TY - GEN
T1 - Partiality, revisited
T2 - 20th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2017
AU - Altenkirch, Thorsten
AU - Danielsson, Nils Anders
AU - Kraus, Nicolai
PY - 2017/3/16
Y1 - 2017/3/16
N2 - Capretta’s delay monad can be used to model partial computations, but it has the “wrong” notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the “right” notion of equality, weak bisimilarity. However, recent work by Chapman et al. suggests that it is impossible to define a monad structure on the resulting construction in common forms of type theory without assuming (instances of) the axiom of countable choice. Using an idea from homotopy type theory—a higher inductive-inductive type—we construct a partiality monad without relying on countable choice. We prove that, in the presence of countable choice, our partiality monad is equivalent to the delay monad quotiented by weak bisimilarity. Furthermore we outline several applications.
AB - Capretta’s delay monad can be used to model partial computations, but it has the “wrong” notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the “right” notion of equality, weak bisimilarity. However, recent work by Chapman et al. suggests that it is impossible to define a monad structure on the resulting construction in common forms of type theory without assuming (instances of) the axiom of countable choice. Using an idea from homotopy type theory—a higher inductive-inductive type—we construct a partiality monad without relying on countable choice. We prove that, in the presence of countable choice, our partiality monad is equivalent to the delay monad quotiented by weak bisimilarity. Furthermore we outline several applications.
UR - http://www.scopus.com/inward/record.url?scp=85015911815&partnerID=8YFLogxK
UR - http://eprints.nottingham.ac.uk/38095/
U2 - 10.1007/978-3-662-54458-7_31
DO - 10.1007/978-3-662-54458-7_31
M3 - Conference contribution
AN - SCOPUS:85015911815
SN - 9783662544570
T3 - Lecture Notes in Computer Science
SP - 534
EP - 549
BT - Foundations of Software Science and Computation Structures
A2 - Esparza, Javier
A2 - Murawski, Andrzej S.
PB - Springer
Y2 - 22 April 2017 through 29 April 2017
ER -