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.
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W.S. Swierstra
End-user scripting for visual software analysis
ACM SIGPLAN Haskell Symposium
Software Analysis and Transformation

van der Ploeg, A., & Kiselyov, O. (2014). Reflection without remorse: revealing a hidden sequence to speed up monadic reflection. In W. S. Swierstra (Ed.), ACM SIGPLAN Notices (pp. 133–144). ACM.