TY - GEN

T1 - Fibrational induction meets effects

AU - Atkey, Robert

AU - Ghani, Neil

AU - Jacobs, Bart

AU - Johann, Patricia

PY - 2012

Y1 - 2012

N2 - This paper provides several induction rules that can be used to prove properties of effectful data types. Our results are semantic in nature and build upon Hermida and Jacobs’ fibrational formulation of induction for polynomial data types and its extension to all inductive data types by Ghani, Johann, and Fumex. An effectful data type μ(TF) is built from a functor F that describes data, and a monad T that computes effects. Our main contribution is to derive induction rules that are generic over all functors F and monads T such that μ(TF) exists. Along the way, we also derive a principle of definition by structural recursion for effectful data types that is similarly generic. Our induction rule is also generic over the kinds of properties to be proved: like the work on which we build, we work in a general fibrational setting and so can accommodate very general notions of properties, rather than just those of particular syntactic forms. We give examples exploiting the generality of our results, and show how our results specialize to those in the literature, particularly those of Filinski and Støvring.

AB - This paper provides several induction rules that can be used to prove properties of effectful data types. Our results are semantic in nature and build upon Hermida and Jacobs’ fibrational formulation of induction for polynomial data types and its extension to all inductive data types by Ghani, Johann, and Fumex. An effectful data type μ(TF) is built from a functor F that describes data, and a monad T that computes effects. Our main contribution is to derive induction rules that are generic over all functors F and monads T such that μ(TF) exists. Along the way, we also derive a principle of definition by structural recursion for effectful data types that is similarly generic. Our induction rule is also generic over the kinds of properties to be proved: like the work on which we build, we work in a general fibrational setting and so can accommodate very general notions of properties, rather than just those of particular syntactic forms. We give examples exploiting the generality of our results, and show how our results specialize to those in the literature, particularly those of Filinski and Støvring.

KW - fibrational induction

KW - polynomial data types

UR - http://www.scopus.com/inward/record.url?scp=84859129534&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-28729-9_3

DO - 10.1007/978-3-642-28729-9_3

M3 - Conference contribution book

VL - 7213

T3 - Lecture Notes in Computer Science

SP - 42

EP - 57

BT - Foundations of Software Science and Computational Structures

A2 - Birkedal, Lars

PB - Springer

T2 - 15th International Conference, FOSSACS 2012, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2012

Y2 - 24 March 2012 through 1 April 2012

ER -