Related papers: On the Elementary Affine Lambda-Calculus with and …
The starting point of algebraic language theory is that regular languages of finite words are exactly those recognized by finite monoids. This finiteness condition gives rise to a topological space whose points, called profinite words,…
We study increasingly expressive type systems, from $F^\mu$ -- an extension of the polymorphic lambda calculus with equirecursive types -- to $F^{\mu;}_\omega$ -- the higher-order polymorphic lambda calculus with equirecursive types and…
Nominal algebra includes $\alpha$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its…
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and…
We develop a natural variant of Dikin's affine-scaling method, first for semidefinite programming and then for hyperbolic programming in general. We match the best complexity bounds known for interior-point methods. All previous…
Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce an affine bounded linear typing discipline on a general notion of resource which can…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
In this work, we will present variants Fixed Point Theorem for the affine and classical contexts, as a consequence of general Brouwer's Fixed Point Theorem. For instance, the affine results will allow working on affine balls, which are…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
We investigate a class of nominal algebraic Henkin-style models for the simply typed lambda-calculus in which variables map to names in the denotation and lambda-abstraction maps to a (non-functional) name-abstraction operation. The…
Models in the supervised learning framework may capture rich and complex representations over the features that are hard for humans to interpret. Existing methods to explain such models are often specific to architectures and data where the…
We study an assignment system of intersection types for a lambda-calculus with records and a record-merge operator, where types are preserved both under subject reduction and expansion. The calculus is expressive enough to naturally…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An…
We propose a model-based approach to the model checking problem for recursive schemes. Since simply typed lambda calculus with the fixpoint operator, lambda-Y-calculus, is equivalent to schemes, we propose the use of a model of…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…