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Getting There and Back Again

Danvy Olivier

Fundamenta Informaticae

2022

Vol. 185, nr 2

185--199

"There and Back Again" (TABA) is a programming pattern where the recursive calls traverse one data structure and the subsequent returns traverse another. This article presents new TABA examples, refines existing ones, and formalizes both their control flow and their data flow using the Coq Proof Assistant. Each formalization mechanizes a pen-and-paper proof, thus making it easier to "get" TABA. In addition, this article identifies and illustrates a tail-recursive variant of TABA, There and Forth Again (TAFA) that does not come back but goes forth instead with more tail calls.

There and Back Again

Danvy O., Goldberg M.

Fundamenta Informaticae

2005

Vol. 66, nr 4

397--413

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.