17,431 research outputs found
Synthesis of Recursive ADT Transformations from Reusable Templates
Recent work has proposed a promising approach to improving scalability of
program synthesis by allowing the user to supply a syntactic template that
constrains the space of potential programs. Unfortunately, creating templates
often requires nontrivial effort from the user, which impedes the usability of
the synthesizer. We present a solution to this problem in the context of
recursive transformations on algebraic data-types. Our approach relies on
polymorphic synthesis constructs: a small but powerful extension to the
language of syntactic templates, which makes it possible to define a program
space in a concise and highly reusable manner, while at the same time retains
the scalability benefits of conventional templates. This approach enables
end-users to reuse predefined templates from a library for a wide variety of
problems with little effort. The paper also describes a novel optimization that
further improves the performance and scalability of the system. We evaluated
the approach on a set of benchmarks that most notably includes desugaring
functions for lambda calculus, which force the synthesizer to discover Church
encodings for pairs and boolean operations
Type classes for efficient exact real arithmetic in Coq
Floating point operations are fast, but require continuous effort on the part
of the user in order to ensure that the results are correct. This burden can be
shifted away from the user by providing a library of exact analysis in which
the computer handles the error estimates. Previously, we [Krebbers/Spitters
2011] provided a fast implementation of the exact real numbers in the Coq proof
assistant. Our implementation improved on an earlier implementation by O'Connor
by using type classes to describe an abstract specification of the underlying
dense set from which the real numbers are built. In particular, we used dyadic
rationals built from Coq's machine integers to obtain a 100 times speed up of
the basic operations already. This article is a substantially expanded version
of [Krebbers/Spitters 2011] in which the implementation is extended in the
various ways. First, we implement and verify the sine and cosine function.
Secondly, we create an additional implementation of the dense set based on
Coq's fast rational numbers. Thirdly, we extend the hierarchy to capture order
on undecidable structures, while it was limited to decidable structures before.
This hierarchy, based on type classes, allows us to share theory on the
naturals, integers, rationals, dyadics, and reals in a convenient way. Finally,
we obtain another dramatic speed-up by avoiding evaluation of termination
proofs at runtime.Comment: arXiv admin note: text overlap with arXiv:1105.275
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