By John A. N. Lee

Книга The Anatomy of a Compiler The Anatomy of a CompilerКниги English литература Автор: John A. N Lee Год издания: 1974 Формат: djvu Издат.:Van Nostrand Reinhold Co Страниц: 470 Размер: 3,3 Mb ISBN: 0442247338 Язык: Английский0 (голосов: zero) Оценка: John A. N Lee “The Anatomy of a Compiler"

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While the approach to modelling the time domain using a scaled version of N might look extraordinarily simple, this does not mean that all modelling problems disappear. The only point we can hope for is that the formalism chosen does not induce many extra complications, in addition to those present in the application area modelled. Many problems which can appear using classical models of quantitative time will reappear in some guise, for example the problem of classical formalisms that a model might be too unrealistic because it allows an inﬁnite amount of activity in a ﬁnite interval of time.

Let x be a limited real number. Then there is a unique standard real number, which we denote by o x, with x o x. o x is called the standard part or the shadow of x. Many theorems of nonstandard analysis are formulated in terms of the standard part of a limited number. The operation of taking the standard part can be understood as an abstraction operation on limited real numbers: using this abstraction means ignoring inﬁnitesimal distances between limited real numbers. Note that o , as introduced above, is not a function, since its domain and range are not sets.

Tn ) is a term. Its value in the extended state q is q((s, (q(t1 ), . . , q(tn )))). In both cases, s is called the head symbol of the term. – EXISTS term and FORALL term. The expressions (∀x : t) and (∃x : t), where x is a variable and t is a term evaluating to a boolean for all values of x in the context of the expression, represent an inﬁnite conjunction and an inﬁnite disjunction, respectively, with a component for each value of x. An extended state is deﬁned as a function only from locations and variables to values, but as already seen in the deﬁnition of the meaning of s(t1 , .