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].