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Hi,
Lee NaishrCOs idea for an infinite tree syntax:
/* Lee NaishrCOs idea */
naish(X, Y) :-
-a-a naish([], X, Y).
naish(S, X, Y) :- compound(X),
-a-a member(Z-Y, S), X == Z, !.
naish(S, X, Y) :- compound(X), !,
-a-a length(S, N),
-a-a X =.. [F|L],
-a-a maplist(naish([X-'$IDX'(N)|S]), L, R),
-a-a Y =.. [F|R].
naish(_, X, X).
Now define a compare:
naish_compare(C, X, Y) :-
-a-a naish(X, A),
-a-a naish(Y, B),
-a-a compare(C, A, B).
Works fine on this example:
?- X = s(s(1,Y),0), Y = s(s(1,X),1),
-a-a naish_compare(C, X, Y).
C = (>).
The residual problem is, that it is extremly slow. Much slower
than the native compare/3 which doesnrCOt use a stack, but a Union
Find structure. So conceptually total order and natural order
compare/3 are easy, the hard part is making them ultra fast!
Bye
Representation based comparison does seem to
work well on everything IrCOve tested, e.g.,
rCLMonkey testrCY for transitivity and anti-symmetry
with repeat counts of 10,000,000.
On the bright side, 500 more posts and we
will have 2030. But then there will be a
lready Artificial General intelligence (AGI),
which will answer all your questions in a blink.
Relieving the community from all pain and headaches.
We say that the hour of discovery cannot be
forecast, but when we say this, we imagine
that the hour is placed in an obscure and
distant future. Never occurs to us that it has
any relation to today. This day, or any day,
could be the event.
Sometimes discovery comes in circles, shows
us the dark hand of completely forgetting we
each must eventually clasp. Nothing is more
difficult than the loss of past knowledge,
especially when it is our own end
and AGI takes over.
~~ Eulogy in Final Destination, Flight 180 Crash
Mild Shock schrieb:
Hi,
Lee NaishrCOs idea for an infinite tree syntax:
/* Lee NaishrCOs idea */
naish(X, Y) :-
-a-a-a naish([], X, Y).
naish(S, X, Y) :- compound(X),
-a-a-a member(Z-Y, S), X == Z, !.
naish(S, X, Y) :- compound(X), !,
-a-a-a length(S, N),
-a-a-a X =.. [F|L],
-a-a-a maplist(naish([X-'$IDX'(N)|S]), L, R),
-a-a-a Y =.. [F|R].
naish(_, X, X).
Now define a compare:
naish_compare(C, X, Y) :-
-a-a-a naish(X, A),
-a-a-a naish(Y, B),
-a-a-a compare(C, A, B).
Works fine on this example:
?- X = s(s(1,Y),0), Y = s(s(1,X),1),
-a-a-a naish_compare(C, X, Y).
C = (>).
The residual problem is, that it is extremly slow. Much slower
than the native compare/3 which doesnrCOt use a stack, but a Union
Find structure. So conceptually total order and natural order
compare/3 are easy, the hard part is making them ultra fast!
Bye
Hi,
Now this might come as a shock for this french
philosopher, who had that much problems with
Tennant's logical system called TROLL LOGIC.
Or was it core logic. Don't remember anymore:
Representation based comparison does seem to
work well on everything IrCOve tested, e.g.,
rCLMonkey testrCY for transitivity and anti-symmetry
with repeat counts of 10,000,000.
Well there is balance between testing and proving
in computer science. You could say there is balance
between Inductive and Deductive science.
https://de.wikipedia.org/wiki/Induktion_(Philosophie)
You donrCOt need to test transitivity. You can
prove it! Mathematicians usually simply say
if < is a total order, then <rC# is a total order:
-a-a-a Theorem on Order Homomorphism
-a-a-a Proof:
-a-a-a Given rep:RraAH, then define x<rC#y:rf|rep(x)<rep(y).
-a-a-a If rep is injective, then <rC# is transitive
-a-a-a and anti-symmetric.
-a-a-a Assume towards a contradiction that <rC# is not
-a-a-a anti-symmetric. Then we would have x,y such
-a-a-a that x<rC#yreoxreayreo-4x<rC#y. By definition of <rC# and
-a-a-a injectivity of rep we would have rep(x)<rep(y)
-a-a-a reorep(x)rearep(y)reo-4rep(x)<rep(y). A contradiction
-a-a-a with < being anti-symmetric.
-a-a-a Assume towards a contradiction that <rC# is
-a-a-a not transitive. Then we would have x,y,z such
-a-a-a that x<rC#yreoy<rC#zreo-4x<rC#z. By definition of <rC# we
-a-a-a would have rep(x)<rep(y)reorep(y)<rep(z)reo
-a-a-a -4rep(x)<rep(z). A contradiction with <
-a-a-a being transitive.
-a-a-a Q.E.D.
Bye
Mild Shock schrieb:
On the bright side, 500 more posts and we
will have 2030. But then there will be a
lready Artificial General intelligence (AGI),
which will answer all your questions in a blink.
Relieving the community from all pain and headaches.
We say that the hour of discovery cannot be
forecast, but when we say this, we imagine
that the hour is placed in an obscure and
distant future. Never occurs to us that it has
any relation to today. This day, or any day,
could be the event.
Sometimes discovery comes in circles, shows
us the dark hand of completely forgetting we
each must eventually clasp. Nothing is more
difficult than the loss of past knowledge,
especially when it is our own end
and AGI takes over.
~~ Eulogy in Final Destination, Flight 180 Crash
Mild Shock schrieb:
Hi,
Lee NaishrCOs idea for an infinite tree syntax:
/* Lee NaishrCOs idea */
naish(X, Y) :-
-a-a-a naish([], X, Y).
naish(S, X, Y) :- compound(X),
-a-a-a member(Z-Y, S), X == Z, !.
naish(S, X, Y) :- compound(X), !,
-a-a-a length(S, N),
-a-a-a X =.. [F|L],
-a-a-a maplist(naish([X-'$IDX'(N)|S]), L, R),
-a-a-a Y =.. [F|R].
naish(_, X, X).
Now define a compare:
naish_compare(C, X, Y) :-
-a-a-a naish(X, A),
-a-a-a naish(Y, B),
-a-a-a compare(C, A, B).
Works fine on this example:
?- X = s(s(1,Y),0), Y = s(s(1,X),1),
-a-a-a naish_compare(C, X, Y).
C = (>).
The residual problem is, that it is extremly slow. Much slower
than the native compare/3 which doesnrCOt use a stack, but a Union
Find structure. So conceptually total order and natural order
compare/3 are easy, the hard part is making them ultra fast!
Bye
Hi,--- Synchronet 3.21a-Linux NewsLink 1.2
I hope @kuniaki.mukai will like this post.
Now that we are past this generic type of
compare/3, where rep/2 is some representation:
rep_compare(C, X, Y) :-
-a-a-a rep(X, A),
-a-a-a rep(Y, B),
-a-a-a compare(C, A, B).
We can now switch gears, an leave naish/2
behind us, and turn to Deutsch-Schorr-Waite
marking algorithm, that can give us as well
a numbering of cycle nodes:
deutsch(X, Y) :-
-a-a deutsch(X, Y, [], _).
deutsch(X, V, S, S) :- compound(X),
-a-a member(v(Z,T,Y,W), S), X == Z, !,
-a-a (var(T) -> V = Y; V = T),
-a-a W = 1.
deutsch(X, Y, S, T) :- compound(X), !,
-a-a length(S, N),
-a-a X =.. [F|L],
-a-a foldl(deutsch, L, R, [v(X,V,'$IDX'(N),W)|S], T),
-a-a Y =.. [F|R],
-a-a (var(W) -> V = Y; V = '$IDX'(N)).
deutsch(X, X, S, S).
The Schorr-Waite graph marking algorithm appeared
first in about 1968; it is also attributed to
Peter Deutsch. So I am calling the above predicate
deutsch/2 because it is a shorter name then
schorr_waite/2 or deutsch_schorr_waite/3.
Bye