Commit a2b4a74e authored by Kim Nguyễn's avatar Kim Nguyễn
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Updated the conclusion w.r.t to the practical section.

parent 7514d60a
In this work we presented to core of our analysis of occurrence
typing, extended it to record types and a proposed a couple of novel
applications of the theory, namely the inference of
applications of the theory, namely the inference of
intersection types for functions and a static analysis to reduce the number of
casts inserted when compiling gradually-typed programs.
One of the by products of our work is the ability to define type
predicates such as those used in \cite{THF10} as plain function and
have the inference procedure deduce automatically the correct
overloaded function type.
There is still a lot of work to do to fill the gap with real-word
programming languages. Some of it should be quite routine such as the
encoding of specific language constructions (e.g., \code{isInt},
\code{typeof},...), the handling of more complex
handling of more complex
kinds of checks (e.g., generic Boolean expression, multi-case
type-checks) and even encompass sophisticated type matching as the one
performed by the language CDuce. Some other will require more
performed by the CDuce language. Some other will require more
work. For example, our analysis cannot handle flow of information. In
particular, the result of a type test can flow only to the branches
but not outside the test. As a consequence the current system cannot
......@@ -20,18 +23,20 @@ type a let binding such as
\end{alltt}
which is clearly safe when $y:\Int\vee\Bool$. Nor can this example be solved by partial evaluation since we do not handle nesting of tests in the condition\code{( ((y\(\in\)Int)?`yes:`no)\(\in\)`yes )? y+1 : not(y)},
and both are issues that system by~\citet{THF10} can handle. We think that it is possible
to reuse some of their ideas to perform a information flow analysis on the top of
to reuse some of their ideas to perform a information flow analysis on top of
our system to remove these limitations.
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Information flow analysis would also be useful to improve
inference of intersection types presented in
Section~\ref{sec:refining}: there we said that type cases in the body of a
function are the tipping points that may change the type of the result
of the function; but they are not the only ones, the other being the
applications of overloaded functions. Therefore we plan to
detect the overloaded functions the parameter of an outer function
flows to, so as to use the partition of their domains to perform a
finer grained analysis of the outer function's type.
Some of the exensions we hinted to in Section~\ref{sec:practical}
warrant a formal treatment. In particular, the rule [{\sc OverApp}]
only detects the application of an overloaded function once, when
type-checking the body of the function against the coarse input type
(that is, $\psi$ is computed only once). But we could repeat this
process whilst type-checking the inferred arrows (that is we would
enrich $\psi$ while using it to find the various arrow types of the
lambda abstraction). Clearly, if untamed, such a process may never
reach a fix point. Studying whether this iterative refining can be
made to converge, and foremost whether it is of use in practice is one
of our objectives.
But the real challenges that lie ahead are the handling of side
effects and the addition of polymorphic types. Our analysis works in a
......
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