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ICFP 2019
Sun 18 - Fri 23 August 2019 Berlin, Germany
Wed 21 Aug 2019 15:20 - 15:43 at Aurora Borealis - Types Chair(s): Zoe Paraskevopoulou

We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing which enhances the safety properties of programs, but also supports non-linear typing as well which makes the type system more convenient for programming. Just like in FPC, we show that LNL-FPC supports type-level recursion which in turn induces term-level recursion. We also provide sound and computationally adequate categorical models for LNL-FPC which describe the categorical structure of the substructural operations of Intuitionistic Linear Logic at all non-linear types, including the recursive ones. In order to do so, we describe a new technique for solving recursive domain equations within the category CPO by constructing the solutions over pre-embeddings. The type system also enjoys implicit weakening and contraction rules which we are able to model by identifying the canonical comonoid structure of all non-linear types. We also show that the requirements of our abstract model are reasonable by constructing a large class of concrete models that have found applications not only in classical functional programming, but also in emerging programming paradigms that incorporate linear types, such as quantum programming and circuit description programming languages.

Wed 21 Aug
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15:20 - 16:30: Research Papers - Types at Aurora Borealis
Chair(s): Zoe ParaskevopoulouPrinceton University
icfp-2019-papers15:20 - 15:43
Bert LindenhoviusTulane University, Michael MisloveTulane, Vladimir ZamdzhievUniversity of Lorraine, CNRS, Inria, LORIA
icfp-2019-papers15:43 - 16:06
Zhao Jinxu, Bruno C. d. S. OliveiraThe University of Hong Kong, Hong Kong, Tom SchrijversKU Leuven
icfp-2019-papers16:06 - 16:30
Victor Cacciari MiraldoUtrecht University, Netherlands, Wouter SwierstraUtrecht University, Netherlands