By Abraham Ginzburg

ISBN-10: 0122850505

ISBN-13: 9780122850509

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2 Motivations and Applications 25 this methodology leads to new and unexpected programs that sometimes surpass the ‘obvious’ implementations in terms of efficiency. A broadly related application of higher-order computation is the technique of normalization by evaluation due to Berger and Schwichtenberg [27]. The idea here is that an interpretation of λ -terms as higher type operators can be used as a way of actually evaluating the λ -terms: roughly speaking, by computing the semantic interpretation of a term M and then converting it back into syntax, we can obtain a normal form for M.

The general concept of a simulation (informally understood) is ubiquitous in computing. For example, an interpreter for a language L written in a language L is in effect a way of simulating L in L ; likewise, a compiler which translates from L to L provides a way of simulating any individual L -program by an L -program. Indeed, any high-level programming language, whether interpreted or compiled, can ultimately be seen as implemented in terms of (hence ‘simulated by’) a low-level machine language.

In particular, the lion’s share of the book (Chapters 5 to 11) will be devoted to simply typed, extensional models—that is, to classes of computable functionals of finite type, typically over a ground type of natural numbers. This is the part of the territory that has been the most comprehensively explored, and here we believe we are in a position to offer a fairly definitive map of the landscape. Other kinds of models, both ‘untyped’ or ‘intensional’, will be surveyed in a much briefer, more fragmentary way in Chapters 3 and 12, in some cases with pointers to more detailed treatments elsewhere.

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Algebraic Theory of Automata by Abraham Ginzburg

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