Algorithms for Extended Alpha-Equivalence and Complexity

Schmidt-Schauß, Manfred; Rau, Conrad; Sabel, David

doi:10.4230/lipics.rta.2013.255

Cited by 2 publications

(1 citation statement)

References 33 publications

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“…Algorithms for α-equivalence extended with further principles (e.g. permutations of let expressions), but not up to sharing unfolding, is studied by Schmidt-Schauß, Rau, and Sabel in [30].…”

Section: Related Problems and Technical Choicesmentioning

confidence: 99%

Sharing Equality is Linear

Condoluci

Accattoli

Coen

2019

Proceedings of the 21st International Symposium on Principles and Practice of Declarative Programming

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e λ-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the speci cation as an execution mechanism, because terms can grow exponentially with the number of β-steps. is is why implementations of functional languages and proof assistants always rely on some form of sharing of subterms. ese frameworks however do not only evaluate λ-terms, they also have to compare them for equality. In presence of sharing, one is actually interested in equality of the underlying unshared λ-terms.e literature contains algorithms for such a sharing equality, that are polynomial in the sizes of the shared terms.is paper improves the bounds in the literature by presenting the rst linear time algorithm. As others before us, we are inspired by Paterson and Wegman's algorithm for rst-order uni cation, itself based on representing terms with sharing as DAGs, and sharing equality as bisimulation of DAGs. Beyond the improved complexity, a distinguishing point of our work is a dissection of the involved concepts. In particular, we show that the algorithm computes the smallest bisimulation between the given DAGs, if any.

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Section: Related Problems and Technical Choicesmentioning

confidence: 99%

Sharing Equality is Linear

Condoluci

Accattoli

Coen

2019

Proceedings of the 21st International Symposium on Principles and Practice of Declarative Programming

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Nominal Unification and Matching of Higher Order Expressions with Recursive Let

Schmidt-Schauß¹,

Kutsia

Levy³

et al. 2022

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A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in nondeterministic polynomial time. We also explore specializations like nominal letrec-matching for expressions, for DAGs, and for garbage-free expressions and determine their complexity. We also provide a nominal unification algorithm for higher-order expressions with recursive let and atom-variables, where we show that it also runs in nondeterministic polynomial time. In addition we prove that there is a guessing strategy for nominal unification with letrec and atom-variable that is a trade-off between exponential growth and non-determinism. Nominal matching with variables representing partial letrec-environments is also shown to be in NP.

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Algorithms for Extended Alpha-Equivalence and Complexity

Cited by 2 publications

References 33 publications

Sharing Equality is Linear

Sharing Equality is Linear

Nominal Unification and Matching of Higher Order Expressions with Recursive Let

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