Monad translating inductive and coinductive types

Authors:
Tarmo Uustalu
Affiliations:
Inst. of Cybernetics, Tallinn Technical University, Tallinn, Estonia
Venue:
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Year:
2002

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Abstract

We show that the call-by-name monad translation of simply typed lambda calculus extended with sum and product types extends to special and general inductive and coinductive types so that its crucial property of preserving typings and β- and commuting reductions is maintained. Specific similar-purpose translations such as CPS translations follow from the general monad translations by specialization for appropriate concrete monads.