cayleygraph/cayley

ForAll / Universal Quantifiers

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#209 opened on Feb 9, 2015

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good first issuequery languages

Description

We have a Not iterator now. It'd be possible to add a shorthand macro in Gremlin to emulate the Universal Quantifier, ForAll.

All queries currently work on existence. That is, each stage depends on "there exists some path X to node Y". Using negation you can achieve "for all paths from X, (rest of query holds)".

The key insight being that (X holds for (ForAll A)) == (X holds for A) AND (X holds for (Not (Not A))) == (X holds for (A AND (Not (Not A))))

In today's parlance, this is: var a = g.M().... g.V().And(a).And(g.V().Except(g.V().Except(a)))...

It's a hack, but one that holds mathematically. Currently can be implemented as a macro on the query level, and is actually really hard to optimize further. (Suggestions, of course, are welcome)

Contributor guide

Tech stack
go
Domain
databasebackend
Issue type
feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
3
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
3-5 days
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
stale
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
needs investigation
Prerequisites
basic knowledge of graph databasesunderstanding of Gremlin query language
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
20
Research direction
The issue proposes adding a ForAll (universal quantifier) macro to Cayley's graph traversal language, building on the existing Not iterator. The mathematical equivalence is described: ForAll A is equivalent to (A AND (Not (Not A))). To implement this, one could create a macro function in Go that combines the existing 'And' and 'Except' steps. The implementation would be challenging to optimize, but a starting point is to replicate the described macro using Cayley's Gremlin like query API. Review the existing Not and And iterators in the codebase (likely in the 'query' package) to understand the pattern.