diff --git a/paper/gtt.tex b/paper/gtt.tex index 8e234e56d2553366ad17023a6f4744bf6b106cf3..6b0e848f18adac58d9232d5076493ea3ca68025d 100644 --- a/paper/gtt.tex +++ b/paper/gtt.tex @@ -1158,7 +1158,7 @@ that can perform effects with the possibility of terminating such computations are delayed values. \begin{longonly} $U \u F$ is a monad on value - types~\citep{moggi}, while $\u F U$ is a comonad on computation types. + types~\citep{moggi91}, while $\u F U$ is a comonad on computation types. \end{longonly} \emph{Computation types} @@ -1987,7 +1987,7 @@ graduality and $\beta,\eta$. Because the GTT term equidynamism relation $\equidyn$ includes the congruence and $\beta\eta$ axioms of the CBPV equational theory, types -inherit the universal properties they have there~\cite{cpbv}. We recall +inherit the universal properties they have there~\cite{levy03cbpvbook}. We recall some relevant definitions and facts. \begin{definition}[Isomorphism] ~ @@ -2006,7 +2006,7 @@ some relevant definitions and facts. \end{definition} Note that a value isomorphism is a strong condition, and an isomorphism in call-by-value between types $A$ and $A'$ corresponds to a computation -isomorphism $\u F A \cong \u F A'$, and dually~\cite{levy16popl}. +isomorphism $\u F A \cong \u F A'$, and dually~\cite{levy17popl}. \smallskip @@ -2060,7 +2060,7 @@ isomorphism $\u F A \cong \u F A'$, and dually~\cite{levy16popl}. %% doesn't seem to be true? \item $\u F 0$ is not \emph{strictly} initial among computation types, though. Proof sketch: a domain model along the lines of - \citep{cbn-gtt} with only non-termination and type errors shows this, + \citep{newlicata2018-fscd} with only non-termination and type errors shows this, because there $\u F 0$ and $\top$ are isomorphic (the same object is both initial and terminal), so if $\u F 0$ were strictly initial (any type $\u B$ with a stack $\bullet : B \vdash S : \u F 0$ is isomorphic @@ -6921,7 +6921,7 @@ the same type. %% translation of each complex value, e.g. %% $\simpp{\caseofXthenYelseZ V {x_1. E_1}{x_2. E_2}} = %% \bindXtoYinZ {\simp V} x \caseofXthenYelseZ x {x_1. \simp {E_1}}{x_2. \simp {E_2}}$. -%% We could replace this translation with one as in \cite{levybook} that +%% We could replace this translation with one as in \cite{levy03cbpvbook} that %% introduces fewer administrative redices, but this translation is simpler %% and suffices for reasoning up to observational equivalence. @@ -6929,7 +6929,7 @@ the same type. The \emph{de-complexification} procedure is defined as follows. % We note that this translation is not the one presented in -\cite{levybook}, but rather a more inefficient version that, in CPS +\cite{levy03cbpvbook}, but rather a more inefficient version that, in CPS terminology, introduces many administrative redices. % Since we are only proving results up to observational equivalence diff --git a/paper/max.bib b/paper/max.bib index aac0b7d5babcc4dcf1b22d6ab3e482a3d0b11789..af0733ec6bd03cbf7a4816fd019cb9bbcb502694 100644 --- a/paper/max.bib +++ b/paper/max.bib @@ -1128,4 +1128,16 @@ pages="396--410", title = {A Spectrum of Type Soundness and Performance}, booktitle = icfp18, year = {2018} -} \ No newline at end of file +} + +@inproceedings{nakano, + title={A modality for recursion}, + author={Nakano, Hiroshi}, + booktitle={Logic in Computer Science, 2000. Proceedings. 15th Annual IEEE Symposium on}, +} +@inproceedings{levy17popl, + author = {Levy, Paul Blain}, + title = {Contextual Isomorphisms}, + booktitle = popl, + year={2017}, +} \ No newline at end of file