A Quantitative Understanding of Pattern Matching

• Type: Article in International Conference Proceedings Book
• Date: 2019

Authors

Sandra Alves (Author) FCUP; Kesner, D (Author) Other; Ventura, D (Author) Other

Conference proceedings International

Title: 25th International Conference on Types for Proofs and Programs, TYPES 2019, June 11-14, 2019, Oslo, Norway.

Pages: 3:1-3:36

25th International Conference on Types for Proofs and Programs, TYPES 2019

11 June 2019 through 14 June 2019

Indexing

Scopus - 5 Citations

Other information

Authenticus ID: P-00S-7F5

DOI: 10.4230/lipics.types.2019.3

Abstract (EN): This paper shows that the recent approach to quantitative typing systems for programming languages can be extended to pattern matching features. Indeed, we define two resource-aware type systems, named U and E , for a λ-calculus equipped with pairs for both patterns and terms. Our typing systems borrow some basic ideas from [19], which characterises (head) normalisation in a qualitative way, in the sense that typability and normalisation coincide. But, in contrast to [19], our systems also provide quantitative information about the dynamics of the calculus. Indeed, system U provides upper bounds for the length of (head) normalisation sequences plus the size of their corresponding normal forms, while system E , which can be seen as a refinement of system U , produces exact bounds for each of them. This is achieved by means of a non-idempotent intersection type system equipped with different technical tools. First of all, we use product types to type pairs instead of the disjoint unions in [19], which turn out to be an essential quantitative tool because they remove the confusion between âbeing a pairâ? and âbeing duplicableâ?. Secondly, typing sequents in system E are decorated with tuples of integers, which provide quantitative information about normalisation sequences, notably time (cf. length) and space (cf. size). Moreover, the time resource information is remarkably refined, because it discriminates between different kinds of reduction steps performed during evaluation, so that beta, substitution and matching steps are counted separately. Another key tool of system E is that the type system distinguishes between consuming (contributing to time) and persistent (contributing to space) constructors. © LIPIcs 2020.

Language: English

Type (Professor's evaluation): Scientific