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Separation logic adds two connectives to assertion languages: separating conjunction * (star) and its adjoint, separating implication -* (magic wand). Comparatively, separating implication is less widely used. This paper demonstrates that by using magic wand to express frames that relate mutable local portions of data structures to global portions, we can exploit its power while proofs are still easily understandable. Many useful separation logic theorems about partial data structures can now be proved by simple automated tactics, which were usually proved by induction. This magic-wand-as-frame technique is especially useful when formalizing the proofs by a high order logic. We verify binary search tree insert in Coq as an example to demonstrate this proof technique.
The theory of program modules is of interest to language designers not only for its practical importance to programming, but also because it lies at the nexus of three fundamental concerns in language design: the phase distinction, computational effe
Tensor kernels in machine learning (ML) often correspond to pure mathematical expressions, making term rewriting an attractive strategy for optimization and mapping to specialized hardware accelerators. However, existing ML intermediate representatio
Context. Galaxies in the Universe form chains (filaments) that connect groups and clusters of galaxies. The filamentary network includes nearly half of the galaxies and is visually the most striking feature in cosmological maps. Aims. We study the
A bug or error is a common problem that any software or computer program may encounter. It can occur from badly writing the program, a typing error or bad memory management. However, errors can become a significant issue if the unsafe program is used
An important question for a probabilistic program is whether the probability mass of all its diverging runs is zero, that is that it terminates almost surely. Proving that can be hard, and this paper presents a new method for doing so; it is expresse