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Encountering "Invalid bounded variable(s)" error in Z3? This guide breaks down the solution to fix the error when working with quantified formulas in Python.
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This video is based on the question https://stackoverflow.com/q/70086689/ asked by the user 'Theo Deep' ( https://stackoverflow.com/u/14082385/ ) and on the answer https://stackoverflow.com/a/70086825/ provided by the user 'alias' ( https://stackoverflow.com/u/936310/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Understanding Z3's Invalid Bounded Variables in Python: A Comprehensive Guide

If you've dabbled in using Z3, the powerful theorem prover known for its capability to handle first-order logic, you may have stumbled upon an error message that reads: "Invalid bounded variable(s)". This can be quite frustrating, especially if you're not sure what's causing the issue. In this post, we'll dive into the reasons behind this error and walk through the steps to resolve it.

The Problem

In the scenario presented, a user attempted to check the validity of a logical sentence in Z3 using Python. Despite meticulously defining various integer variables and logical expressions, the user encountered the dreaded "Invalid bounded variable(s)" error message. This suggests issues related to how the quantified variables were structured in the provided code.

The Code Overview

Here's a simplified breakdown of the user's code:

[[See Video to Reveal this Text or Code Snippet]]

Analyzing the Issue

The problem arises due to how variables are defined and used in the context of quantifiers:

Universal and Existential Quantifiers: In Z3, when using ForAll or Exists, you must ensure that all the variables that are quantified must be declared beforehand.

Empty Lists: An empty list (like neg_lts in this case) can also contribute to confusion in how the logic is formed.

The Solution

To fix the issue, you'll need to ensure that all quantified variables are properly declared and that you hold onto the correct logical structure for the formulas. Here’s the corrected approach:

Step-by-Step Fix

Correct Variable Declaration & Structure: Instead of using lists in all cases, sometimes simpler direct definitions work better for quantifying variables.

Consolidation for Clarity: Keep your logical expressions neat and tidy. Avoid unnecessary nesting as this can complicate the interpretation by Z3.

Here’s the corrected version of the code:

[[See Video to Reveal this Text or Code Snippet]]

Conclusion

By understanding the implications of how bounded variables are structured and adhering to Z3’s requirements, you can avoid the invalid bounded variable errors. With the correct implementation, you should find that running the corrected code produces consistent and valid results when solving quantified statements.

Feel free to use the above sample code and modify it to suit your requirements. Happy coding and problem solving with Z3!