9,466 research outputs found
Signature Compilation for the Edinburgh Logical Framework
AbstractThis paper describes the Signature Compiler, which can compile an LF signature to a custom proof checker in either C++ or Java, specialized for that signature. Empirical results are reported showing substantial improvements in proof-checking time over existing LF checkers on benchmarks
A Lambda Term Representation Inspired by Linear Ordered Logic
We introduce a new nameless representation of lambda terms inspired by
ordered logic. At a lambda abstraction, number and relative position of all
occurrences of the bound variable are stored, and application carries the
additional information where to cut the variable context into function and
argument part. This way, complete information about free variable occurrence is
available at each subterm without requiring a traversal, and environments can
be kept exact such that they only assign values to variables that actually
occur in the associated term. Our approach avoids space leaks in interpreters
that build function closures.
In this article, we prove correctness of the new representation and present
an experimental evaluation of its performance in a proof checker for the
Edinburgh Logical Framework.
Keywords: representation of binders, explicit substitutions, ordered
contexts, space leaks, Logical Framework.Comment: In Proceedings LFMTP 2011, arXiv:1110.668
A dependent nominal type theory
Nominal abstract syntax is an approach to representing names and binding
pioneered by Gabbay and Pitts. So far nominal techniques have mostly been
studied using classical logic or model theory, not type theory. Nominal
extensions to simple, dependent and ML-like polymorphic languages have been
studied, but decidability and normalization results have only been established
for simple nominal type theories. We present a LF-style dependent type theory
extended with name-abstraction types, prove soundness and decidability of
beta-eta-equivalence checking, discuss adequacy and canonical forms via an
example, and discuss extensions such as dependently-typed recursion and
induction principles
Amalia -- A Unified Platform for Parsing and Generation
Contemporary linguistic theories (in particular, HPSG) are declarative in
nature: they specify constraints on permissible structures, not how such
structures are to be computed. Grammars designed under such theories are,
therefore, suitable for both parsing and generation. However, practical
implementations of such theories don't usually support bidirectional processing
of grammars. We present a grammar development system that includes a compiler
of grammars (for parsing and generation) to abstract machine instructions, and
an interpreter for the abstract machine language. The generation compiler
inverts input grammars (designed for parsing) to a form more suitable for
generation. The compiled grammars are then executed by the interpreter using
one control strategy, regardless of whether the grammar is the original or the
inverted version. We thus obtain a unified, efficient platform for developing
reversible grammars.Comment: 8 pages postscrip
Maude: specification and programming in rewriting logic
Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude
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