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arXiv · 2505.08633

D-Hammer: Efficient Equational Reasoning for Labelled Dirac Notation

Yingte Xu·Li Zhou·Gilles Barthe
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Abstract

Labelled Dirac notation is a formalism commonly used by physicists to represent many-body quantum systems and by computer scientists to assert properties of quantum programs. It is supported by a rich equational theory for proving equality between expressions in the language. These proofs are typically carried on pen-and-paper, and can be exceedingly long and error-prone. We introduce D-Hammer, the first tool to support automated equational proof for labelled Dirac notation. The salient features of D-Hammer include: an expressive, higher-order, dependently-typed language for labelled Dirac notation; an efficient normalization algorithm; and an optimized C++ implementation. We evaluate the implementation on representative examples from both plain and labelled Dirac notation. In the case of plain Dirac notation, we show that our implementation significantly outperforms DiracDec.

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Yingte Xu, Li Zhou, Gilles Barthe. 2025-05-13. D-Hammer: Efficient Equational Reasoning for Labelled Dirac Notation. https://arxiv.org/abs/2505.08633

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