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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
Grupo de Teoria da Computa¸c~ao, Departamento de Matem´atica, Universidade de Bras´ilia, Bras´ilia D.F., Brasil
School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, Scotland
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