منابع مشابه
Generic Fibrational Induction
This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, a sound in...
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This paper provides several induction rules that can be used to prove properties of effectful data types. Our results are semantic in nature and build upon Hermida and Jacobs’ fibrational formulation of induction for polynomial data types and its extension to all inductive data types by Ghani, Johann, and Fumex. An effectful data type μ(TF ) is built from a functor F that describes data, and a ...
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This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an inducti...
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We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coin-ductively deened types. Our main results provide suucient criteria for the validity of such principles: in the presence of comprehension, the induction principle for initial algebras is admissible, and dually, in the presence of quotient types, the coinduction principle fo...
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System F supports induction over data types in a manner that is polymorphic with respect to the data held in the structure. Reduction is strongly normalising, so that operations on data always terminate. However, since the induction principles are encoded in the types, it is unable to express a significant class of queries that should work uniformly over all data types, queries such as equality...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2012
ISSN: 1860-5974
DOI: 10.2168/lmcs-8(2:12)2012