Ghani, Neil and Hancock, Peter (2016) Containers, monads and induction recursion. Mathematical Structures in Computer Science, 26 (Specia). pp. 89-113.Full text not available in this repository. (Request a copy from the Strathclyde author)
Induction recursion offers the possibility of a clean, simple and yet powerful meta-language for the type system of a dependently typed programming language. At its crux, induction recursion allows us to define a universe, that is a set U of codes and a decoding function T : U → D which assigns to every code u : U, a value T, u of some type D, e.g. the large type Set of small types or sets. The name induction recursion refers to the build-up of codes in U using inductive clauses, simultaneously with the definition of the function T, by structural recursion on codes. Our contribution is to (i) bring out explicitly algebraic structure which is less visible in the original type-theoretic presentation – in particular showing how containers and monads play a pivotal role within induction recursion; and (ii) use these structures to present a clean and high level definition of induction recursion suitable for use in functional programming.
|Keywords:||codes (symbols), computational linguistics, containers, algebraic structures, dependently typed programming, meta language, recursions, structural recursion, type systems, functional programming, Electronic computers. Computer science, Mathematics (miscellaneous), Computer Science Applications|
|Subjects:||Science > Mathematics > Electronic computers. Computer science|
|Department:||Faculty of Science > Computer and Information Sciences|
|Depositing user:||Pure Administrator|
|Date Deposited:||08 Jan 2016 14:32|
|Last modified:||22 Mar 2017 12:06|