∂ for Data: Differentiating Data Structures (2008)
Michael Abbott, Neil Ghani, Thorsten Altenkirch, Conor Mcbride
This paper and our conference paper (Abbott, Altenkirch, Ghani, and McBride, 2003b) explain and analyse the notion of the derivative of a data structure as the type of its one-hole contexts based on...
Abstract. Modular rewriting seeks criteria under which rewrite systems inherit properties from their smaller subsystems. This divide and conquer methodology is particularly useful for reasoning about...
Constructing polymorphic programs with quotient types (2004)
Michael Abbott, Thorsten Altenkirch, Neil Ghani, Conor Mcbride
Abstract. The efficient representation and manipulation of data is one of the fundamental tasks in the construction of large software systems. Parametric polymorphism has been one of the most...
Representing nested inductive types using W-types (2004)
Michael Abbott, Thorsten Altenkirch, Neil Ghani
Abstract. We show that strictly positive inductive types, constructed from polynomial functors, constant exponentiation and arbitrarily nested inductive types exist in any Martin-Löf category...
Derivatives of containers (2003)
Michael Abbott, Thorsten Altenkirch, Neil Ghani, Conor Mcbride
Abstract. We are investigating McBride’s idea that the type of one-hole contexts are the formal derivative of a functor from a categorical perspective. Exploiting our recent work on containers we...
Categories of Containers (2003)
Michael Abbott, Thorsten Altenkirch, Neil Ghani
Abstract. We introduce the notion of containers as a mathematical formalisation of the idea that many important datatypes consist of templates where data is stored. We show that containers have good...
Categories of Containers (2003)
Michael Abbott, Thorsten Altenkirch, Neil Ghani
Abstract. We introduce the notion of containers as a mathematical formalisation of the idea that many important datatypes consist of templates where data is stored. We show that containers have good...
Derivatives of containers (2003)
Michael Abbott, Thorsten Altenkirch, Neil Ghani, Conor Mcbride
Abstract. We are investigating McBride’s idea that the type of one-hole contexts are the formal derivative of a functor from a categorical perspective. Exploiting our recent work on containers we...
Derivatives of Containers (2002)
Michael Abbott, Thorsten Altenkirch, Neil Ghani, Conor Mcbride
Abstract. We are investigating McBride's idea that the type of onehole contexts are the formal derivative of a functor from a categorical perspective. Exploiting our recent work on containers we...
James Joyce : artist and idealist / (1975)
Thesis (M.A.)--University of Texas at El Paso.
Abbott, Michael, Beach, Charles M.
This paper provides preliminary results from the IMDB panel database on the earnings distribution and earnings mobility of Canadian immigrants over their first post-landing decade in Canada. In this...