A formulae-as-types interpretation of Subtractive Logic

Abstract : We present a formulae-as-types interpretation of Subtractive Logic (i.e. bi-intuitionistic logic). This presentation is two-fold: we first define a very natural restriction of the lambda-mu-calculus which is closed under reduction and whose type system is a constructive restriction of the Classical Natural Deduction. Then we extend this deduction system conservatively to Subtractive Logic. From a computational standpoint, the resulting calculus provides a type system for first-class coroutines (a restricted form of first-class continuations).
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https://hal.archives-ouvertes.fr/hal-00094584
Contributor : Tristan Crolard <>
Submitted on : Thursday, September 14, 2006 - 4:47:40 PM
Last modification on : Thursday, January 11, 2018 - 6:19:28 AM

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  • HAL Id : hal-00094584, version 1

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Tristan Crolard. A formulae-as-types interpretation of Subtractive Logic. Journal of Logic and Computation, Oxford University Press (OUP), 2004, 14:4, pp.529-570. ⟨hal-00094584⟩

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