2015/05/14 by Raphaëlle Crubillé, Crubillé, Raphaëlle, Ugo Dal Lago +1 · 1 citation
Computer Science · #Bayesian Modeling and Causal Inference #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies #cs.LO
paper · pdf · doi:10.48550/arxiv.1505.03638
46 pages
arxiv created 2015/05/14 · arxiv updated 2015/05/15
Terms of Church's λ-calculus can be considered equivalent along many different definitions, but context equivalence is certainly the most direct and universally accepted one. If the underlying calculus becomes probabilistic, however, equivalence is too discriminating: terms which have totally unrelated behaviours are treated the same as terms which behave very similarly. We study the problem of evaluating the distance between affine λ-terms. The most natural definition for it, namely a natural generalisation of context equivalence, is shown to be characterised by a notion of trace distance, and to be bounded from above by a coinductively defined distance based on the Kantorovich metric on distributions. A different, again fully-abstract, tuple-based notion of trace distance is shown to be able to handle nontrivial examples.