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Principal Typings for Explicit Substitutions Calculi Daniel Lima Ventura , Mauricio Ayala-Rincon , and Fairouz Kamareddine2
 

Summary: Principal Typings for Explicit Substitutions Calculi
Daniel Lima Ventura , Mauricio Ayala-Rinc´on , and Fairouz Kamareddine2
1
Grupo de Teoria da Computa¸c~ao, Departamento de Matem´atica, Universidade de Bras´ilia, Bras´ilia D.F., Brasil
{ayala,ventura}@mat.unb.br
2
School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, Scotland
fairouz@macs.hw.ac.uk
Abstract. Having principal typings (for short PT) is an important property of type systems. This
property guarantees the possibility of type deduction which means it is possible to develop a complete
and terminating type inference mechanism. It is well-known that the simply typed -calculus has this
property, but recently, J. Wells has introduced a system-independent definition of PT which allows to
prove that some type systems do not satisfy PT. The main computational drawback of the -calculus
is the implicitness of the notion of substitution, a problem which in the last years gave rise to a number
of extensions of the -calculus where the operation of substitution is treated explicitly. Unfortunately,
some of these extensions do not necessarily preserve basic properties of the simply typed -calculus
such as preservation of strong normalization. We consider two systems of explicit substitutions ( and
se) and we show that they can be accommodated with an adequate notion of PT. Specifically, our
results can be summarized as follows:
· We introduce PT notions for the simply typed versions of the and the se-calculus according to

  

Source: Ayala-Rincón, Mauricio - Departamento de Matemática, Universidade de Brasília

 

Collections: Mathematics