Summary: MSFP 2008
A Partial Type Checking Algorithm for
Type : Type
Andreas Abel 1 ,3
Institut f˜ur Informatik, Ludwigs­Maximilians­Universit˜at M˜unchen
Oettingenstr. 67, D­80538 M˜unchen
Thorsten Altenkirch 1 ,2 ,4
School of Computer Science, The University of Nottingham
Nottingham, NG8 1BB, UK
Abstract
We analyze a partial type checking algorithm for the inconsistent domain­free pure type system Type:Type
(##). We show that the algorithm is sound and partially complete using a coinductive specification of
algorithmic equality. This entails that the algorithm will only diverge due to the presence of diverging
computations, in particular it will terminate for all typeable terms.
Keywords: Dependent Types, Pure Type Systems, Type Checking, Type:Type
1 Introduction
In this paper, we analyze and implement a partial type checking algorithm for the
inconsistent theory Type:Type (##) similar to the one presented in [6]. This is an
instance of a domain­free pure type system [4] and it seems possible to extend it to
any functional pure type system (PTS). The motivation for this work is to implement

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München

Collections: Computer Technologies and Information Sciences