Calculating a backtracking algorithm: an exercise in monadic program derivation
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Equational reasoning is among the most important tools that functional programming provides us. Curiously, relatively less attention has been paid to reasoning about monadic programs. In this report we derive a backtracking algorithm for problem specifications that use a monadic unfold to generate possible solutions, which are filtered using a 𝑠𝑐𝑎𝑛𝑙-like predicate. We develop theorems that convert a variation of 𝑠𝑐𝑎𝑛𝑙 to a 𝑓𝑜𝑙𝑑𝑟 that uses the state monad, as well as theorems constructing hylomorphism. The algorithm is used to solve the n-queens puzzle, our running example. The aim is to develop theorems and patterns useful for the derivation of monadic programs, focusing on the intricate interaction between state and non-determinism.
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