Since Parigot designed the λμ-calculus to algorithmically interpret classical natural deduction, several variants of λμ-calculus have been proposed. Some of these variants derived from an alteration of the original syntax due to de Groote, leading in particular to the Λμ-calculus of the second author, a calculus truly different from λμ-calculus since, in the untyped case, it provides a Böhm sep...

Calculus is the mathematical study of change. Process Calculus models the changing behavior of computer processes. Usually a process refers to a running program. λcalculus is a form of process calculus that has been heavily used in the functional programming arena. While, λ-calculus model changes in sequential computer processes, π-calculus formalizes behavior of a concurrent process. In this p...

In this paper, the scaling-law vector calculus, which is related to connection between calculus and scaling law in fractal geometry, addressed based on Leibniz derivative Stieltjes integral for first time. The Gauss-Ostrogradsky-like theorem, Stokes-like Green-like identities are considered sense of calculus. Navier-Stokes-like equations obtained detail. result as a potentially mathematical too...

a novel and eective method based on haar wavelets and block pulse functions(bpfs) is proposed to solve nonlinear fredholm integro-dierential equations of fractional order.the operational matrix of haar wavelets via bpfs is derived and together with haar waveletoperational matrix of fractional integration are used to transform the mentioned equation to asystem of algebraic equations. our new m...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

Λμ-calculus is an extension of Parigot's λμ-calculus which (i) satis es Separation theorem: it is Böhm-complete, (ii) corresponds to CBN delimited control and (iii) is provided with a stream interpretation. In the present paper, we study solvability and investigate Böhm trees for Λμ-calculus. Moreover, we make clear the connections between Λμcalculus and in nitary λ-calculi. After establishing ...

We present a calculus, called the scheme-calculus, that permits to express natural deduction proofs in various theories. Unlike λ-calculus, the syntax of this calculus sticks closely to the syntax of proofs, in particular, no names are introduced for hypotheses. We show that despite its nondeterminism, this scheme-calculus has the same expressivity as the corresponding typed λ-calculus.