Related papers: Extensional Models of Untyped Lambda-mu Calculus
We study the semantics of an untyped lambda-calculus equipped with operators representing read and write operations from and to a global store. We adopt the monadic approach to model side-effects and treat read and write as algebraic…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
One takes advantage of some basic properties of every homotopic $\lambda$-model (e.g.\ extensional Kan complex) to explore the higher $\beta\eta$-conversions, which would correspond to proofs of equality between terms of a theory of…
We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…
Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic…
Modern applications of algebraic topology to point cloud data analysis have motivated active investigation of combinatorial clique complexes -- high-dimensional extensions of combinatorial graphs. We show that meaningful invariants of such…
This paper is a concise and painless introduction to the $\lambda$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular…
We propose a simple calculus for processing data streams (infinite flows of data series), represented by finite sets of equations built on stream operators. Furthermore, functions defining streams are regularly corecursive, that is, cyclic…
An extended formulation of a polytope is a linear description of this polytope using extra variables besides the variables in which the polytope is defined. The interest of extended formulations is due to the fact that many interesting…
In this paper we use finite vector spaces (finite dimension, over finite fields) as a non-standard computational model of linear logic. We first define a simple, finite PCF-like lambda-calculus with booleans, and then we discuss two finite…
The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a…
We give a characterization, with respect to a large class of models of untyped lambda-calculus, of those models that are fully abstract for head-normalization, i.e., whose equational theory is H* (observations for head normalization). An…
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…
Programs that transform other programs often require access to the internal structure of the program to be transformed. This is at odds with the usual extensional view of functional programming, as embodied by the lambda calculus and SK…
The Wess-Zumino-Witten model defined on the group SU(2) has a unique (non-trivial) simple current of conformal dimension k/4 for each level k. The extended algebra defined by this simple current is carefully constructed in terms of…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
We characterize type isomorphisms in the multiplicative-additive fragment of linear logic (MALL), and thus in *-autonomous categories with finite products, extending a result for the multiplicative fragment by Balat and Di Cosmo. This…
We present the system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric…
Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms…