(_, mscj, [PREM], CONC, GOAL) :-
% mscj((PREM, CONC, GOAL)).
infer(e, speq, [PREM], CONC, GOAL) :-
speq((PREM, CONC, GOAL)).
infer(_, scj, [PREM], CONC, GOAL) :-
rp([d], [CONC], GOAL, [HYP0], GOAL0),
rp([c], [PREM], GOAL0, [HYP1], GOAL1),
scj((HYP1, HYP0, GOAL1)).
infer(v, vnnf, PREMS, CONC, GOAL) :-
member(PREM, PREMS),
vnnf((PREM, CONC, GOAL)).
infer(_, para_clausal, PREMS, CONC, GOAL) :-
rp([d, n], [CONC], GOAL, [HYP_C], GOAL_C),
member(PREM, PREMS),
rp([c, n], [PREM], GOAL_C, [HYP_P], GOAL_P),
para_clausal((HYP_P, HYP_C, GOAL_P)).
infer(v, simp, PREMS, CONC, GOAL) :-
member(PREM, PREMS),
para_simp(v, (PREM, CONC, GOAL)).
report_infer_failure(MODE, PRVR, HINTS, PREMS, CONC, GOAL) :-
write("\nInference failed, hints : "),
write(HINTS),
write("\n\n"),
(
MODE = verbose ->
write("\nInference failed, premises =\n\n"),
writeln_list(PREMS)
;
true
),
write("\nInference failed, conclusion =\n\n"),
write(CONC),
write("\n\n"),
(
MODE = verbose ->
open("proof_trace.pl", write, STRM),
write(STRM, ":- [basic].\n\n"),
write_term_punct(STRM, debug_prvr(PRVR)),
write_term_punct(STRM, debug_hints(HINTS)),
write_term_punct(STRM, debug_ctx(PREMS)),
write_term_punct(STRM, debug_hyp(CONC)),
write_term_punct(STRM, debug_goal(GOAL)),
close(STRM),
throw(compilation_failed)
;
true
).
timed_infer(TIME, SLVR, HINT, PREMS, CONC, GOAL) :-
timed_call(
TIME,
infer(SLVR, HINT, PREMS, CONC, GOAL),
(
write("Inference failed prematurely. "),
report_infer_failure(verbose, SLVR, HINT, PREMS, CONC, GOAL),
false
),
(
write("Inference timed out. "),