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Pré-Publication, Document De Travail Année : 2009

Untyping Typed Algebraic Structures

Résumé

Algebraic structures sometimes need to be typed. For example, matrices over a ring form a ring, but the product is a only a partial operation: dimensions have to agree. Therefore, an easy way to look at matrices algebraically is to consider ``typed rings''. We prove some ``untyping'' theorems: in some algebras (semirings, Kleene algebras, residuated monoids), types can be reconstructed from valid untyped equalities. As a consequence, the corresponding untyped decision procedures can be extended to the typed setting.
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Dates et versions

hal-00421158 , version 1 (30-09-2009)
hal-00421158 , version 2 (18-01-2010)
hal-00421158 , version 3 (07-04-2010)
hal-00421158 , version 4 (14-06-2010)

Identifiants

  • HAL Id : hal-00421158 , version 1

Citer

Damien Pous. Untyping Typed Algebraic Structures. 2009. ⟨hal-00421158v1⟩
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