I am back now
Is there a gapt meeting today?
:D, ah yes that is why I was on vacation, right.
Happy easter to you too
see you next week then
I have a question about importing TIP problems. The file tip2015/list_return_2.smt2 looks like this:
; List monad laws
(declare-datatypes (a)
((list (nil) (cons (head a) (tail (list a))))))
(define-fun (par (a) (return ((x a)) (list a) (cons x (_ nil a)))))
(define-fun-rec
(par (a)
(++
((x (list a)) (y (list a))) (list a)
(match x
(case nil y)
(case (cons z xs) (cons z (++ xs y)))))))
(define-fun-rec
(par (a b)
(>>=
((x (list a)) (y (=> a (list b)))) (list b)
(match x
(case nil (_ nil b))
(case (cons z xs) (++ (@ y z) (>>= xs y)))))))
(prove
(par (a)
(forall ((xs (list a)))
(= (>>= xs (lambda ((x a)) (return x))) xs))))and after fixupAndLoad becomes:
∀x0 ∀x1 head(cons(x0, x1)) = x0,
∀x0 ∀x1 tail(cons(x0, x1)) = x1,
∀x return(x) = cons(x, nil),
lam2 = lam,
∀y ++(nil, y) = y,
∀y ∀z ∀xs ++(cons(z, xs), y) = cons(z, ++(xs, y)),
∀y >>=(nil, y) = nil,
∀y ∀z ∀xs >>=(cons(z, xs), y) = ++(apply1(y, z), >>=(xs, y)),
∀y0 ∀y1 nil != cons(y0, y1),
∀x apply1(lam, x) = return(x)
⊢
∀xs >>=(xs, lam2) = xs
So the
apply1 must be introduced by the tip tool, but it does not show up in TipProblem.functions which I am using to generate reduction rules for testing.
Here's an update:
mode
analytic_independent 43
analytic_sequential 75
spind 34
treegrammar 16All the problems solved by the analytic independent mode are affected by the tip importer thing mentioned above which makes my testing of conjectures less efficient or straight up breaks it. Three of them are solved if I just disable testing.
Spind is currently a little slower in total on the problems they have in common:
spind 118,666ms
analytic_independent 93,527ms
@shetzl We talked about going to and from an expansion proof to reduce the proof, but I've got one here (for isaplanner/prop_57.smt2) which has around 2000 steps as an LK proof and going back from expansion to LK is taking more than 20 minutes. So that doesn't seem feasible(?)
@gebner I am asking this because I ran into a problem with the syntactic unification where the resulting substitution does not unfiy the expressions but I am not sure whether this is a bug in the unification algorithm or in the way the substitution is applied to the term.
@gebner Here is the example
object Example extends scala.App {
implicit var ctx = Context()
ctx += hoc"P{?a}: ?a > o"
ctx += Ti
ctx += hoc"c:i"
val t1 = le"P(x:?a)"
val t2 = le"P(c)"
val Some( subst ) = syntacticMGU( t1, t2 )
require( subst( t1 ) == subst( t2 ) )
}
Treating true/false as atoms can easily lead to bugs: e.g. gapt/gapt#309 If they are not atoms, it's clear that you need to treat them specially.
You can integrate clausification into the saturation loop using this inference: https://github.com/gapt/gapt/blob/2c46e4e159b34fd24969bba15c39b6f02ddbb1a7/core/src/main/scala/gapt/provers/escargot/inferences.scala#L179
But for first-order problems, clausification happens before the main loop is even started.
@gebner At https://github.com/gapt/gapt/blob/2c46e4e159b34fd24969bba15c39b6f02ddbb1a7/core/src/main/scala/gapt/provers/escargot/inferences.scala#L454 what are the positions
pos2 supposed to represent?
The first line of the function arguments describes the equation (
i1th formula in clause c1, we want to rewrite t_ to s_), the second line describes the other clause that we want to rewrite (i2th formula in clause c2). pos2 are positions in c2.conclusion(i2) that can be unified with t_ (the left-hand side of the equation, if leftToRight is true). https://github.com/gapt/gapt/blob/2c46e4e159b34fd24969bba15c39b6f02ddbb1a7/core/src/main/scala/gapt/provers/escargot/inferences.scala#L460 These positions are then replaced by the right-hand side of the equation, i.e., mgu(s_).