Mechanizing the Traditional Approach to Partial Functions
نویسنده
چکیده
In traditional mathematics it is legitimate to apply a (partial) function to an argument outside of its domain, but the resulting term is treated as having no value. Moreover, the informal logic of traditional mathematics is two-valued despite the presence of nondenoting terms. This paper shows how this traditional approach to partial functions can be implemented in mechanized mathematics systems.
منابع مشابه
A new approach to using the cubic B-spline functions to solve the Black-Scholes equation
Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...
متن کاملPartial second-order subdifferentials of -prox-regular functions
Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2 functions. The class of prox-regular functions covers all convex functions, lower C2 functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...
متن کاملTotal and Partial efficiency indexes in data envelopment analysis
Introduction: Data envelopment analysis (DEA) is a data-oriented method for measuring and benchmarking the relative efficiency of peer decision making units (DMUs) with multiple inputs and multiple outputs. DEA was initiated in 1978 when Charnes, Cooper and Rhodes (CCR) demonstrated how to change a fractional linear measure of efficiency into a linear programming format. This non-parametric app...
متن کاملAN OPTIMUM APPROACH TOWARDS SEISMIC FRAGILITY FUNCTION OF STRUCTURES THROUGH METAHEURISTIC HARMONY SEARCH ALGORITHM
Vulnerability assessment of structures encounter many uncertainties like seismic excitations intensity and response of structures. The most common approach adopted to deal with these uncertainties is vulnerability assessment through fragility functions. Fragility functions exhibit the probability of exceeding a state namely performance-level as a function of seismic intensity. A common approach...
متن کاملSkeletons and the Shapes of Bundles
Skeletons model partial information about regular (honest) behavior in an execution of a cryptographic protocol. A homomorphism between skeletons is an information-preserving map. Much protocol analysis may be regarded as an exploration of the properties of the category of skeletons and homomorphisms. In particular, the strand space authentication tests are special homomorphisms. These ideas su...
متن کامل