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Higher-Order Pattern Anti-Unification in Linear Time.

Alexander Baumgartner1, Temur Kutsia1, Jordi Levy2

  • 11Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria.

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|September 4, 2018
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Summary
This summary is machine-generated.

We developed a Huet's style anti-unification algorithm for lambda-terms. This algorithm efficiently finds the least general higher-order pattern generalization for typed and untyped lambda-terms with linear time complexity.

Keywords:
Anti-unificationGeneralizations of lambda termsHigher-order patterns

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Area of Science:

  • Theoretical Computer Science
  • Logic in Computer Science
  • Automated Reasoning

Background:

  • Anti-unification is crucial for program synthesis and automated reasoning.
  • Higher-order pattern generalization is essential for complex symbolic manipulation.
  • Existing algorithms may lack efficiency or generality.

Purpose of the Study:

  • To present a novel rule-based Huet's style anti-unification algorithm.
  • To compute the least general higher-order pattern generalization for lambda-terms.
  • To ensure the algorithm's efficiency and applicability to both typed and untyped lambda-terms.

Main Methods:

  • A rule-based algorithm inspired by Huet's style anti-unification.
  • Application to simply typed lambda-terms to compute generalizations.
  • A modification for handling untyped lambda-terms.

Main Results:

  • The algorithm computes a unique least general higher-order pattern generalization for any pair of same-typed lambda-terms.
  • The generalization is unique modulo $\beta$-equivalence and variable renaming.
  • The algorithm demonstrates linear time complexity for both typed and untyped cases.

Conclusions:

  • The presented algorithm provides an efficient and general method for higher-order pattern generalization.
  • It offers a valuable tool for applications in automated reasoning and program synthesis.
  • The linear time complexity makes it practical for large-scale computations.