prolog-unification

Unify logical terms with variables and compound structures using the Martelli–Montanari algorithm.

1|Updated Mar 15, 2026

Search Tags:#substitution #backtracking #unification #prolog #logic-programming #occurs-check

Ready to run

npx skills add https://github.com/hafley66/claude-research --skill prolog-unification

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: prolog-unification
Source: https://github.com/hafley66/claude-research/tree/main/skills/prolog-unification
Command: npx skills add https://github.com/hafley66/claude-research --skill prolog-unification

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Unification is the single operation that drives all of Prolog's computation. Given two terms, unification finds a substitution -- a set of variable bindings -- that makes the two terms syntactically identical. If no such substitution exists, unification fails.

Core Features & Use Cases

Bidirectional variable binding and aliasing, enabling both sides to carry unbound variables that resolve during solving.
Handling constants, variables, and compound terms (including lists) with recursive, structural matching and backtracking support.
Occurs check discussion and practical tradeoffs used to prevent infinite terms, with guidance on when to enable a full occurs check.
Substitution environment semantics: write-once bindings, transitive resolution, and backtracking rollback.

Quick Start

Demonstrate unifying f(X, g(Y, a)) with f(h(Z), g(b, Z)) and display the final substitution.

Frequently Asked Questions about prolog-unification

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How does Prolog unification work when matching compound terms?▼

Unification in Prolog finds a substitution set of variable bindings that makes two terms syntactically identical. It structurally decomposes constants, variables, and compound terms, binding variables bidirectionally until the terms match or fail.

How do I unify terms with unbound variables on both sides in logic programming?▼

Bidirectional variable binding allows both terms to carry unbound variables that resolve during solving. The unification process creates write-once aliases and transitively resolves substitutions until both terms become identical.

What is the occurs check in Prolog and when should I enable it?▼

The occurs check prevents infinite terms by verifying a variable does not appear within the term it binds to. Enable it during constraint solving when logically sound substitutions are required, accepting the performance tradeoff.

How do I unify f(X, g(Y, a)) with f(h(Z), g(b, Z)) step by step?▼

Unifying f(X, g(Y, a)) with f(h(Z), g(b, Z)) matches compound structures recursively. The resulting substitution binds X to h(Z) and Y to b, resolving Z transitively to produce a consistent binding environment.

Does the Martelli-Montanari algorithm support backtracking for unification?▼

The Martelli-Montanari algorithm provides backtracking-ready solutions through write-once substitution environments with rollback semantics. If unification fails, the environment rolls back previous bindings to explore alternative matching paths.