This chapter discusses the syntax of higher-order logic. The generic objects and the appropriate fibred structures to capture higher-order logic are also discussed. For higher-order predicate logic, signatures
We describe a novel logic, called HiLog, and show that it provides a more suitable basis for logic programming than does traditional predicate logic. HiLog has a higher-order syntax and allows arbitrary terms to appear in places where predicates, functions, and atomic formulas occur in predicate...
As you might have guessed, all of these functions are higher-order functions. In this section, I will talk more in depth about higher-order functions that return (and sometimes also take) functions and closures. To start, recall my use of repeatedly, which used a function that ignored its...
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We describe two checkers for verifying termination and reduction properties about higher-order logic programs. The reduction checker verifies that the resu
A new class of methods with higher order of convergence for solving systems of nonlinear equations 热度: ACompositionalLogicforPolymorphicHigher-OrderFunctions KoheiHonda DepartmentofComputerScience QueenMary,London kohei@dcs.qmul.ac.uk NobukoYoshida ...
We consider how mode (such as input and output) and termination properties of typed higher-order constraint logic programming languages may be declared and checked effectively. The systems that we present have been validated through an implementation and
first-ordertohigher-orderlogicrequiresamorecomplicatedproofcalculus,but itoftenallowsmuchsimplerproblemstatements.Higher-orderlogic’sbuilt-in supportforfunctionsandsetsoftenleadstoshorterproofs.Conversely,elemen- taryidentities(suchasthedistributivelawforunionandintersection)turninto ...
In Rust, higher-order functions are used extensively for various operations on collections. They provide a way to perform operations like transformation, filtering, and accumulation without the need…
Now consider following implementation of map & filter transformation functions: function map(f, source) { return reducible(function accumulator(next, initial) { return reduce(source, function reducer(result, input) { return next(result, f(input)) }, initial) }) } function filter(predicate, sourc...