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There and Back Again
Olivier Danvy
January 2005 |
Abstract:
We present a programming pattern where a recursive function
defined over a data structure traverses another data structure at return
time. The idea is that the recursive calls get us `there' by traversing the
first data structure and the returns get us `back again' while traversing the
second data structure. We name this programming pattern of traversing a data
structure at call time and another data structure at return time ``There And
Back Again'' (TABA).
The TABA pattern directly applies to computing symbolic convolutions and to multiplying polynomials. It also blends well with other programming patterns such as dynamic programming and traversing a list at double speed. We illustrate TABA and dynamic programming with Catalan numbers. We illustrate TABA and traversing a list at double speed with palindromes and we obtain a novel solution to this traditional exercise. Finally, through a variety of tree traversals, we show how to apply TABA to other data structures than lists. A TABA-based function written in direct style makes full use of an ALGOL-like control stack and needs no heap allocation. Conversely, in a TABA-based function written in continuation-passing style and recursively defined over a data structure (traversed at call time), the continuation acts as an iterator over a second data structure (traversed at return time). In general, the TABA pattern saves one from accumulating intermediate data structures at call time Available as PostScript, PDF, DVI. |