TY - JOUR
TI - The Enriched Eﬀect Calculus: Syntax and Semantics
LA - eng
AU - Møgelberg, Rasmus Ejlers
AU - Simpson, Alex
AU - Egger, Jeff
JF - Journal of Logic and Computation
VL - 24
IS - 3
SP - 615
EP - 654
PY - 2014
SN - 1465363x, 0955792x
AB - This article introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; e.g. the linear usage of imperative features such as state and/or continuations. The enriched effect calculus is implemented as an extension of a basic effect calculus without linear primitives, which is closely related to Moggi's computational metalanguage, Filinski's effect PCF and Levy's call-by-push-value. We present syntactic results showing: the fidelity of the behaviour of the linear connectives of the enriched effect calculus; the conservativity of the enriched effect calculus over its non-linear core (the effect calculus); and the non-conservativity of intuitionistic linear logic when considered as an extension of the enriched effect calculus. The second half of the article investigates models for the enriched effect calculus, based on enriched category theory. We give several examples of such models, relating them to models of standard effect calculi (such as those based on monads), and to models of intuitionistic linear logic. We also prove soundness and completeness.
DO - 10.1093/logcom/exs025
ER -