BiGUL: a formally verified core language for putback-based bidirectional programming

Abstract

Putback-based bidirectional programming allows the programmer to write only one putback transformation, from which the unique corresponding forward transformation is derived for free. The logic of a putback transformation is more sophisticated than that of a forward transformation and does not always give rise to well-behaved bidirectional programs; this calls for more robust language design to support development of well-behaved putback transformations. In this paper, we design and implement a concise core language BiGUL for putback-based bidirectional programming to serve as a foundation for higher-level putback-based languages. BiGUL is completely formally verified in the dependently typed programming language Agda to guarantee that any putback transformation written in BiGUL is well-behaved.