Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and LLvy to internalise substitutions into-calculus and to propose a mechanism for computing on substitutions. is another view of the same concept which aims to explain the process of substitution and to decompose it in small steps. It favours simplicity and preservation of strong normalisation. This way, another important ...

Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and Lvy to internalise substitutions into λ-calculus and to propose a mechanism for computing on substitutions. λυ is another view of the same concept which aims to explain the process of substitution and to decompose it in small steps. It favours simplicity and preservation of strong normalisation. This way, another import...

Recently, Courtois and Pieprzyk proposed an attack on symmetric ciphers that takes advantage of a previously-unexploited property of substitution boxes, or s-boxes, in the round function. This paper gives a brief overview of this “overdefined system of equations” attack and shows how the attack may be avoided through the use of round functions that contain a variety of protection mechanisms, in...

A new oscillator model with different form of the nonminimal substitution within the framework of the DuffinKemmer-Petiau equation is offered. The model possesses exact solutions and a discrete spectrum of high degeneracy. The distinctive property of the proposed model is the lack of the spin-orbit interaction, being typical for other relativistic models with the non-minimal substitution, and t...

In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit control of resources due to the presence of weakening and contraction operators. Along this journey, we propose intersection type assignment systems for all thre...

We present a method of lifting to explicit substitution calculi some characterizations of the strongly normalizing terms of λ-calculus by means of intersection type systems. The method is first illustrated by applying to a composition-free calculus of explicit substitutions, yielding a simpler proof than the previous one by Lengrand et al. Then we present a new intersection type system in the s...

A neutrosophic number (NN) presented by Smarandache can express determinate and/or indeterminate information in real life. NN (z = a + uI) consists of the determinate part a and the indeterminate part uI for a, u ∈ R (R is all real numbers) and indeterminacy I, and is very suitable for representing and handling problems with both determinate and indeterminate information. Based on the concept o...

In this paper, we show the correspondence existing between normalization in calculi with explicit substitution and cut elimination in sequent calculus for Linear Logic, via Proof Nets. This correspondence allows us to prove that a typed version of the λx-calculus [30, 29] is strongly normalizing, as well as of all the calculi isomorphic to it such as λυ [24], λs [19], λd [21], and λf [11]. In o...

In this paper, we show the correspondence existing between normalization in calculi with explicit substitution and cut elimination in sequent calculus for Linear Logic,via Proof Nets. This correspondence allows us to prove that a typed version of the λx-calculus [34, 5] is strongly normalizing, as well as of all the calculi that can be translated to it keeping normalization properties such as λ...