Titlebook: Introduction to Computation; Haskell, Logic and A Donald Sannella,Michael Fourman,Philip Wadler Textbook 2021 The Editor(s) (if applicable)

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Testing Your Programs, your fingers will type something different from what your brain intended. Nobody’s perfect!. Fortunately, Haskell will detect some of your mistakes automatically. These include syntax?and type errors?as well as typos, like misspelled function names.

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Patterns of Reasoning,tudy patterns of reasoning that allow true statements to be combined to give other statements that are guaranteed to be true. We’ll start with ideas that go all the way back to Aristotle, the founder of logic, who looked at simple patterns of logical argument with two premises and a conclusion, call

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Coeval

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More Fun with Recursion,?the notation .. Underlying this notation is the following Prelude function, where . . stands for .?.?.: Here the recursion is on integers rather than lists. We’ve learned how important it is that recursion is well-founded: it’s okay to define the result of applying a function to a value in terms of

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Expression Trees,representing the syntax of languages involving nesting, and for representing data in a way that is amenable to processing by recursive algorithms. We have already seen some pictures of trees in Chap.?., in the explanation of . and ., and the sequent calculus proofs in Chap.?. have a tree-like struct

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Donald Sannella,Michael Fourman,Haoran Peng,Philip Wadlerse of elliptic curves in computing theory and coding theory. In the third appendix we discuss the role of elliptic curves in homotopy theory. In these three introductions the reader can get a clue to the far-reaching implications of the theory of elliptic curves in mathematical sciences. During the

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Donald Sannella,Michael Fourman,Haoran Peng,Philip Wadlerptic curves in computing theory and coding theory. In the third appendix we discuss the role of elliptic curves in homotopy theory. In these three introductions the reader can get a clue to the far-reaching implications of the theory of elliptic curves in mathematical sciences. During the ?nal produ