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Programming from galois connections
 In Relational and Algebraic Methods in Computer Science  12th International Conference, RAMICS 2011, volume 6663 of LNCS
, 2011
"... Abstract. Problem statements often resort to superlatives such as in ..."
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Abstract. Problem statements often resort to superlatives such as in
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 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 refactoring 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.