Taha and Nielsen have developed a multi-stage calculus λ with a sound type system using the notion of environment classifiers. They are special identifiers, with which code fragments and variable declarations are annotated, and their scoping mechanism is used to ensure statically that certain code fragments are closed and safely runnable. In this paper, we investigate the Curry-Howard isomorphi...

CORDIC or CO-ordinate Rotation DIgital Computer is a fast, simple, efficient and powerful algorithm used for diverse Digital Signal Processing applications. Primarily developed for real-time airborne computations, it uses a unique computing technique [7] which is especially suitable for solving the trigonometric relationships involved in plane co-ordinate rotation and conversion from rectangula...

In this article, a speed control of DC motor is designed and illustrated using fuzzy logic-based programmable logic controller (PLC). The DC motor is an attractive part of electrical equipment in many industrial applications requiring variable speed and load specifications due to its ease of controllability. The designed system is consisted of three main parts including programmable logic contr...

Using Soft Linear Logic (SLL) as case study, we analyze a method for transforming a light logic into a type assignment system for the λ-calculus, inheriting the complexity properties of the logics. Namely the typing assures the strong normalization in a number of steps polynomial in the size of the term, and moreover all polynomial functions can be computed by λ-terms that can be typed in the s...

The λ-calculus is destructive: its main computational mechanism – beta reduction – destroys the redex and makes it thus impossible to replay the computational steps. Combinatory logic is a variant of the λ-calculus which maintains irreversibility. Recently, reversible computational models have been studied mainly in the context of quantum computation, as (without measurements) quantum physics i...

Lambda tree syntax (a variant of HOAS) and nominal techniques are two approaches to representing and reasoning about languages containing bindings. Although they are based on separate foundations, recent advances in the proof theory of generic judgments have shown that one may be able to incorporate some aspects of nominal techniques (i.e., the equivariant principle) to simplify reasoning about...

We study an output-based translation of the λ-calculus with explicit substitution into the synchronous π-calculus – enriched with pairing – that has its origin in mathematical logic, and show that this translation respects reduction. We will define the notion of (explicit) head reduction -which encompasses (explicit) lazy reductionand show that the translation fully represents this reduction in...