# Inverting Functions as Folds

Conference paper

- First Online:

DOI: 10.1007/3-540-45442-X_13

- Cite this paper as:
- Mu SC., Bird R. (2002) Inverting Functions as Folds. In: Boiten E.A., Möller B. (eds) Mathematics of Program Construction. MPC 2002. Lecture Notes in Computer Science, vol 2386. Springer, Berlin, Heidelberg

## Abstract

This paper is devoted to the proof and applications of a theorem giving conditions under which the inverse of a partial function can be expressed as a relational hylomorphism. The theorem is a generalisation of a previous result, due to Bird and de Moor, that gave conditions under which a total function can be expressed a relational fold. The theorem is illustrated with three problems, all dealing with constructing trees with various properties.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 2002