Abstract

We formalize the meaning of lazy memo-functions in Haskell with an extension to the lazy -calculus, Haskell's computational model. The semantics enable reasoning about memoization 's effect on space and time complexity. Based on the semantics, we present a prototype implementation that requires no changes to the garbage-collector; memo-tables are simply reclaimed when no references to them remain. 1 Introduction A memo-function remembers the arguments to which it has been applied, together with the result. If applied to a repeated argument, memo-functions return the cached answer rather than recomputing it from scratch. Memoization improves the time complexity of algorithms with repeated computations --- but can consume vast amounts of memory. Some implementations of memoization use heuristic cache replacement policies (such as LRU or FIFO) to manage memory. Although implementations try to minimize space consumption, in their essence, memo-functions trade better runtime performance f...

Citations