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Thunks and the λ-calculus

Published online by Cambridge University Press:  01 May 1997

JOHN HATCLIFF
Affiliation:
Computer Science Department, Copenhagen University; Universitetsparken 1, DK-2100 Copenhagen Ø, Denmark. e-mail: hatcliff@diku.dk
OLIVIER DANVY
Affiliation:
Computer Science Department, Aarhus University, Ny Munkegade, Building 540, DK-8000 Aarhus C, Denmark; e-mail: danvy@brics.dk
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Abstract

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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 [Cscr ]n with a thunk-based call-by-name simulation [Tscr ] followed by the continuation-based call-by-value simulation [Cscr ]v, extended to thunks.

formula here

We show that [Tscr ] actually satisfies all of Plotkin's correctness criteria for [Cscr ]n (i.e. his Indifference, Simulation and Translation theorems). Furthermore, most of the correctness theorems for [Cscr ]n can now be seen as simple corollaries of the corresponding theorems for [Cscr ]v and [Tscr ].

Type
Research Article
Copyright
© 1997 Cambridge University Press
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