Related papers: Evaluating Linear Functions to Symmetric Monoidal …
Semantic role labeling (SRL) aims at elaborating the meaning of a sentence by forming a predicate-argument structure. Recent researches depicted that the effective use of syntax can improve SRL performance. However, syntax is a complicated…
We introduce APPL (Abstract Program Property Logic), a unifying Hoare-style logic that subsumes standard Hoare logic, incorrectness logic, and several variants of Hyper Hoare logic. APPL provides a principled foundation for abstract program…
The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework,…
Bernardy et al. [2018] proposed a linear type system $\lambda^q_\to$ as a core type system of Linear Haskell. In the system, linearity is represented by annotated arrow types $A \to_m B$, where $m$ denotes the multiplicity of the argument.…
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…
Monoidal closed categories naturally model NMILL, non-commutative multiplicative intuitionistic linear logic: the monoidal unit and tensor interpret the multiplicative verum and conjunction; the internal hom interprets linear implication.…
We introduce monoidal streams. Monoidal streams are a generalization of causal stream functions, which can be defined in cartesian monoidal categories, to arbitrary symmetric monoidal categories. In the same way that streams provide…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We introduce context-free languages of morphisms in monoidal categories, extending recent work on the categorification of context-free languages, and regular languages of string diagrams. Context-free languages of string diagrams include…
Instead of a monolithic programming language trying to cover all features of interest, some programming systems are designed by combining together simpler languages that cooperate to cover the same feature space. This can improve usability…
Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural…
String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs,…
We present a new, uniform semantics for Haskell-style overloading. We realize our approach in a new core language, System F$_\mathrm{D}$, whose metatheory we mechanize in the Lean4 interactive theorem prover. System F$_\mathrm{D}$ is…
String diagrams can nicely express numerous computations in symmetric strict monoidal categories (SSMC). To be entirely exact, this is only true for props: the SSMCs whose monoid of objects are free. In this paper, we show a propification…
We propose a graphical language that accommodates two monoidal structures: a multiplicative one for pairing and an additional one for branching. In this colored PROP, whether wires in parallel are linked through the multiplicative structure…
The place and role of parsing analysis in formation of professional informatics competences of future informatics teachers is determined. Separated automation tools for lexical (lex) and syntax (yacc) analysis invariant to the programming…
We introduce monoidal streams: a generalization of causal stream functions to monoidal categories. In the same way that streams provide semantics to dataflow programming with pure functions, monoidal streams provide semantics to dataflow…
While machine learning (ML) architectures have evolved rapidly to account for complex data, loss functions like cross-entropy remain mostly structure-agnostic in many real-world applications. However, the `class-symmetric' nature of these…
Aliasing, or sharing, is prominent in many domains, denoting that two differently-named objects are in fact identical: a change in one object (memory cell, circuit terminal, disk block) is instantly reflected in the other. Languages for…
Conflict detection in policy languages is a solved problem -- as long as every rule condition is a crisp Boolean predicate. BDDs, SMT solvers, and NetKAT all exploit that assumption. But a growing class of routing and access-control systems…