Classical Cut - elimination in the π - calculus

نویسندگان

  • Steffen van Bakel
  • Luca Cardelli
  • Maria Grazia Vigliotti
چکیده

We study the π-calculus, enriched with pairing, and define a notion of type assignment that uses the type constructor →. We encode the terms of the calculus X into this variant of π, and show that all reduction and assignable types are preserved. Since X enjoys the CurryHoward isomorphism for Gentzen’s calculus LK, this implies that all proofs in LK have a representation in π, and cut-elimination is simulated by π’s synchronisation of processes. We then enrich the logic with the connector ¬, and show that this also can be represented in π.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Classical Cut - elimination in the π - calculus ( In memory of

We define the calculus LK a variant of the calculus X that enjoys the Curry-Howard correspondence for Gentzen’s calculus lk; the variant consists of allowing arbitrary progress of cut over cut. We study the π-calculus enriched with pairing, for which we define a notion of implicative type assignment. We translate the terms of LK into this variant of π, and show that reduction and assignable typ...

متن کامل

From X to π Representing the Classical Sequent Calculus in π - calculus

We study the π-calculus, where the family of names is enriched with pairing, and define a notion of type assignment that uses the type constructor →. We encode the circuits of the calculus X into this variant of π, and show that reduction and type assignment are preserved. Since X enjoys the Curry-Howard isomorphism for Gentzen’s calculus LK, this implies that all proofs in LK have an encoding ...

متن کامل

Classical Cut - elimination in the π - calculus Steffen

We study the π-calculus, enriched with pairing, and define a notion of type assignment that uses the type constructor →. We encode the terms of the calculus X into this variant of π, and show that all reduction (cut -elimination) and assignable types are preserved. Since X enjoys the Curry-Howard isomorphism for Gentzen’s calculu LK, this implies that all proofs in LK have a representation in π...

متن کامل

Representing the Classical Sequent Calculus in the π-calculus

We study the π-calculus, enriched with pairing and non-blocking input, and define a notion of type assignment that uses the type constructor →. We encode the circuits of the calculus X into this variant of π, and show that all reduction (cut-elimination) and assignable types are preserved. Since X enjoys the Curry-Howard isomorphism for Gentzen’s calculus LK, this implies that all proofs in LK ...

متن کامل

From X to π Representing the Classical Sequent

We study the π-calculus, enriched with pairing and non-blocking input, and define a notion of type assignment that uses the type constructor →. We encode the circuits of the calculus X into this variant of π, and show that all reduction (cut-elimination) and assignable types are preserved. Since X enjoys the Curry-Howard isomorphism for Gentzen’s calculus LK, this implies that all proofs in LK ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010