Archive for 15th October 2008

Composing memo tries

The post Elegant memoization with functional memo tries showed a simple type of search tries and their use for functional memoization of functions. This post provides some composition tools for memo tries, whose definitions are inevitable, in that they are determined by the principle presented in Simplifying semantics with type class morphisms.

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Elegant memoization with functional memo tries

Function memoization goes back at least as far as Donald Michie’s 1968 paper. The idea is to stash away results of a function call for reuse when a function is called more than once with the same argument. Given an argument, the memoized function looks up the argument in the internal memo table (often a hash table). If found, the previously computed result is reused. Otherwise, the function is applied, and the result is stored in the table, keyed by the argument. The table and its mutation are kept private from clients of the memo function.

Perhaps surprisingly, memoization can be implemented simply and purely functionally in a lazy functional language. Laziness allows the implementation to build the memo table once and for all, filling in all the results for the function at all domain values. Thanks to laziness, the values don’t actually get computed until they’re used. As usual with lazy data structures, once a component has been evaluated, future accesses come for free.

The implementation described in this post is based one I got from Spencer Janssen. It uses the essential idea of Ralf Hinze’s paper Generalizing Generalized Tries. The library is available on Hackage and a darcs repository. See the wiki page and hackage page for documentation and source code. I’ve compiled it successfully with ghc versions 6.8.2 through 6.10.3.


  • 2009-02-12: Fixed typo.
  • 2009-11-14: Hackage page pointer.
  • 2009-11-20: Fixed source code pointer.

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