Shin-Cheng Mu and José Nuno Oliveira. In the *Journal of Logic and Algebraic Programming*, Vol 81(6), pages 680–704, August 2012.

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Problem statements often resort to superlatives such as in eg. “… the smallest such number”, “… the best approximation”, “… the longest such list” which lead to specifications made of two parts: one defining a broad class of solutions (the *easy* part) and the other requesting the optimal such solution (the *hard* part).

This article introduces a binary relational combinator which mirrors this linguistic structure and exploits its potential for calculating programs by optimization. This applies in particular to specifications written in the form of Galois connections, in which one of the adjoints delivers the optimal solution.

The framework encompasses re-factoring of results previously developed by Bird and de Moor for greedy and dynamic programming, in a way which makes them less technically involved and therefore easier to understand and play with.

This is an extended version of our conference paper published in RAMiCS 2011.