Lambda-Free Logical Frameworks
نویسنده
چکیده
We present the definition of the logical framework TF, the Type Framework. TF is a lambda-free logical framework; that is, it does not include lambda-abstraction or product kinds. We give formal proofs of several results in the metatheory of TF, and show how it can be conservatively embedded in the logical framework LF: its judgements can be seen as the judgements of LF that are in beta-normal, eta-long normal form. We show how several properties, such as adequacy theorems for object theories and the injectivity of constants, can be proven more easily in TF, and then ‘lifted’ to LF.
منابع مشابه
Pal + : a Lambda-free Logical Framework 1 Motivations and Introduction 2.2 Judgement Forms
A lambda-free logical framework takes parameterisation and deenitions as the basic notions to provide schematic mechanisms for speciication of type theories and their use in practice. The framework presented here, PAL + , is a logical framework for speciication and implementation of type theories, such as Martin-LL of's type theory or UTT. As in Martin-LL of's logical framework NPS90], computat...
متن کاملPAL+: a lambda-free logical framework
A lambda-free logical framework takes parameterisation and cut as the basic notions to provide a schematic mechanism for speciication of type theories and a deenitional mechanism for their use in practice. The framework presented here, PAL + , is in the spirit of de Bruijn's PAL for Automath dB80]. PAL + is a logical framework for speciication and implementation of type theories. As in Martin-L...
متن کاملA Framework for Defining Logical Frameworks
In this paper, we introduce a General Logical Framework, called GLF, for defining Logical Frameworks, based on dependent types, in the style of the well known Edinburgh Logical Framework LF. The framework GLF features a generalized form of lambda abstraction where β-reductions fire provided the argument satisfies a logical predicate and may produce an n-ary substitution. The type system keeps t...
متن کاملElimination of Negation in a Logical Framework
We address the issue of endowing a logical framework with a logically justi ed notion of negation. Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae cannot directly express negative information, although negation is a useful speci cation tool. Since negation-as-failure does not t well in a logical framework, especially one endowed with hypothetical an...
متن کاملA Framework for Defining Logical Frameworks ? dedicated to Gordon D . Plotkin , on the occasion of his 60 th birthday
In this paper, we introduce aGeneral Logical Framework, calledGLF, for defining Logical Frameworks, based on dependent types, in the style of the well known Edinburgh Logical Framework LF. The framework GLF features a generalized form of lambda abstraction where β-reductions fire provided the argument satisfies a logical predicate and may produce an n-ary substitution. The type system keeps tra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/0804.1879 شماره
صفحات -
تاریخ انتشار 2008