Jump-With-Argument

Abstract

In Sect. 5.4.6, we presented a continuation semantics for CBPV+control, together with printing. (We use printing as our leading example of a non- control effect in this discussion, but others would work as well.) We used CBPV as the semantic metalanguage, and we gave not just one model, but a whole family, parametrized by an, A-set $\underline {Ans}$. What we described there was, in effect, a translation

$$\begin{array}{*{20}c}{CBPV + control} \\{ + print} \\\end{array} \to \begin{array}{*{20}c}{CBPV + \underline {Ans} } \\{ + print} \\\end{array}$$

where $\underline {Ans}$ is a free computation type identifier. Any A-set $\underline {Ans}$ induces a denotational semantics for CBPV + $\underline {Ans}$ + print (where we interpret $\underline {Ans}$ by $\underline {Ans}$) and so, via this translation, a denotational semantics for CBPV + control + print. The translation is called the stack-passing style (StkPS) transform, because every computation is regarded as taking its stack as a parameter. (In the CBV setting, it is called the continuation-passing style (CPS) transform because all stacks are continuations.)