3 research outputs found
Quantitative Behavioural Reasoning for Higher-order Effectful Programs: Applicative Distances (Extended Version)
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 -calculus with a linear type system that can express
programs sensitivity, enriched with algebraic operations \emph{\`a 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 (or 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
Quantitative Behavioural Reasoning for Higher-order Effectful Programs: Applicative Distances
International audienceThis paper studies quantitative refinements of Abramsky's applica-tive 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 program 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 introduced according to Lawvere's analysis of generalised metric spaces. Barr's notion of relator (or 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