Related papers: On Equivalences, Metrics, and Polynomial Time (Lon…
A conversation with a large language model (LLM) is a sequence of prompts and responses, with each response generated from the preceding conversation. AI agents build such conversations automatically: given an initial human prompt, a…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with…
We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one…
Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of…
The predictions of Large Language Models (LLMs) on downstream tasks often improve significantly when including examples of the input--label relationship in the context. However, there is currently no consensus about how this in-context…
We investigate program equivalence for linear higher-order(sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear…
We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…
Contextuality is central to both the foundations of quantum theory and to the novel information processing tasks. Although it was recognized before Bell's nonlocality, despite some recent proposals, it still faces a fundamental problem: how…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
We study the equational theory of Parigot's second-order λμ-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order λ-calculus. It is observed that the…
The Functional Machine Calculus (FMC) was recently introduced as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The…
We present a comprehensive study of the behavioral theory of an untyped $\lambda$-calculus extended with the delimited-control operators shift and reset. To that end, we define a contextual equivalence for this calculus, that we then aim to…
The $\lambda\mu$-calculus plays a central role in the theory of programming languages as it extends the Curry-Howard correspondence to classical logic. A major drawback is that it does not satisfy B\"ohm's Theorem and it lacks the…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
We define a new cost model for the call-by-value lambda-calculus satisfying the invariance thesis. That is, under the proposed cost model, Turing machines and the call-by-value lambda-calculus can simulate each other within a polynomial…
Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience.…