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A Partial Type Checking Algorithm for Type : Type
 

Summary: MSFP 2008
A Partial Type Checking Algorithm for
Type : Type
Andreas Abel1,3
Institut f¨ur Informatik, Ludwigs-Maximilians-Universit¨at M¨unchen
Oettingenstr. 67, D-80538 M¨unchen
Thorsten Altenkirch1,2,4
School of Computer Science, The University of Nottingham
Nottingham, NG8 1BB, UK
Abstract
We analyze a partial type checking algorithm for the inconsistent domain-free 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 [Coq96].
This is an instance of a domain-free pure type system [BC06] and it seems possible
to extend it to any functional pure type system (PTS). The motivation for this

  

Source: Altenkirch, Thorsten - School of Computer Science, University of Nottingham

 

Collections: Computer Technologies and Information Sciences