# [Retros] Proof game terminology

Francois Labelle flab at EECS.Berkeley.EDU
Fri Feb 11 04:08:57 EST 2005

Andrew Buchanan wrote:

> Here is a gentleman (F.Labelle of Berkeley CA) who is using the terms

> SPG & PG in a sense which implies uniqueness.

Actually my view (i.e. my attempt at a theory which fits best the usage
I've seen) is that a PG composition can have one or more solutions, BUT by
default we assume it has one solution.

Here are some examples:

"a PG": Without a context, we assume a one-solution PG.

"a PG with 2 solutions": This isn't a logical impossibility (a proof game
with 1 and 2 solutions). The expression "with 2 solutions" simply
overrides the default of "1 solution".

If the topic is PGs with multiple solutions, we're not going to say "a PG
with possibly many solutions" all the time, we're going to say just "PG".
The default has been overridden again. Ex: my Feb 8 post.

"a dual-free PG": This is used to confirm that we're talking about a PG
with 1 solution in case the default has been overridden, or just to be
absolutely clear.

A PG can be shortest or non-shortest. The default is "unspecified". To
specify that it is shortest, write "SPG". Because of English ambiguity,
it's not clear if a PG in X.Y moves means in exactly X.Y moves or in X.Y
moves or less. A SPG is sound for both interpretations so there's no
problem. If a PG is non-shortest, one can write "PG in exactly X.Y moves"
to be clear.

Earlier, Andrew wrote:

> (c) SPG without specified number of moves. This is just like a PG

> except that the solver has to find the number of moves, which is the

> minimum possible in which the position can be reached, and is unique.

> (d) SPG in X.Y moves. This is just like a PG except that in addition

> the composer asserts that the position cannot be reached in a shorter

> number of moves. Of course there is no reason why the composer should

> do this: the composition would be sound if defined as PG (b) or SPG in

> X.Y (c). However, I find definition (d) more satisfying somehow, and I

> guess others do too.

There's a very good reason for (d) instead of (c). It allows the solver to
know if he found the correct solution without actually seeing the
solution.

Personally I find the concept "PG in exactly X.Y moves" most satisfying.
This is what my program finds and what proof game solvers search for. We
only need this one and the definition is shorter. We saw from the at-home
statistics that PGs that are not shortest are rare, therefore interesting.
Writing "SPG" instead of "PG" is like saying "oh, and by the way, this is
not one of these cool tempo problems". Why bother? I predict the death of
the term "SPG" in favor of just "PG".

> PS: I reckon in composition competitions, Francois' program should be

> given a two half-move handicap versus humanity!

Well, I haven't won an official composition competition yet. For that I
need a computer-friendly theme.

> PPS: What is the 7.0 "at home" composition with castling, and both R & K

> on the board?

Joost didn't notice the rook was captured in my examples. :)

Francois