A compositional generalisation of logical relations

نویسنده

  • Gordon Plotkin
چکیده

Binary logical relations do not compose. So we generalise the notion of logical relation to one of lax logical relation, so that binary lax logical relations do compose. We give both a direct generalisation and a corresponding category theoretic formulation. We generalise the Basic Lemma for logical relations to a Basic Lemma for lax logical relations. Finally, we give an axiomatic category theoretic analysis of our deenition.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Generalisation of Pre-logical Predicates to Simply Typed Formal Systems

We generalise the notion of pre-logical predicates [HS02] to arbitrary simply typed formal systems and their categorical models. We establish the basic lemma of pre-logical predicates and composability of binary pre-logical relations in this generalised setting. This generalisation takes place in a categorical framework for typed higher-order abstract syntax and semantics [Fio02,MS03].

متن کامل

A generalisation of pre-logical predicates and its applications

This thesis proposes a generalisation of pre-logical predicates to simply typed formal systems and their categorical models. We analyse the three elements involved in pre-logical predicates — syntax, semantics and predicates — within a categorical framework for typed binding syntax and semantics. We then formulate generalised pre-logical predicates and show two distinguishing properties: a) equ...

متن کامل

Lax Logical Relations

Lax logical relations are a categorical generalisation of logical relations; though they preserve product types, they need not preserve exponential types. But, like logical relations, they are preserved by the meanings of all lambda-calculus terms. We show that lax logical relations coincide with the correspondences of Schoett, the algebraic relations of Mitchell and the pre-logical relations o...

متن کامل

Compositional Compiler Correctness with Quantified Types

We define operational logical relations between terms of a polymorphically typed functional language and low-level programs for a variant SECD machine. The relations, defined using biorthogonality and step-indexing, give extensional and compositional specifications expressing when low-level code and machine values realize typed source-level terms. We prove the correctness of a compiler and of s...

متن کامل

Compositional Safety Logics

In this paper we present a generalisation of a promising composi-tional model–checking technique introduced for finite–state systems by Andersen in [And95] and extended to networks of timed automata by Larsen et al in [LPY95a, LL95, LPY95b, KLL + 97a]. In our generalized setting, programs are modelled as arbitrary (possibly infinite–state) transition systems and verified with respect to propert...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1998