diff --git a/paper/gtt.tex b/paper/gtt.tex index fdb8face946cff536613772dc1501282cfa2a1df..e14ed2cfffd23154c7dc28648cc31da41d28de62 100644 --- a/paper/gtt.tex +++ b/paper/gtt.tex @@ -9380,6 +9380,27 @@ language, the $\eta$ principles do hold and so it must be graduality that fails, which corresponds to their failure of meaning preservation. +Henglein's work on dynamic typing also uses an axiomatic semantics of +casts, but axiomatizes behavior of casts at each type directly whereas +we give a uniform definition of all casts and derive implementations +for each type \cite{henglein94:dynamic-typing}. +% +Because of this, the theorems proven in that paper are more closely +related to our model construction in section +\secref{sec:contract-models}. +% +More specifically, many of the lemmas proven in the extended version +of the paper have direct analogues in Henglein's work. +% +We have not included these lemmas in the paper because they are quite +similar to lemmas proven in \citet{newahmed18}, and see there for a +more detailed comparison. +% +Finally, we note that our assumption of compositionality, i.e., that +all casts can be decomposed into an upcast followed by a downcast, is +based on Henglein's analysis, where it was proven to hold in his +coercion calculus. + \iflong \paragraph{Gradual Typing Frameworks} \fi @@ -9400,8 +9421,9 @@ statically typed language, whereas our approach is to ``gradualize'' the axiomatic semantics of the typed language. % This means our approach accomplishes something quite different: their -frameworks produce specific implementations, whereas our approach is -about finding commonalities across different implementations. +frameworks produce specific implementations, whereas GTT (without +$\eta$ principles) axiomatizes the commonalities across different +implementations. % AA: Perhaps the above point should also be made in the intro. Furthermore, while both the AGT and Gradualizer approaches prove various gradual typing correctness theorems by construction (gradual type