Efficient memo-table management strategies

Summary

A large, automatically detectable class of non-linear functions is defined and their evaluation graphs are characterised. These results are then used to develop space-efficient implementation ofmemo-functions. We generate a variant of memo-functions which can be used to linearise the time cost of calls of a non-linear function to itself whilst executing in bounded space. These memo-functions dynamically garbage collect (or reuse) memo-table entries when it is known that such entries will not be useful again. For each non-linear function a function called the “table-manager” function is synthesised by a static analysis of the definition of the non-linear function. The table-managers delete (or reuse) entries that are guaranteed to be obsolete as a result of any insertion into the memo-tables. In this way they ensure that the size of the tables is minimised. Furthermore, the sizes of the tables for these memo-functions are guaranteed not to exceed a compile-time constant found by the same static analysis which synthesises the table-managers. The applicability of the method also includes many problems which have been previously solved by applyingdynamic programming techniques. An implementation of these memo-functions for the functional language HOPE is also outlined.