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Thinking Functionally with Haskell by Richard Bird

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Chapter 6

Proofs

We have seen a lot of laws in the previous two chapters, though perhaps the word ‘law’ is a little inappropriate because it suggests something that is given to us from on high and which does not have to be proved. At least the word has the merit of being short. All of the laws we have encountered so far assert the equality of two functional expressions, possibly under subsidiary conditions; in other words, laws have been equations or identities between functions, and calculations have been point-free calculations (see Chapter 4, and the answer to Exercise K for more on the point-free style). Given suitable laws to work with, we can then use equational reasoning to prove other laws. Equational logic is a simple but powerful tool ...

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