Related papers: Typed lambda-calculi and superclasses of regular f…
This paper provides an alternate characterization of type-two polynomial-time computability, with the goal of making second-order complexity theory more approachable. We rely on the usual oracle machines to model programs with subroutine…
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…
Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…
In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
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…
A number of domain specific languages, such as circuits or data-science workflows, are best expressed as diagrams of boxes connected by wires. Unfortunately, functional languages have traditionally been ill-equipped to embed this sort of…
Lambda calculi with algebraic data types lie at the core of functional programming languages and proof assistants, but conceal at least two fundamental theoretical problems already in the presence of the simplest non-trivial data type, the…
We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some…
We present a marriage of functional and structured imperative programming that embeds in pure lambda calculus. We describe how we implement the core of this language in a monadic DSL which is structurally equivalent to our intended source…
We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…
The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and…
Results in interpretability suggest that large vision and language models learn implicit linear encodings when models are biased by in-context prompting. However, the existence of similar linear representations in more general adaptation…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
In view of training increasingly complex learning architectures, we establish a nonsmooth implicit function theorem with an operational calculus. Our result applies to most practical problems (i.e., definable problems) provided that a…
In this paper we develop a formalism for working with twisted realizations of vertex and conformal algebras. As an example, we study realizations of conformal algebras by twisted formal power series. The main application of our technique is…
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…
The so-called light logics have been introduced as logical systems enjoying quite remarkable normalization properties. Designing a type assignment system for pure lambda calculus from these logics, however, is problematic. In this paper we…
To formalize calculations in linear algebra for the development of efficient algorithms and a framework suitable for functional programming languages and faster parallelized computations, we adopt an approach that treats elements of linear…