A Simple Abstract Semantics for Equational Theories

نویسنده

  • Gilles Barthe
چکیده

We show that a suitable abstraction of the notion of term-algebra, called compositum, can be used to capture in a precise mathematical way the intuition that the category of algebras of most (order-sorted) equational theories is completely characterised by their term-model. We also use the relationship between composita and order-sorted equa-tional theories to show that every order-sorted compositum can be canon-ically embedded into an unsorted one.

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

Equational Theories of Abnormal Termination Based on Kleene Algebra

We study at an abstract level imperative while programs with an explicit fail operation that causes abnormal termination or irreparable failure, and a try-catch operation for error handling. There are two meaningful ways to define the semantics of such programs, depending on whether the final state of the computation can be observed upon failure or not. These two semantics give rise to differen...

متن کامل

Optimization of Equational Logic Programs using Abstract Narrowing

Solving equations in equational theories is a relevant programming paradigm which integrates logic and equational programming into one unified framework. Efficient methods based on narrowing strategies to solve systems of equations have been devised. In this work, we define an abstract narrower for equational theories which can be used to obtain a finite description of the set of solutions. We ...

متن کامل

On Reduction-Based Process Semantics

A formulation of semantic theories for processes which is based on reduction relation and equational reasoning is studied. The new construction can induce meaningful theories for processes, both in strong and weak settings. The resulting theories in many cases coincide with, and sometimes generalise, observation-based formulation of behavioural equivalence. The basic construction of reduction-b...

متن کامل

Using Narrowing Approximations to Optimize Equational Logic Programs

Solving equations in equational theories is a relevant programming paradigm which integrates logic and equational programming into one unified framework. Efficient methods based on narrowing strategies to solve systems of equations have been devised. In this paper, we formulate a narrowing-based equation solving calculus which makes use of a top-down abstract interpretation strategy to control ...

متن کامل

Multiversal Polymorphic Algebraic Theories

We formalise and study the notion of polymorphic algebraic theory, as understood in the mathematical vernacular as a theory presented by equations between polymorphically-typed terms with both type and term variable binding. The prototypical example of a polymorphic algebraic theory is System F, but our framework applies more widely. The extra generality stems from a mathematical analysis that ...

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 1995