Thunks and the lambda-Calculus

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 [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 hereWe 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 ].