Abstract
Using the well-known categorical notion of ‘functor’, one may define the concept of datatype (algebra) without being forced to introduce a signature (that is, names and typings for the individual sorts (types) and operations involved). This has proved to be advantageous for those theory developments where one is not interested in the syntactic appearance of an algebra.The categorical notion of ‘transformer’ developed in this paper allows the same approach to laws: without using signatures one can define the concept of law for datatypes (lawful algebras), and investigate the equational specification of datatypes in a syntax-free manner. A transformer is a special kind of functor and also a natural transformation on the level of dialgebras. Transformers are quite expressive, satisfy several closure properties, and are related to naturality and Wadler'' Theorems For Free Theorem. In fact, any colimit is an initial lawful algebra.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.