A Functional Programming Language with Patterns and Copatterns

Abstract

Since the emergence of coinductive data types in functional programming languages, various languages such as Haskell and Coq tried different ways in dealing with them. Yet, none of them dealt with coinductive data types properly. In lazy languages such as Haskell, both inductive data types and coinductive data types are gathered and mixed in one list. Moreover, some languages such as Coq used the same constructors that are used for inductive data types as a tool to tackle coinductive data types, and while other languages such as Haskell did use destructors, they did not use them properly. Coinductive data types behave differently than inductive data types and therefore, it is more appropriate to deal with them differently. In this thesis, we propose a new functional programming language where coinductive data types are dealt with in a dual approach in which coinductive data types are defined by observation and inductive data types are defined by constructors. This approach is more appropriate in dealing with coinductive data types whose importance comes from their role in creating a safer and more sophisticated software.