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Section: New Results

Exp-log normal form of types and the axioms for η-equality of the λ-calculus with sums

Participant : Danko Ilik.

In the presence of sum types, the λ-calculus has but one implemented (and incomplete) heuristic for deciding βη-equality of terms, in spite of a dozen of meta-theoretic works showing that the equality is decidable.

In the work discussed here, we first used the exp-log decomposition of the arrow type—inspired from the analytic transformation ab=exp(b×loga)—to obtain a type normal form for the type languages {,×,+}. We then made a quotient of the βη-equality of terms modulo the terms coerced into their representation at the exp-log normal form of their type. This allows to obtain a simplification of the so far standard axioms for βη-equality.

Moreover, we provided a Coq implementation of a heuristic decision procedure for this equality. Although a heuristic, this implementation manages to tackle examples of equal terms that need a complex program analysis in the only previously implemented heuristic of Vincent Balat.

This work is described in a paper accepted for presentation at POPL 2017, [27].