Toward a Curry-Howard Equivalence for Linear, Reversible Computation [chapter]

Kostia Chardonnet, Alexis Saurin, Benoît Valiron
2020 Lecture Notes in Computer Science  
In this paper, we present a linear and reversible language with inductive and coinductive types, together with a Curry-Howard correspondence with the logic : linear logic extended with least and greatest fixed points allowing inductive and coinductive statements. Linear, reversible computation makes an important sub-class of quantum computation without measurement. In the latter, the notion of purely quantum recursive type is not yet well understood. Moreover, models for reasoning about quantum
more » ... algorithms only provide complex types for classical datatypes: there are usually no types for purely quantum objects beside tensors of quantum bits. This work is a first step towards understanding purely quantum recursive types.
doi:10.1007/978-3-030-52482-1_8 fatcat:t6un5bqp4zhtbpwcdr2c5orqxu