Related papers: Evaluating Linear Functions to Symmetric Monoidal …
Domain specific languages (DSLs) are increasingly used today. Coping with complex language definitions, evolving them in a structured way, and ensuring their error freeness are the main challenges of DSL design and implementation. The use…
We reflect on programming with complicated effects, recalling an undeservingly forgotten alternative to monadic programming and checking to see how well it can actually work in modern functional languages. We adopt and argue the position of…
In previous work ("From signatures to monads in UniMath"), we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof assistant. In the present work, we…
We study categorical models for the unitless fragment of multiplicative linear logic. We find that the appropriate notion of model is a special kind of promonoidal category. Since the theory of promonoidal categories has not been developed…
Large language models (LLMs) were invented for natural language tasks such as translation, but they have proved that they can perform highly complex functions across domains. Additionally, they have been thought to develop new skills…
When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning,…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
Traditionally, in linearly typed languages, consuming a linear resource is synonymous with its syntactic occurrence in the program. However, under the lens of non-strict evaluation, linearity can be further understood semantically, where a…
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…
Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes,…
As originally proposed, type classes provide overloading and ad-hoc definition, but can still be understood (and implemented) in terms of strictly parametric calculi. This is not true of subsequent extensions of type classes. Functional…
A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
This paper is about a categorical approach to model a very simple Semantically Linear lambda calculus, named Sll-calculus. This is a core calculus underlying the programming language SlPCF. In particular, in this work, we introduce the…
Software frequently converts data from one representation to another and vice versa. Naively specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming…
Semilinear maps are a generalization of linear maps between vector spaces where we allow the scalar action to be twisted by a ring homomorphism such as complex conjugation. In particular, this generalization unifies the concepts of linear…
We present a formalization in Lean 4, within the framework of the mathematical library Mathlib, of the unbiasing process for symmetric monoidal categories. This is realized by extending the data of a symmetric monoidal category to a…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
We present a statically typed embedding of relational programming (specifically a dialect of miniKanren with disequality constraints) in Haskell. Apart from handling types, our dialect extends standard relational combinator repertoire with…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…