50 citations · 180 across the 26 of their papers we have counts for
17 papers · 1 filter
Proof Identity and Categorical Models of BV
Matteo Acclavio, Lutz Straßburger, Vladimir Zamdzhiev
BV-categories are a recent development that aims to give categorical semantics to proofs in the logic BV. However, due to the absence of a coherence theorem on one side and a well-…
A programming language combining quantum and classical control
Kinnari Dave, Louis Lemonnier, Romain Péchoux +1
The two main notions of control in quantum programming languages are often referred to as "quantum control" and "classical control". With the latter, the control flow is based on c…
IMALL with a Mixed-State Modality: A Logical Approach to Quantum Computation
Kinnari Dave, Alejandro Díaz-Caro, Vladimir Zamdzhiev
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language s…
Operator Spaces, Linear Logic and the Heisenberg-Schrödinger Duality of Quantum Theory
Bert Lindenhovius, Vladimir Zamdzhiev
We show that the category OS of operator spaces, with complete contractions as morphisms, is locally countably presentable and a model of Intuitionistic Linear Logic in the sense o…
Central Submonads and Notions of Computation: Soundness, Completeness and Internal Languages
TItouan Carette, Louis Lemonnier, Vladimir Zamdzhiev
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally…
The Central Valuations Monad
Xiaodong Jia, Michael Mislove, Vladimir Zamdzhiev
We give a commutative valuations monad Z on the category DCPO of dcpo's and Scott-continuous functions. Compared to the commutative valuations monads given in [Jia et al., 2021], o…
Semantics for Variational Quantum Programming
Xiaodong Jia, Andre Kornell, Bert Lindenhovius +2
We consider a programming language that can manipulate both classical and quantum information. Our language is type-safe and designed for variational quantum programming, which is…
Commutative Monads for Probabilistic Programming Languages
Xiaodong Jia, Bert Lindenhovius, Michael Mislove +1
A long-standing open problem in the semantics of programming languages supporting probabilistic choice is to find a commutative monad for probability on the category DCPO. In this…
Computational Adequacy for Substructural Lambda Calculi
Vladimir Zamdzhiev
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many…
Semantics for first-order affine inductive data types via slice categories
Vladimir Zamdzhiev
Affine type systems are substructural type systems where copying of information is restricted, but discarding of information is permissible at all types. Such type systems are well…
Quantum Programming with Inductive Datatypes: Causality and Affine Type Theory
Romain Péchoux, Simon Perdrix, Mathys Rennela +1
Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive dat…
Reflecting Algebraically Compact Functors
Vladimir Zamdzhiev
A compact T-algebra is an initial T-algebra whose inverse is a final T-coalgebra. Functors with this property are said to be algebraically compact. This is a very strong property u…
Enriching a Linear/Non-linear Lambda Calculus: A Programming Language for String Diagrams
Bert Lindenhovius, Michael Mislove, Vladimir Zamdzhiev
Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a c…
Equational reasoning with context-free families of string diagrams
Aleks Kissinger, Vladimir Zamdzhiev
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allo…
Quantomatic: A Proof Assistant for Diagrammatic Reasoning
Aleks Kissinger, Vladimir Zamdzhiev
Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra,…
!-Graphs with Trivial Overlap are Context-Free
Aleks Kissinger, Vladimir Zamdzhiev
String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can b…
The ZX-calculus is incomplete for quantum mechanics
Christian Schröder de Witt, Vladimir Zamdzhiev
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 whi…