Thunks and the λ-calculus

  • Authors:
  • John Hatcliff;Olivier Danvy

  • Affiliations:
  • Computer Science Department, Copenhagen University/ Universitetsparken 1, DK-2100 Copenhagen Ø/, Denmark. e-mail: hatcliff@diku.dk;Computer Science Department, Aarhus University, Ny Munkegade, Building 540, DK-8000 Aarhus C, Denmark/ e-mail: danvy@brics.dk

  • Venue:
  • Journal of Functional Programming
  • Year:
  • 1997

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Abstract

Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations by factorizing the continuation-based call-by-name simulation 𝒞n with a thunk-based call-by-name simulation 𝒯 followed by the continuation-based call-by-value simulation 𝒞v, extended to thunks.formula hereWe show that 𝒯 actually satisfies all of Plotkin's correctness criteria for 𝒞n (i.e. his Indifference, Simulation and Translation theorems). Furthermore, most of the correctness theorems for 𝒞n can now be seen as simple corollaries of the corresponding theorems for 𝒞v and 𝒯.