Call-by-Value Is Dual to Call-by-Name – Reloaded

  • Philip Wadler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3467)


We consider the relation of the dual calculus of Wadler(2003) to the λμ-calculus of Parigot (1992). We give translations from the λμ-calculus into the dual calculus and back again. The translations form an equational correspondence as defined by Sabry and Felleisen (1993). In particular, translating from λμ to dual and then ‘reloading’ from dual back into λμ yields a term equal to the original term. Composing the translations with duality on the dual calculus yields an involutive notion of duality on the λμ-calculus. A previous notion of duality on the λμ-calculus has been suggested by Selinger (2001), but it is not involutive.

Note: This paper uses color to clarify the relation of types and terms, and of source and target calculi. If the URL below is not in blue please download the color version from
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Statement Context Reduction Rule Critical Pair Natural Deduction Dual Statement 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Philip Wadler
    • 1
  1. 1.Edinburgh University 

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