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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Higher-Order Functions,The same patterns of computation keep coming up in function definitions. An example from the beginning of Chap. . was in the definitions of . and .:

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Higher and Higher,Sections are convenient for supplying functional arguments to higher-order functions. For instance, we can replace

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Sequent Calculus,Chapters . and . covered 2000 years of logic, up to the mid-nineteenth century, but using modern notation which makes things much simpler. We’re now going to study modern symbolic logic.

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Algebraic Data Types,So far, we’ve done a lot using the types that come “out of the box” with Haskell. The type of lists has been particularly useful, and higher-order functions have revealed the power of the function type .. Both of these actually provide an infinite number of types: there is a type . . for every type . and a type . . . for every . and ..

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Karnaugh Maps,Complex logical expressions like . are hard to understand and hard to work with. The much simpler expression ., to which it is equivalent, is obviously an improvement. When logical expressions are used to design hardware circuits, simpler expressions produce circuits that are cheaper because they have fewer components.

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Checking Satisfiability,You’ve seen how to use sequent calculus to check whether a sequent is universally true or has a counterexample. We’re now going to look into the problem of checking .: whether a logical expression is true for at least one combination of values for the variables, or predicates, that the expression contains.

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Features and Predicates,ional logic is a very simple form of logic where the focus is on ways of building up complex statements from simpler ones using . including conjunction (., or . in Haskell), disjunction (., or .) and negation (., or .).