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A complete V-equational system for graded lambda-calculus

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Resumo:Modern programming frequently requires generalised notions of program equivalence based on a metric or a similar structure. Previous work addressed this challenge by introducing the notion of a V-equation, i.e. an equation labelled by an element of a quantale V, which covers inter alia (ultra-)metric, classical, and fuzzy (in)equations. It also introduced a V-equational system for the linear variant of lambda-calculus where any given resource must be used exactly once. In this paper we drop the (often too strict) linearity constraint by adding graded modal types which allow multiple uses of a resource in a controlled manner. We show that such a control, whilst providing more expressivity to the programmer, also interacts more richly with V-equations than the linear or Cartesian cases. Our main result is the introduction of a sound and complete V-equational system for a lambda-calculus with graded modal types interpreted by what we call a Lipschitz exponential comonad. We also show how to build such comonads canonically via a universal construction, and use our results to derive graded metric equational systems (and corresponding models) for programs with timed and probabilistic behaviour.
Autores principais:Dahlqvist, Fredrik
Outros Autores:Neves, Renato Jorge Araújo
Assunto:λ-calculus graded modal type quantitative equational theory enriched category theory
Ano:2023
País:Portugal
Tipo de documento:comunicação em conferência
Tipo de acesso:acesso aberto
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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