A-logic
نویسندگان
چکیده
Mathematics and computer science pervasively use logics formal languages for reasoning in. One of the most common is classical First-Order Logic with equality (FOL) [Bell and Machover, 1977, Gabbay and Günthner, 1986]. For example FOL is routinely used as a foundational tool to express Zermelo-Fraenkel set theory (ZF sets) [Johnstone, 1987, Machover, 1996] and thus as a (language to express) a foundation for classical mathematics. The implication is that first-order logic is a minimal and convenient logical framework for doing, well, triangles and numbers and other mathematical objects. But is it so good for the mathematics of computation, i.e. for computer science? Perhaps not, since it cannot express substitution as an object-level operation on its own terms. The λ-calculus [Barendregt, 1984] can and does, in the sense that we can write (λa.s)t, which β-reduces [Barendregt, 1984]:
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تاریخ انتشار 2005