Existing meta-programming languages operate on encodings of programs as data. This paper presents a new meta-programming language, based on an untyped lambda calculus, in which structurally reflective programming is supported directly, without any encoding. The language features call-by-value and call-by-name lambda abstractions, as well as novel reflective features enabling the intensional man...

This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author’s classic The Lambda Calculus (1984). The formalism has since been extended with types...

Many familiar models of the type-free lambda calculus are constructed by order theoretic methods. This paper provides some basic new facts about ordered models of the lambda calculus. We show that in any partially ordered model that is complete for the theory ofβorβη-conversion, the partial order is trivial on term denotations. Equivalently, the open and closed term algebras of the type-free la...

Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental properties of complex systems. This formal language allows the expression of quantumized algorithms, which are extensions of randomized algorithms in that probabilit...

The equational theories at the core of most functional programming are variations on the standard lambda calculus. The bestknown of these is the call-by-value lambda calculus whose core is the value-beta computation rule (λx.M)V → M [V/x] where V is restricted to be a value rather than an arbitrary term. This paper investigates the transformational power of this core theory of functional progra...

Existing meta-programming languages operate on encodings of programs as data. This paper presents a new meta-programming language, based on an untyped lambda calculus, in which structurally reflective programming is supported directly, without any encoding. The language features call-by-value and call-by-name lambda abstractions, as well as novel reflective features enabling the intensional man...

This article presents an approach in the design of music programming languages based on Lambda Calculus. It shows, through several examples, that a purely descriptive language, that is to say a language without any programming capability, can be equipped with programming capabilities by the addition of a limited number of simple constructs.

A multiobjective variational problem involving higher order derivatives is considered and optimality conditions for this problem are derived. A Mond-Weir type dual to this problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the al...

* Correspondence: lijueyou@163. com Department of Mathematics, Chongqing Normal University, Chongqing, 400047, PR China Abstract The objective of this paper is to obtain a mixed symmetric dual model for a class of non-differentiable multiobjective nonlinear programming problems where each of the objective functions contains a pair of support functions. Weak, strong and converse duality theorems...