A first order logic for partial functions

Lucio, Paqui; Gavilanes-Franco, Antonio

doi:10.1007/bfb0028972

Cited by 5 publications

(1 citation statement)

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“…Capturing partial functions in a formal system is not just of theoretical interest. It is also a practical concern that has arisen in the formal verification of programs with exceptional expressions, such as division by zero or the head of an empty list, and has resulted in work on partial algebras [Burmeister 1993], exception algebras [Bernot et al 1986], error algebras [Gogolla et al 1984], order-sorted algebras [Goguen and Meseguer 1992], and various logics for partial functions [Abdallah 1995;Lucio-Carrasco and Gavilanes-Franco 1989].…”

Section: Inhabitant Symbol and Related Instrumentsmentioning

confidence: 99%

A general approach to define binders using matching logic

Chen

Roşu

2020

Proc. ACM Program. Lang.

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We propose a novel definition of binders using matching logic, where the binding behavior of object-level binders is directly inherited from the built-in ∃ binder of matching logic. We show that the behavior of binders in various logical systems such as-calculus, System F,-calculus, pure type systems, can be axiomatically defined in matching logic as notations and logical theories. We show the correctness of our definitions by proving conservative extension theorems, which state that a sequent/judgment is provable in the original system if and only if it is provable in matching logic, in the corresponding theory. Our matching logic definition of binders also yields models to all binders, which are deductively complete with respect to formal reasoning in the original systems. For-calculus, we further show that the yielded models are representationally complete, a desired property that is not enjoyed by many existing-calculus semantics. This work is part of a larger effort to develop a logical foundation for the programming language semantics framework K (http://kframework.org).

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