Abstract
We revisit the connection between three notions of computation: Moggi s monads, Hughes s arrows and McBride and Paterson s idioms (also called applicative functors). We show that idioms are equivalent to arrows that satisfy the type isomorphism A→B 1→(A→B) and that monads are equivalent to arrows that satisfy the type isomorphism A→B←A→(1→B). Further, idioms embed into arrows and arrows embed into monads.
Original language | English |
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Pages (from-to) | 97-117 |
Number of pages | 21 |
Journal | Electronic Notes in Theoretical Computer Science |
Volume | 229 |
Issue number | 5 |
DOIs | |
Publication status | Published - 8 Mar 2011 |
Keywords
- applicative functors
- arrows
- idioms
- monads
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)