60,049 research outputs found
Relating Nominal and Higher-order Abstract Syntax Specifications
Nominal abstract syntax and higher-order abstract syntax provide a means for
describing binding structure which is higher-level than traditional techniques.
These approaches have spawned two different communities which have developed
along similar lines but with subtle differences that make them difficult to
relate. The nominal abstract syntax community has devices like names,
freshness, name-abstractions with variable capture, and the new-quantifier,
whereas the higher-order abstract syntax community has devices like
lambda-binders, lambda-conversion, raising, and the nabla-quantifier. This
paper aims to unify these communities and provide a concrete correspondence
between their different devices. In particular, we develop a
semantics-preserving translation from alpha-Prolog, a nominal abstract syntax
based logic programming language, to G-, a higher-order abstract syntax based
logic programming language. We also discuss higher-order judgments, a common
and powerful tool for specifications with higher-order abstract syntax, and we
show how these can be incorporated into G-. This establishes G- as a language
with the power of higher-order abstract syntax, the fine-grained variable
control of nominal specifications, and the desirable properties of higher-order
judgments.Comment: To appear in PPDP 201
Structural abstract interpretation, A formal study using Coq
interpreters are tools to compute approximations for behaviors of a program.
These approximations can then be used for optimisation or for error detection.
In this paper, we show how to describe an abstract interpreter using the
type-theory based theorem prover Coq, using inductive types for syntax and
structural recursive programming for the abstract interpreter's kernel. The
abstract interpreter can then be proved correct with respect to a Hoare logic
for the programming language
Nominal Logic Programming
Nominal logic is an extension of first-order logic which provides a simple
foundation for formalizing and reasoning about abstract syntax modulo
consistent renaming of bound names (that is, alpha-equivalence). This article
investigates logic programming based on nominal logic. We describe some typical
nominal logic programs, and develop the model-theoretic, proof-theoretic, and
operational semantics of such programs. Besides being of interest for ensuring
the correct behavior of implementations, these results provide a rigorous
foundation for techniques for analysis and reasoning about nominal logic
programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as
of July 23, 200
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