Related papers: Genericity Through Stratification
The Church-Turing Thesis confuses numerical computations with symbolic computations. In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is…
We study the complexity of deciding the equality of infinite objects specified by systems of equations, and of infinite objects specified by lambda-terms. For equational specifications there are several natural notions of equality: equality…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
Concept Bottleneck Models (CBMs) provide inherent interpretability by first mapping input samples to high-level semantic concepts, followed by a combination of these concepts for the final classification. However, the annotation of…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…
We present an effective criterion to determine if a normal analytic compactification of C^2 with one irreducible curve at infinity is algebraic or not. As a by product we establish a correspondence between normal algebraic compactifications…
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
The elegant theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are…
The Algebraic lambda-calculus and the Linear-Algebraic lambda-calculus extend the lambda-calculus with the possibility of making arbitrary linear combinations of terms. In this paper we provide a fine-grained, System F-like type system for…
Recently, Miller and Wu introduced the positive $\lambda$-calculus, a call-by-value $\lambda$-calculus with sharing obtained by assigning proof terms to the positively polarized focused proofs for minimal intuitionistic logic. The positive…
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…
With the increasing demands for accountability, interpretability is becoming an essential capability for real-world AI applications. However, most methods utilize post-hoc approaches rather than training the interpretable model. In this…
The intuitionistic fragment of the call-by-name version of Curien and Herbelin's \lambda\_mu\_{\~mu}-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed lambda-calculus. Our embedding is a…
Natural Language Processing is rapidly evolving into a primary instrument for Computational Social Science, with researchers increasingly using embeddings to measure latent constructs such as novelty, creativity, and bias. However, this…
The theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are…
With the maturing of deep learning systems, trustworthiness is becoming increasingly important for model assessment. We understand trustworthiness as the combination of explainability and robustness. Generative classifiers (GCs) are a…
In this work we study randomised reduction strategies,a notion already known in the context of abstract reduction systems, for the $\lambda$-calculus. We develop a simple framework that allows us to prove a randomised strategy to be…
The lambda-calculus with de Bruijn indices assembles each alpha-class of lambda-terms in a unique term, using indices instead of variable names. Intersection types provide finitary type polymorphism and can characterise normalisable…
Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence…