We give a canonical program refinement calculus based on the lambda calculus and classical first-order predicate logic, and study its proof theory and semantics. The intention is to construct a metalanguage for refinement in which basic principles of program development can be studied. The idea is that it should be possible to induce a refinement calculus in a generic manner from a programming ...

Lambda lifting transforms local function deenitions in functional programming languages into global ones to facilitate their eecient implementation. When considered as a source-to-source transformation for an ML-style typed language, all published algorithms for lambda lifting break typability. We break down two representative lambda lifting algorithms into four elementary transformation steps,...

Bector et al., (1994) introduced the concept of univexity. Mishra (1998), Mishra and Reuda (2001) and Mishra et al., (2005) have applied and generalized these functions. Mathematical programming in complex spaces originated from Levinson’s discussion of linear problems (Levinson, 1966). Mishra and Reuda (2003) have generalized these upto first orders, second order with symmetric duality. Furthe...

Recent activity in nonlinear H∞ control has sparked renewed interest in the theory of dissipative nonlinear systems. This theory was initiated byWillems (1972) and developed further by Hill & Moylan (1976). Central to this theory are the so-called storage functions. These functions are generalized energy functions defined in terms of dissipation inequalities. The natural infinitesimal versions ...

In this paper, we study Fritz John type optimality for nonlinear multiobjective programming problems under new classes of generalized invex vector functions. Relationships between these classes of vector functions are established by giving several examples. Furthermore, optimality conditions and characterizations of efficient and weakly efficient solutions are obtained under weak pseudoinvexity...

Many problems in science and engineering must solve nonlinear necessary conditions for defining meaningful solutions. For example, a standard problem in optimization involves solving for the roots of nonlinear functions defined by f(x) = 0, where x is the unknown variable. Classically one develops a first-order Taylor series model which provides the necessary condition that must be iteratively ...

The variety (equational class) of lambda abstraction algebras was introduced to algebraize the untyped lambda calculus in the same way Boolean algebras algebraize the classical propositional calculus. The equational theory of lambda abstraction algebras is intended as an alternative to combinatory logic in this regard since it is a rst-order algebraic description of lambda calculus, which allow...