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University of Strathclyde

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Representative Papers

A Rig of Transformations

Aug 11, 2026

This work addresses the gap between high-level abstractions and efficient or compatible binary layouts in functional languages, where users lack precise control over the low-level representation of data types. It formalizes layout transformations of finite algebraic data types as isomorphisms in a commutative rig (a ring without additive inverses), leveraging rig equations to characterize data layouts and their conversions. The approach introduces partial isomorphisms to accommodate type embeddings such as bit padding. Grounded in the categorical theory of rig algebras and isomorphisms, this framework uniformly handles both total and partial representation mappings, ensuring correctness and composability of layout transformations within the type system. Consequently, it provides an expressive, verifiable, and efficient mechanism for controlling low-level data representations.

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Latest Papers

A Rig of Transformations

Aug 11, 2026

This work addresses the gap between high-level abstractions and efficient or compatible binary layouts in functional languages, where users lack precise control over the low-level representation of data types. It formalizes layout transformations of finite algebraic data types as isomorphisms in a commutative rig (a ring without additive inverses), leveraging rig equations to characterize data layouts and their conversions. The approach introduces partial isomorphisms to accommodate type embeddings such as bit padding. Grounded in the categorical theory of rig algebras and isomorphisms, this framework uniformly handles both total and partial representation mappings, ensuring correctness and composability of layout transformations within the type system. Consequently, it provides an expressive, verifiable, and efficient mechanism for controlling low-level data representations.

0 citationsRead paper