Affiliations: Yale-NUS College & School of Computing, National University of Singapore, danvy@acm.org
Correspondence:
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Address for correspondence: Yale-NUS College & School of Computing, National University of Singapore.
Abstract: “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.
Keywords: TABA, recursion pattern, list processing, symbolic convolutions, eta redexes, Coq Proof Assistant, There and Forth Again (TAFA), defunctionalization and refunctionalization, lambda-lifting and lambda-dropping, lightweight fusion and lightweight fission, continuations
