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Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in…
Containers capture the concept of strictly positive data types in programming. The original development of containers is done in the internal language of locally cartesian closed categories (LCCCs) with disjoint coproducts and W-types, and…
We use finite group topological lattice gauge theory, also known as the quantum double model, as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order,…
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…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
Reservoir computing is a framework which is primarily used for temporal information processing, using the intrinsic dynamics of an underlying physical system. The framework, in a quantum setup, is implemented using ergodic dynamics…
We propose a new type-theoretic approach to SLD-resolution and Horn-clause logic programming. It views Horn formulas as types, and derivations for a given query as a construction of the inhabitant (a proof-term) for the type given by the…
We combine quantified differential dynamic logic (QdL) for reasoning about the possible behavior of distributed hybrid systems with temporal logic for reasoning about the temporal behavior during their operation. Our logic supports…
Time-dependent response theories are foundational to the development of algorithms that determine quantum properties of electronic excited states of molecules and periodic systems. They are employed in wave-function, density-functional, and…
A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…
Deadlocks occur in concurrent programs as a consequence of cyclic resource acquisition between threads. In this paper we present a novel type system that guarantees deadlock freedom for a language with references, unstructured locking…
Motivated by the recent interest in models of guarded (co-)recursion we study its equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and Esik. Models of these…
Motivated by the recent interest in models of guarded (co-)recursion, we study their equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and \'Esik. Models of…
By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the…
In this paper we propose a robust Model Predictive Control where a Gated Recurrent Unit network model is used to learn the input-output dynamic of the system under control. Robust satisfaction of input and output constraints and recursive…
Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…