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We consider, as a means of making programming languages more flexible and powerful, a parsing algorithm in which the parser may freely modify the grammar while parsing. We are particularly interested in a modification of the canonical LR(1)…
This paper introduces the hybrid quantum language with general recursion $\mathtt{Hyrql}$, driven towards resource-analysis. By design, $\mathtt{Hyrql}$ does not require the specification of an initial set of quantum gates. Hence, it is…
We propose a quantum programming language that generalizes the $\lambda$-calculus. The language is non-linear; duplicated variables denote, not cloning of quantum data, but sharing a qubit's state; that is, producing an entangled pair of…
We show the Standard Model and SuperString Theories can be naturally based on a Quantum Computer foundation. The Standard Model of elementary particles can be viewed as defining a Quantum Computer Grammar and language. A Quantum Computer in…
Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…
Despite significant progress in transformer interpretability, an understanding of the computational mechanisms of large language models (LLMs) remains a fundamental challenge. Many approaches interpret a network's hidden representations but…
We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…
Our aim here is to illustrate how the benefits of structural corecursion can be found in a broader swath of the programming landscape than previously thought. Beginning from a tutorial on structural corecursion in the total, pure functional…
In recent developments, deep learning methodologies applied to Natural Language Processing (NLP) have revealed a paradox: They improve performance but demand considerable data and resources for their training. Alternatively, quantum…
It is now clear that the use of resilient encoding schemes will be required for any quantum computing device to be realised. However, quantum programmers of the future will not wish to be tied up in the particulars of such encoding schemes.…
Applied category theory provides powerful mathematical tools for modelling processes and their composition. Symmetric monoidal categories, which involve series and parallel composition, are particularly well-suited for describing the…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics. A simulator for quantum algorithms must be capable of performing heavy mathematical matrix transforms. The design of the simulator…
Normal forms for logic programs under stable/answer set semantics are introduced. We argue that these forms can simplify the study of program properties, mainly consistency. The first normal form, called the {\em kernel} of the program, is…
Creating quantum algorithms is a difficult task, especially for computer scientist not used to quantum computing. But quantum algorithms often use similar elements. Thus, these elements provide proven solutions to recurring problems, i.e. a…
Quantum natural language processing (QNLP) offers a novel approach to semantic modeling by embedding compositional structure directly into quantum circuits. This paper investigates the application of QNLP models to the task of Natural…
Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for…
We introduce the monoidal closed category qCPO of quantum cpos, whose objects are "quantized" analogs of omega-complete partial orders (cpos). The category qCPO is enriched over the category CPO of cpos, and contains both CPO, and the…
Generic quantum-circuit simulation appears intractable for conventional computers and may be unnecessary because useful quantum circuits exhibit significant structure that can be exploited during simulation. For example, Gottesman and Knill…
Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing…