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ranImpFormulas.pro
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ranImpFormulas.pro
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% random implicational logic formulas
% relies on ranPartition and RemyR (random binary trees)
ranImpFormula(N,T):-ranImpFormula(random,N,T).
ranHornFormula(N,T):-ranImpFormula(N,I),toHorn(I,T).
ranImpFormula(Seed,N,T):-
set_random(seed(Seed)),
N1 is N+1,
ranSetPart(N1,Vs),
remy(N,T,Vs).
ranImpFormulas(N,K,T):-ranImpFormulas(random,N,K,T).
% variant neede for gold standard tester
genRanImpFormulas(K,N,T):-ranImpFormulas(N,K,T).
ranImpFormulas(Seed,N,K,T):-
Count is round(sqrt(K)),
ranImpFormulas(Seed,N,Count,Count,T).
ranImpFormulas(Seed,N,PartCount,TreeCount,T):-
set_random(seed(Seed)),
N1 is N+1,
bell(N1,Bell),
between(1,TreeCount,_),
remy(N,T,Vs),
between(1,PartCount,_),
ranPart(N1,Bell,Vs).
ranTypedImp(MaxSeed,M,N,T):-
between(1,MaxSeed,Seed),
ranImpFormula(Seed,M,T),
hprove(T),
sprove(T,X),
type_of(X,TT),
tsize(TT,Size),
Size>N.
bigTypedImp(T):-ranTypedImp(20000,36,16,T).
bigtest:-do((bigTypedImp(T),hprove(T),ppp(T))).
ranShow:-MSeed=1000,M=7,
do((
between(0,MSeed,Seed),
ranImpFormula(Seed,M,T0),
sprove1(T0,X),lsize(X,S),S>=M,
varvars(T0,T),
ppp(T),
ppp(X),
nl,
ppt(X:T),
qqq(X:T),
nl,
ppp('-------------')
)).
/*
Can we generate a formula (that has a proof!) that is so hard that we cannot prove it?
*/
ranX(N,M,T):-
repeat,
remy(N,X),
xtype_of(X,T),
tsize(T,S),
S>=M,
!,
natvars(T).
xtype_of(x,T):-xType(T).
xtype_of((A*B),T):-
xtype_of(A,ST),
xtype_of(B,S),
unify_with_occurs_check(ST,(S->T)).
/*
?- ranX(100,80,T),ahprove(T),ppp(T),fail.
(((((0->1->2)->(0->1)->0->2)->(3->4->3)->(0->1->2)->(0->1)->0->2)->(((5->6->5)->((7->8->9)->(7->8)->7->9)->(10->11->10)->12)->12)->((0->1->2)->(0->1)->0->2)->(3->4->3)->(0->1->2)->(0->1)->0->2)->((13->14->15)->(13->14)->13->15)->(((0->1->2)->(0->1)->0->2)->(3->4->3)->(0->1->2)->(0->1)->0->2)->(((5->6->5)->((7->8->9)->(7->8)->7->9)->(10->11->10)->12)->12)->((0->1->2)->(0->1)->0->2)->(3->4->3)->(0->1->2)->(0->1)->0->2)->((0->1->2)->(0->1)->0->2)->(3->4->3)->(0->1->2)->(0->1)->0->2
*/
ranSK(N,M,T):-ranSK(random,N,M,T).
ranSK(Seed,N,M,T):-
set_random(seed(Seed)),
repeat,
remy_sk(N,X),
sk_type_of(X,T),
tsize(T,S),
S>=M,
!,
natvars(T).
sType((A->B->C)->(A->B)->A->C).
kType(A->_B->A).
sk_type_of(s,T):-sType(T).
sk_type_of(k,T):-kType(T).
sk_type_of((A*B),T):-
sk_type_of(A,ST),
sk_type_of(B,S),
unify_with_occurs_check(ST,(S->T)).
/*
?- ranSK(60,60,T),ppp(T),ahprove(T),ppp(ok),fail.
(0->(((((((1->2)->1)->1->2)->(1->2)->1)->((1->2)->1)->1->2)->(((1->2)->1)->1->2)->(1->2)->1)->(((((1->2)->1)->1->2)->(1->2)->1)->((1->2)->1)->1->2)->3->2)->4)->0->(((((((1->2)->1)->1->2)->(1->2)->1)->((1->2)->1)->1->2)->(((1->2)->1)->1->2)->(1->2)->1)->(((((1->2)->1)->1->2)->(1->2)->1)->((1->2)->1)->1->2)->3->2)->4
ok
*/
% UNFINISHED - TODO
hilbert_gen(N,Ts):-hilbert_gen_(N,Ts,_).
hilbert_gen_(N,Ts,Vs):-hilbert_gen(N,_,Vs,[],Ts,[]).
hilbert_gen(N1,N3,Vs1,Vs3)-->{ppp(N1)},
{N1>0,N2 is N1-1},
( subst_rule(Vs1,Vs2)
; modus_ponens(Vs1,Vs2)
),
( {N3 is N2-1}
;
hilbert_gen(N2,N3,Vs2,Vs3)
).
hilbert_ax( ((A->B->C)->(A->B)->A->C),[A,B,C]).
hilbert_ax((A->B->C),[A,B,C]).
subst_rule(NewVs,Vs,[T|Ts],Ts):-
hilbert_ax(T,Vs),
member(V,Vs),
( V=(X->Y),NewVs=[X,Y|Vs]
; NewVs=Vs
).
modus_ponens(Vs,Vs,Ts,[T|NewTs]):-
select(S1,Ts,NewTs),
select((S2->T),Ts,NewTs),
unify_with_occurs_check(S1,S2).