Abstract
A Fibrational Method of Indexed Coinductive Data Types
Highlights
The coinductive data type [1] analyses the semantic behaviours of data types in program languages and type theory; it is a dual concept of inductive data types with coalgebra as its math support [2, 3]
Inductive and coinductive data types form a complementary solution to improve the abilities of syntax construction and the semantic computation of program languages
Our work focuses on semantics behaviors and coinductive rules of ICDT through fibrations
Summary
The coinductive data type [1] analyses the semantic behaviours of data types in program languages and type theory; it is a dual concept of inductive data types with coalgebra as its math support [2, 3]. Traditional methods of ICDT, including category theory and coalgebra, make type theory models in the local Cartesian closed category, which gives rise to two consequences: one is that indexed coinductive data types and the relation categories which describe their semantics co-exist in the same category together; another is that functor and its lifting are identical. This has some limitations to analyse semantic behaviours and depict coinductive rules. We summarize our conclusions and discuss future researching work
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