diff --git a/thesis.tex b/thesis.tex index b1c873f..251a46b 100644 --- a/thesis.tex +++ b/thesis.tex @@ -948,7 +948,9 @@ computation to syntactically \emph{appear in tail position}. % \begin{itemize} \item The body $M$ of a $\lambda$-abstraction ($\lambda x. M$) appears in - tail position. + tail position. + \item The body $M$ of a $\Lambda$-abstraction $(\Lambda \alpha.M)$ + appears in tail position. \item If $\Case\;V\;\{\ell\,x \mapsto M; y \mapsto N\}$ appears in tail position, then both $M$ and $N$ appear in tail positions. \item If $\Let\;\Record{\ell = x; y} = V \;\In\;N$ appears in tail @@ -2114,7 +2116,17 @@ not consume stack space. \cps{\lambda x.M} &=& \lambda x.\lambda k.\cps{M}\\ \cps{V\,W} &=& \cps{V}\,\cps{W}\,k. \end{equations} -\end{definition} + \end{definition} + +\[ + \ba{@{~}l@{~}l} + \pcps{(\lambda x.(\lambda y.\Return\;y)\,x)\,\Unit} &= (\lambda x.(\lambda y.\lambda k.k\,y)\,x)\,\Unit\,(\lambda x.x)\\ + &\reducesto ((\lambda y.\lambda k.k\,y)\,\Unit)\,(\lambda x.x)\\ + &\reducesto (\lambda k.k\,\Unit)\,(\lambda x.x)\\ + &\reducesto (\lambda x.x)\,\Unit\\ + &\reducesto \Unit + \ea +\] \section{Initial target calculus} \label{sec:target-cps} @@ -3807,8 +3819,7 @@ of the resumption construction primitive. A major aesthetic improvement due to the generalised continuation representation is that continuation construction and deconstruction is -now uniform: only a single continuation frame is inspected at any -time. +now uniform: only a single continuation frame is inspected at a time. \subsubsection{Correctness} \label{sec:cps-gen-cont-correctness}