Questions tagged [unification]
The unification tag has no usage guidance.
1
vote
0answers
22 views
Unification algorithm that directly finds multiple substitutions?
Systems of formal logic generally have inference rules that
require certain expressions to be syntactically the same
in multiple steps. Typically two steps are involved, as
for modus ponens, where ...
2
votes
1answer
57 views
Why this pattern matching fails in Agda?
Consider function wa'' (need natural number definition, either in stdlib or Agda.Builtin.Nat):
...
4
votes
1answer
49 views
E-Unification: “Goal seeking” pattern matching between directed trees
Preamble
Suppose we have some symbols x, y, ... and wildcards (ξ), ...
2
votes
0answers
86 views
Most efficient unification algorithm?
I've been trying to find the most efficient unification algorithm by following reference chains on the Wikipedia article on unification. As far as I can tell, the fastest one is the one presented in "...
2
votes
0answers
71 views
Unification algorithm - need clarification
I have these two terms:
{P(a,x,x),P(a,b,c)}
I'm supposed to find if the terms and unifiable using the unification algorithm.
I'd do the following substitutions:
b/x, resulting in : {P(a,b,b),P(a,b,...
3
votes
1answer
47 views
“not provable”, what does this to do with unification?
I found one interesting point in nominal unification. Just after proposition 2.16 of Nominal Unification by Urban, Pitts, and Gabbay, it said the following, which I found confusing:
For non-ground ...
2
votes
1answer
73 views
Are these examples of unification problems?
I have been studying unification, especially nominal unification (paper) gets my attention.
I read the theory and examples. But I am wondering that what kind of problems occur in unifications.
For ...
1
vote
1answer
47 views
is this an example of nominal unification?
I am thinking that is the following a problem solved by nominal unification.
$\lambda a.X = \lambda b.\lambda c.c $
where we find $X$. The answer is obvious.
The reason is that it seems in nominal ...
2
votes
0answers
15 views
Need clarification in theorem about syntactic equations and substitutions
In the book "Constraint Handling Rules", Thom Frühwirth explains (on p. 50) "Substitutions, variants and equality" over a usual first-order logic language composed of variables, function symbols and ...
1
vote
1answer
107 views
Comparison Procedure in Robinson's Unification Algorithm
I'm studying the Principal Type (PT) Algorithm in Basic Simple Type Theory by J. Roger Hindley.
One step to find the PT of a term is the Unification of types. The Robinson's Unification Algorithm uses ...
8
votes
1answer
138 views
Is there a general algorithm to fill holes in terms of the Calculus of Constructions?
Suppose that you extend the Calculus of Constructions with "holes" - i.e., incomplete pieces of code that you didn't fill yet. I wonder if there is an algorithm to fill those roles automatically. For ...
0
votes
0answers
91 views
what is a disagreement set in nominal unification?
In unification, for example set $s=\{ f(a,Y),f(X,d) \}$ has a disagreement set $\{ (a,X),(Y,d) \}$, since these two elements does not match on their fields. simply speaking that is a set disagreement ...
0
votes
1answer
40 views
occur-check, does nominal unification has it?
In unification, there is a "occur-check". Such as $X = a \, X$ fails to find a substitution for $X$ since it appears on right hand side too.
The first-order unification, higher-order unification all ...
4
votes
1answer
835 views
How can unifying 2 sentences in first-order logic result in a variable becoming 2 different things?
I'm working on a program which must use inference in first-order logic, and everything is working great except for 1 thing which I don't understand.
The book I'm using, "Artificial Intelligence A ...
7
votes
1answer
170 views
why nominal unification is a first-order unification?
In my understanding, if a unification solves equations of terms that are not higher-order terms, then it is a first-order unification.
If a unification solves equations of terms that are higher-order ...
5
votes
1answer
579 views
What is a unifier?
Currently I read up on unifiers, however have some problem understanding its concept. Thus far I found an example of an equation:
add(suc(x); y) $\stackrel{.}{=}$ add(y; suc(z))
and unifiers to it:...
7
votes
2answers
315 views
Generating constraints to solve dependently-typed metavariables?
In dependent-types, Miller pattern unification is used to solve a decidable fragment of higher-order unification. This allows dependently-typed languages to contain metavariables or implicit arguments....
1
vote
1answer
61 views
Unification Functions
I need to apply the unification function to unify the following expression:
foo(X,X,Y) and foo(Z,p(Z),w)
So far, I've determined that I must substitute 'w's for occurances of 'Y', making
foo(X,X,w) ...
2
votes
1answer
32 views
Can high-order unification be applied to programming by example?
In 2007, it has been proven that high-order unification is decidable on the pattern matching case. If that is true, what is stopping someone to write an equation like:
...
3
votes
1answer
312 views
Term Rewriting vs Unification
How is term rewriting different from unification, and what's the difference between term rewriting languages and logic programming, like Prolog?
3
votes
2answers
645 views
Skolemization with multiple arguments — how to unify
Edit: answerers keep finding (valid!) problems with my example. I'll try again. The older version is below the horizontal line. Thanks to Klaus below for pointing out the last problem.
My ...
1
vote
1answer
106 views
Unification — removing equations and updating the solution
This question is concerned with the first order unification. Suppose I have a set $D$ of equations and a solution to these equations. Let this solution be a set $S$ of substitutions. Now, suppose I ...
6
votes
3answers
5k views
Can someone clarify this unification algorithm?
I've been having trouble understanding a unification algorithm for first order logic, as I don't know what a compound expression is. I googled it, but found nothing relevant. I also don't know what a ...
4
votes
2answers
287 views
Unification — most specific unifier
In unification, given a set of equations, a standard problem is to compute a most general unifier (mgu). I am interested in a somewhat reversed problem. Imagine having a set of equations that do not ...
3
votes
1answer
144 views
Type inference of pair (product) types
I am looking into Hindler-Milney type system and I am trying to add support for
the pair type. In Pierces book, he introduces special language constructs for creation of pairs and getting their ...
10
votes
1answer
537 views
Unification vs. SAT solver
I read on Wikipedia that unification is a process of solving the satisfability problem.
At the same time, I know that such solvers are called "SAT solvers" or "SMT solvers". So, are they different ...
15
votes
3answers
2k views
Why is unification so important to inference engines?
I am learning Automated Theorem Proving / SMT solvers / Proof Assistants by myself and post a series of questions about the process, starting here.
I keep reading about the Unification Algorithm.
...
