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Quantomatic: A proof assistant for diagrammatic reasoning
TLDR
This work briefly outlines the theoretical basis of Quantomatic's rewriting engine, then gives an overview of the core features and architecture and gives a simple example project that computes normal forms for commutative bialgebras. Expand
The ZX calculus is incomplete for quantum mechanics
We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect mayExpand
Quantum Programming with Inductive Datatypes: Causality and Affine Type Theory
TLDR
This paper constructs a sound categorical model for the quantum programming language QPL and provides the first detailed semantic treatment of user-defined inductive datatypes in quantum programming, and shows the denotational interpretation is invariant with respect to big-step reduction. Expand
Commutative Monads for Probabilistic Programming Languages
TLDR
This paper shows how to use these monads to provide a sound and adequate denotational semantics for the Probabilistic FixPoint Calculus (PFPC) – a call-by-value simply-typed lambda calculus with mixed-variance recursive types, term recursion and probabilistic choice. Expand
Mixed linear and non-linear recursive types
TLDR
A type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus) and a new technique for solving recursive domain equations within the category CPO by constructing the solutions over pre-embeddings is described. Expand
LNL-FPC: The Linear/Non-linear Fixpoint Calculus
TLDR
A type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus) and a new technique for solving recursive domain equations within cartesian categories by constructing the solutions over pre-embeddings is described. Expand
Enriching a Linear/Non-linear Lambda Calculus: A Programming Language for String Diagrams
TLDR
This work presents an adequacy result for the diagram-free fragment of the language which corresponds to a modified version of Benton and Wadler's adjoint calculus with recursion, and extends the language with general recursion and proves soundness. Expand
MathML-aware Article Conversion from LaTeX
Publishing in Mathematics and theoretical areas in Computer Science and Physics has been predominantly using TeX/LaTeX as a formatting language in the last two decades. This large corpus ofExpand
Conversion d’articles en LaTeX vers XML avec MathML : une étude comparative@@@MathML-aware article conversion from LaTeX — A comparison study
TLDR
Five LTEX-to-XML transformers in three dimensions are investigated and compared: a) ergonomic factors like documentation, ease of installation, b) coverage, and c) quality of the resulting documents (in particular the MathML parts). Expand
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