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We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a…
We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…
The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Here, in a series of articles, we show methods for calculating propositional statements using algebraic polynomials as symbols for the connectives, which are named operators. These polynomials originate from the transformation between the…
An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "history-free" strategies. This model is shown to capture definability in PCF. More precisely,…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
Many calculi exist for modelling various features of object-oriented languages. Many of them are based on $\lambda$-calculus and focus either on statically typed class-based languages or dynamic prototype-based languages. We formalize…
Traditional analytical reflectance models, while compact and interpretable, lack the capacity to accurately represent physical measurements. Recent neural models, which closely fit input data, are less generalizable and often more expensive…
The elementary affine lambda-calculus was introduced as a polyvalent setting for implicit computational complexity, allowing for characterizations of polynomial time and hyperexponential time predicates. But these results rely on type…
Configurable systems typically consist of reusable assets that have dependencies between each other. To specify such dependencies, feature models are commonly used. As feature models in practice are often complex, automated reasoning is…
We present a base class of automata that induce a numeration system and we give an algorithm to give the n-th word in the language of the automaton when the expansion of n in the induced numeration system is feeded to the automaton.…
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…
Existing work has analyzed the representational capacity of the transformer architecture by means of formal models of computation. However, the focus so far has been on analyzing the architecture in terms of language \emph{acceptance}. We…
We present the type 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…
This paper introduces a special type of systems, defines their properties, and then demonstrates that a reduction machine for pure untyped extensional lambda calculus can be implemented as a system of the introduced type. Specifically, we…
Dataflow matrix machines are self-referential generalized recurrent neural nets. The self-referential mechanism is provided via a stream of matrices defining the connectivity and weights of the network in question. A natural question is:…
Recursive processing is considered a hallmark of human linguistic abilities. A recent study evaluated recursive processing in recurrent neural language models (RNN-LMs) and showed that such models perform below chance level on embedded…
The paper extends the expectation transformer based analysis of higher-order probabilistic programs to the quantum higher-order setting. The quantum language we are considering can be seen as an extension of PCF, featuring unbounded…
We show how to smoothly incorporate in the object-oriented paradigm constructs to raise, compose, and handle effects in an arbitrary monad. The underlying pure calculus is meant to be a representative of the last generation of OO languages,…