Related papers: Functional Pearl: The Distributive $\lambda$-Calcu…
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational…
This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional…
We introduce a type and effect system, for an imperative object calculus, which infers "sharing" possibly introduced by the evaluation of an expression, represented as an equivalence relation among its free variables. This direct…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating…
One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…
We introduce a linear infinitary $\lambda$-calculus, called $\ell\Lambda_{\infty}$, in which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
Wu's positive $\lambda$-calculus is a recent call-by-value $\lambda$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
The aim of this work is to characterize three fundamental normalization proprieties in lambda-calculus trough the Taylor expansion of $ \lambda$-terms. The general proof strategy consists in stating the dependence of ordinary reduction…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the…
We introduce a call-by-name lambda-calculus $\lambda Jn$ with generalized applications which is equipped with distant reduction. This allows to unblock $\beta$-redexes without resorting to the standard permutative conversions of generalized…
We apply recent constructions of free Baxter algebras to the study of the umbral calculus. We give a characterization of the umbral calculus in terms of Baxter algebra. This characterization leads to a natural generalization of the umbral…
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
A very simple closed-form formula for Sheppard's corrections is recovered by means of the classical umbral calculus. By means of this symbolic method, a more general closed-form formula for discrete parent distributions is provided and the…
The apparent difficulty of efficient distribution-free PAC learning has led to a large body of work on distribution-specific learning. Distributional assumptions facilitate the design of efficient algorithms but also limit their reach and…
With the wide spread of deep learning and gradient descent inspired optimization algorithms, differentiable programming has gained traction. Nowadays it has found applications in many different areas as well, such as scientific computing,…