We introduce Analytic Program Repair, a data-driven
strategy for providing feedback for type-errors via
repairs for the erroneous program.
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Our strategy is based on
insight that similar errors have similar repairs.
Thus, we show how to use a training dataset of
pairs of ill-typed programs and their fixed versions to:
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(1)~\emph{learn} a collection of candidate repair templates
by abstracting and partitioning the edits made in the
training set into a representative set of templates;
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(2)~\emph{predict} the appropriate template from a given error,
by training multi-class classifiers on the repair templates
used in the training set;
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(3)~\emph{synthesize} a concrete repair from the template
by enumerating and ranking correct (e.g. well-typed)
terms matching the predicted template.
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We have implemented our approach in \textsc{Rite}: a type error reporting
tool for OCaml programs. We present an evaluation of the
\emph{accuracy} and \emph{efficiency} of \textsc{Rite} on a corpus
of 4,500 ill-typed Ocaml programs drawn from two instances of an
introductory programming course, and a user-study of the \emph{quality}
of the generated error messages that shows the locations and
final repair quality to be better than the state-of-the-art tool
in a statistically-significant manner.