Reflection without remorse Revealing a hidden sequence to speed up monadic reflection

Atze Van Der Ploeg, Oleg Kiselyov

Research output: Contribution to journalArticlepeer-review


A series of list appends or monadic binds for many monads performs algorithmically worse when left-associated. Continuation-passing style (CPS) is well-known to cure this severe dependence of performance on the association pattern. The advantage of CPS dwindles or disappears if we have to examine or modify the intermediate result of a series of appends or binds, before continuing the series. Such examination is frequently needed, for example, to control search in non-determinism monads. We present an alternative approach that is just as general as CPS but more robust: it makes series of binds and other such operations efficient regardless of the association pattern - and also provides efficient access to intermediate results. The key is to represent such a conceptual sequence as an efficient sequence data structure. Efficient sequence data structures from the literature are homogeneous and cannot be applied as they are in a type-safe way to series of monadic binds. We generalize them to type aligned sequences and show how to construct their (assuredly order-preserving) implementations. We demonstrate that our solution solves previously undocumented, severe performance problems in iteratees, LogicT transformers, free monads and extensible effects.

Original languageEnglish
Pages (from-to)133-144
Number of pages12
JournalACM SIGPLAN Notices
Issue number12
Publication statusPublished - 2014 Sept 3


  • data structures
  • monads
  • performance
  • reflection


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