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

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Summary

INTRODUCTION

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

RELATED WORKS
Single-Sorted Indexed Fibration and its Equation Functor
Quotient Functor and its Lifting
Semantic Behaviours of Single-Sorted ICDT
Coinductive Rule of Single-Sorted ICDT
Instance Analysis of Single-Sorted ICDT
SEMANTIC BEHAVIORS AND COINDUCTIVE RULE OF MANY-SORTED ICDT
Fibered Fibration
Semantic Behaviours of Many-Sorted ICDT
Coinductive Rule of Many-Sorted ICDT
Instance Analysis of Many-Sorted ICDT
CONCLUSIONS
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