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Linear dependent types: Complexity of PCF terms evaluation

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Joint Lab-Lunch and Theory Seminar

Linear dependent types bring together the ideas of Bounded Linear Logic with the simulation of the lambda calculus in a linear setting, in order to capture the type complexity of functional programs. Ugo Dal Lago and Marco Gaboardi proposed (in LICS ’11) such a type system for PCF terms, that guarantees the correctness of the extensional behaviour of programs but also provides a precise complexity bound for their call-by-name evaluation. In this talk, we will see how this type system is related to the call-by-name translation of the simply typed lambda-calculus into linear logic (that is well known since the mid 90’s). We will then look at the corresponding call-by-value translation, and see how we can define a type system capturing the complexity of the call-by-value evaluation of PCF terms.

This talk is part of the Lab Lunch series.

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