Extending the Quantitative Pattern-Matching Paradigm
We show how (well-established) type systems based on non-idempotent intersection types can be extended to characterize termination properties of functional programming languages with pattern matching features. To model such programming languages, we use a (weak and closed) λ-calculus integrating a pattern matching mechanism on algebraic data types (ADTs) (to avoid repetition of extension). Remarkably, we also show that this language not only encodes Plotkin’s CBV and CBN λ-calculus as well as other subsuming frameworks, such as the bang-calculus, but can also be used to interpret the semantics of effectful languages with exceptions. After a thorough study of the untyped language, we introduce a type system based on intersection types, and we show through purely logical methods that the set of terminating terms of the language corresponds exactly to that of well-typed terms. Moreover, by considering non-idempotent intersection types, this characterization turns out to be quantitative, i.e. the size of the type derivation of a term t gives an upper bound for the number of evaluation steps from t to its normal form.
Wed 23 OctDisplayed time zone: Osaka, Sapporo, Tokyo change
10:30 - 12:00 | Type theory and Semantic Frameworks IIResearch Papers at Yamauchi Hall Chair(s): Pierre-Evariste Dagand IRIF / CNRS | ||
10:30 30mTalk | Building A Correct-By-Construction Type Checker for a Dependently Typed Core Language Research Papers | ||
11:00 30mTalk | Extending the Quantitative Pattern-Matching Paradigm Research Papers Sandra Alves University of Porto, Delia Kesner Université Paris Cité - CNRS - IRIF; Institut Universitaire de France, Miguel Ramos Universidade do Porto, LIACC; Université Paris Cité, IRIF, CNRS | ||
11:30 30mTalk | On Computational Indistinguishability and Logical Relations Research Papers Ugo Dal Lago University of Bologna & INRIA Sophia Antipolis, Zeinab Galal University of Bologna, Giulia Giusti ENS Lyon |