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**1 - 2**of**2**### Why Galois connections?

, 2010

"... The ‘G’alculator is not the GTK 2 based calculator which Google offers you in the first place...‘G’alculator GCs as specs Examples Fold/Unfold Conclusions Postscriptum Annex References Context • ‘G’alculator Project — design of a proof assistant solely based on Galois connections (GCs), eg. and indi ..."

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The ‘G’alculator is not the GTK 2 based calculator which Google offers you in the first place...‘G’alculator GCs as specs Examples Fold/Unfold Conclusions Postscriptum Annex References Context • ‘G’alculator Project — design of a proof assistant solely based on Galois connections (GCs), eg. and indirect equality (IE) 〈 ∀ x, y:: f x ≤ y ⇔ x ≤ g y〉 n = m ⇔ 〈 ∀ x:: x ≤ n ⇔ x ≤ m〉 See PhD thesis by Paulo Silva on his implementation of a prototype of the ‘G’alculator in Haskell and our PPDP’08

### Programming from Galois Connections

"... 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 one particular su ..."

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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 one particular such solution, optimal in some sense (the hard part). This article introduces a binary relational combinator which mirrors this linguistic structure and exploits its potential for calculating programs by op-timization. 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 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.