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Simple overloading for type theories Peter Aczel

Summary: Simple overloading for type theories
Peter Aczel
Departments of Mathematics and Computer Science
Manchester University
June 23, L994
In this note I describe a simple disciplined scheme for overloading of functions in the
type theories like those implemented in Alf, Coq or Lego. This form of overloading is
intended to be useful in the formalisation of mathematics in these computer systems. To
be specific I will focus on the Lego system.
Direct Overloading
Before describing the disciplined approach that I will caII oaerloading by inheritance I
will start by describing a direct version of overloading that is my understanding of an
idea explained to me by Chet Murthy. Recall that in Lego a context may have a function
definition of the form
flx : Al: s
where / must be an identifier that is new to the context of the definition and cannot be
redefi.ned in the context. The idea for direct ouerloading is to allow a context to have
several oaerload definitions for the same identifi.er /:-
overload flr: Al : 1


Source: Aczel, Peter - Departments of Mathematics & Computer Science, University of Manchester


Collections: Mathematics