Quantitative Behavioural Reasoning for Higher-order Effectful Programs: Applicative Distances (Extended Version) [article]

Francesco Gavazzo
2018 arXiv   pre-print
This paper studies the quantitative refinements of Abramsky's applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value λ-calculus with a linear type system that can express programs sensitivity, enriched with algebraic operations à la Plotkin and Power. To do so a general, abstract framework for studying behavioural relations taking values over quantales is defined according to Lawvere's analysis of generalised metric spaces. Barr's notion of relator
more » ... r lax extension) is then extended to quantale-valued relations adapting and extending results from the field of monoidal topology. Abstract notions of quantale-valued effectful applicative similarity and bisimilarity are then defined and proved to be a compatible generalised metric (in the sense of Lawvere) and pseudometric, respectively, under mild conditions.
arXiv:1801.09072v3 fatcat:hvpl33atmjaorlruldhne35ine