/
counts.pro
478 lines (378 loc) · 9.72 KB
/
counts.pro
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% generic counting mechanisms for generator F, sizes up to M
countGen3(F,M,Rs):-
findall(R,(
between(1,M,N),
sols(call(F,N,_,_),R)
),Rs).
countGen2(F,M,Rs):-
findall(R,(
between(1,M,N),
sols(call(F,N,_),R)
),Rs).
% A000108: Catalan numbers [1,2,5,14,42,132,429,1430,4862,16796]
countHornTrees(M,Rs):-countGen3(genHorn,M,Rs).
% A004111 Number of rooted identity trees
% 1,1,2,3,6,12,25,52,113,247,548,1226
countSetTrees(M,Rs):-countGen2(genSetTree,M,Rs).
% A105633: [1,2,4,9,22,57,154,429,1223,3550,10455,31160,93802,284789]
countSortedHorn(M,Rs):-countGen3(genSortedHorn,M,Rs).
% A105633: 1,2,4,9,22,57,154,429,1223,3550,10455,31160
countStrictHorn(M,Rs):-countGen3(genStrictHorn,M,Rs).
% 1,2,4,8,20,47,122,316,845,2284,6264,17337,48424,136196,385548
countSortedHorn3(M,Rs):-countGen3(genSortedHorn3,M,Rs).
% [1,1,2,5,13,37,109,331,1027,3241,10367,33531,109463] this
% [1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012] vs Catalans
countHorn3(M,Rs):-countGen2(genHorn3,M,Rs).
countTestSortedHorn(M,Ks):-countGen2(testSortedHorn,M,Ks).
% 1, 4, 21, 145, 1208, 11664, 127019
countAllStrictHorn(M,Rs):-countGen2(allStrictHorn,M,Rs).
bellHornTest(M,Ks):-
findall(K,(
between(1,M,I),succ(I,SI),
sols(testSortedHorn(I,_),K1),
bell(SI,K2),
K is K1*K2
),
Ks
).
% A105633 1,2,4,9,22,57,154,429,1223,3550,10455,31160
countSortedHornTrees(M):-countGen3(genSortedHorn,M,R),ppp(R).
% 2, 7, 38, 266, 2263, 22300, 247737
countSortedHorn(M):-
findall(R,(
N to M,
gen_and_count(N,allSortedHorn,hprove,R)
),
Rs
),
maplist(ppp,Rs).
countSortedFlatHorn(M):-
findall(R,(
N to M,
gen_and_count(N,allSortedHorn,flat_hprove,R)
),
Rs
),
maplist(ppp,Rs).
countStrictFlatHorn(M):-
findall(R,(
N to M,
gen_and_count(N,allStrictHorn,flat_hprove,R)
),
Rs
),
maplist(ppp,Rs).
countStrictHorn(M):-
findall(R,(
N to M,
gen_and_count(N,allStrictHorn,hprove,R)
),
Rs
),
maplist(ppp,Rs).
countSortedEqHorn(M):-
findall(R,(
N to M,
gen_and_count(N,allSortedHorn,haprove,R)
),
Rs
),
maplist(ppp,Rs).
countHorn(M):-
findall(R,(
N to M,
gen_and_count(N,allHornFormulas,hprove,R)
),
Rs
),
maplist(ppp,Rs).
countSortedHorn3(M):-
findall(R,(
N to M,
gen_and_count(N,allSortedHorn3,hprove,R)
),
Rs
),
maplist(ppp,Rs).
countAllHorn(M):-ncounts(M,allHornFormulas(_,_)).
countAllSortedHorn(M,Ks):-countGen2(allSortedHorn,M,Ks).
countAllSortedHorn(M):-ncounts(M,allSortedHorn(_,_)).
countAllSortedHorn3(M):-ncounts(M,allSortedHorn3(_,_)).
countFull(M,Rs):-countGen3(genOpTree,M,Rs).
countEqNeg(M,Rs):-countGen2(allEqNegFormulas,M,Rs).
countFullSorted(M,Rs):-countGen3(genSortedTree,M,Rs).
countFullTrimmed(M,Rs):-countGen3(genTrimmedTree,M,Rs).
countAllFull(M):-
findall(N-R,(
N to M,
gen_and_count(N,allFullFormulas,faprove,R)
),
Rs
),
maplist(ppp,Rs).
countAllFullDyckhoff(M):-
findall(R,(
N to M,
gen_and_count(N,allFullFormulas,dprove,R)
),
Rs
),
maplist(ppp,Rs).
countAllTrimmedFull(M):-
findall(R,(
N to M,
gen_and_count(N,allTrimmedFormulas,faprove,R)
),
Rs
),
maplist(ppp,Rs).
countAllSortedFullDyckhoff(M):-
findall(R,(
N to M,
gen_and_count(N,allSortedFullFormulas,dprove,R)
),
Rs
),
maplist(ppp,Rs).
/*
?- countAllFull(9).
same as
?- countAllFullDyckhoff(9).
[proven=0,total=1,ratio=0]
[proven=0,total=1,ratio=0]
[proven=2,total=10,ratio=0.2]
[proven=0,total=26,ratio=0]
[proven=29,total=283,ratio=0.102]
[proven=41,total=1488,ratio=0.027]
[proven=887,total=17626,ratio=0.05]
[proven=3168,total=173636,ratio=0.018]
[proven=46798,total=2510404,ratio=0.018]
*/
% just to compare the overhead for provers
parCountImpFormulas(N,Total):-
thread_count(M1),M0 is M1-1,
G=seqCountImpFormulas(I/M1,N,_),
findall(G,between(0,M0,I),Gs),
concurrent(M1,Gs,[]),
maplist(arg(3),Gs,Ts),sum_list(Ts,Total).
/*
A289679: Catalan(n)*Bell(n+1)
?- findall(S,(between(0,7,N),sols(allImpFormulas(N,_),S)),Xs).
Xs = [1, 2, 10, 75, 728, 8526, 115764, 1776060].
*/
seqCountProvenFormulas(N,P,ProvenCount,TotalCount):-
seqCountProvenFormulas(_,N,P,ProvenCount,TotalCount).
seqCountProvenFormulas(I/M,N,P,ProvenCount,TotalCount):-
new_ctr(Total),new_ctr(Proven),
do((
nthImpFormula(N,T,K),
(integer(I)->I=:=K mod M;true),
ctr_inc(Total),
call(P,T),
ctr_inc(Proven)
)),
ctr_get(Proven,ProvenCount),
ctr_get(Total,TotalCount).
parCountProvenFormulas(N,P,Proven,Total):-
thread_count(M1),M0 is M1-1,
G=seqCountProvenFormulas(I/M1,N,P,_,_),
findall(G,between(0,M0,I),Gs),
concurrent(M1,Gs,[]),
maplist(arg(4),Gs,Ps),sum_list(Ps,Proven),
maplist(arg(5),Gs,Ts),sum_list(Ts,Total).
parCountProvenFormulas1(N,P,Proven,Total):-
init(total_imp),
nondet_count(call(P,T),gen_and_count(N,T),Proven),
total(total_imp,Total).
gen_and_count(N,T):-
allImpFormulas(N,T),
inc(total_imp).
gen_and_count_and_prove1(N,P):-
allImpFormulas(N,T),
inc(total_imp),
prove(P,T),
inc(total_proven).
% some stats
itautVSforms(
[0/1,1/2, 3/10, 24/75, 201/728, 2201/8526, 27406/115764, 391379/1776060, 6215192/30240210 , 108722929/563870450]).
ctautVSforms([0/1,1/2, 3/10, 25/75, 206/728, 2298/8526, 28504/115764, 409543/1776060, 6504136/30240210,114013199/563870450]).
itratio:-tratio(itautVSforms).
ctratio:-tratio(ctautVSforms).
icratio:-itautVSforms(Is),ctautVSforms(Cs),
maplist(safe_div,Is,Cs,Rs),
ppp(Rs),
plotl(Rs).
safe_div(_,0/_,R):-!,R=undef.
safe_div(X,Y,Z):-Z is X/Y.
tratio(D):-
call(D,Ps),
maplist(is,Xs,Ps),
maplist(nice_num,Xs,Qs),
ppp(Qs),
plotl(Qs).
% 1,0,1,1,4,7,23,53,163,432,1306
countUnInhabitableTree(M):-ncounts(M,unInhabitableTree(_,_)).
% 0,1,1,4,9,30,122,528,2517,12951,71455
countUnInhabitableVars(M):-ncounts(M,unInhabitableVars(_,_)).
% 1,0,1,1,5,11,41,120,421,1381
countUnInhabitableImplTree(M):-ncounts(M,unInhabitableImplTree(_,_)).
/*
?- time(seqCountProvenFormulas(8,hprove,A,B)).
% 2,243,311,670 inferences, 217.446 CPU in 217.577 seconds (100% CPU, 10316659 Lips)
A = 6215192,
B = 30240210.
?- time(parCountProvenFormulas(8,hprove,A,B)).
% 32,990 inferences, 0.010 CPU in 200.569 seconds (0% CPU, 3356394 Lips)
A = 6215192,
B = 30240210.
?- findall(A/B,(between(0,9,N),parCountProvenFormulas(N,hprove,A,B)),R).
R = [0/1,1/2, 3/10, 24/75, 201/728, 2201/8526, 27406/115764, 391379/1776060, 6215192/30240210 108722929/563870450].
?- time(parCountProvenFormulas(9,hprove,A,B)).
% 1,121 inferences, 0.075 CPU in 4008.850 seconds (0% CPU, 14852 Lips)
A = 108722929,
B = 563870450.
?- findall(A/B,(between(0,9,N),parCountProvenFormulas(N,tautology,A,B)),R).
R = [0/1,1/2, 3/10, 25/75, 206/728, 2298/8526, 28504/115764, 409543/1776060, 6504136/30240210,114013199/563870450].
- itratio.
[0,0.5,0.3,0.32,0.27,0.25,0.23,0.22,0.2,0.19]
x,y
0,0
1,0.5
2,0.3
3,0.32
4,0.27
5,0.25
6,0.23
7,0.22
8,0.2
9,0.19
true.
?- ctratio.
[0,0.5,0.3,0.33,0.28,0.26,0.24,0.23,0.21,0.2]
x,y
0,0
1,0.5
2,0.3
3,0.33
4,0.28
5,0.26
6,0.24
7,0.23
8,0.21
9,0.2
true.
?- icratio.
[undef,1.0,1.0,0.9600000000000001,0.975728155339806,0.9577893820713663,0.9614790906539433,0.9556481248611258,0.9555753446729897,0.9535994950900377]
x,y
1,1.0
2,1.0
3,0.9600000000000001
4,0.975728155339806
5,0.9577893820713663
6,0.9614790906539433
7,0.9556481248611258
8,0.9555753446729897
9,0.9535994950900377
true.
?- countSortedHorn(9).
[proven=0,total=1,ratio=0]
[proven=1,total=2,ratio=0.5]
[proven=1,total=7,ratio=0.142]
[proven=9,total=38,ratio=0.236]
[proven=42,total=266,ratio=0.157]
[proven=335,total=2263,ratio=0.148]
[proven=2772,total=22300,ratio=0.124]
[proven=27699,total=247737,ratio=0.111]
[proven=303645,total=3049928,ratio=0.099]
true.
?- countSortedHorn3(9).
[proven=0,total=1,ratio=0]
[proven=1,total=2,ratio=0.5]
[proven=1,total=7,ratio=0.142]
[proven=9,total=38,ratio=0.236]
[proven=42,total=214,ratio=0.196]
[proven=329,total=1977,ratio=0.166]
[proven=2438,total=16004,ratio=0.152]
[proven=24342,total=174377,ratio=0.139]
[proven=240323,total=1876093,ratio=0.128]
true.
*/
countAllNegImp(M,P):-
findall(R,(
N to M,
gen_and_count(N,allNegImpFormulas,P,R)
),
Rs
),
maplist(ppp,Rs).
countAllHarrop(M):-
findall(R,(
N to M,
gen_and_count(N,allHarropFormulas,eprove,R)
),
Rs
),
maplist(ppp,Rs).
/*
?- countAllSortedFull(6).
[proven=0,total=1,ratio=0]
[proven=2,total=9,ratio=0.222]
[proven=19,total=119,ratio=0.159]
[proven=403,total=2652,ratio=0.151]
[proven=9684,total=75458,ratio=0.128]
[proven=293579,total=2578164,ratio=0.113]
*/
countAllSortedFull(M):-
findall(R,(
N to M,
gen_and_count(N,allSortedFullFormulas,faprove,R)
),
Rs
),
maplist(ppp,Rs).
:-dynamic(yes/1).
gen_and_count(N,G,P,[proven=Proven,total=Total,ratio=Ratio]):-
retractall(proven(_)),
init(total_count),
init(proven_count),
do((
call(G,N,T),
inc(total_count),
call(P,T),
inc(proven_count),
form2tuple(T,TT),
assertz(yes(TT))
)),
total(total_count,Total),
total(proven_count,Proven),
R is Proven/Total,
%save_proven,
nice_num(R,Ratio).
save_proven:-
findall(X,yes(X),Xs),
tell('yes.py'),
write('yes = '),write_canonical(Xs),nl,
told.
countAllImp(M):-
findall(R,(
N to M,
gen_and_count(N,allImpFormulas,hprove,R)
),
Rs
),
maplist(ppp,Rs).
seqCountImpFormulas(N,TotalCount):-
seqCountImpFormulas(_,N,TotalCount).
seqCountImpFormulas(I/M,N,TotalCount):-
new_ctr(Total),
do((
nthImpFormula(N,_T,K),
(integer(I)->I=:=K mod M;true),
ctr_inc(Total)
)),
ctr_get(Total,TotalCount).
nthImpFormula(N,T,K):-
new_ctr(C),
allImpFormulas(N,T),
ctr_get(C,K),
ctr_inc(C).