# A Constructor-Based Approach for Positive/Negative-Conditional Equational Specifications

@inproceedings{Wirth1992ACA, title={A Constructor-Based Approach for Positive/Negative-Conditional Equational Specifications}, author={Claus-Peter Wirth and Bernhard Gramlich}, booktitle={CTRS}, year={1992} }

We present a constructor-based approach for assigning appropriate semantics to algebraic specifications given by finite sets of positive/negative-conditional equations. Under the assumption of confluence of the reduction relation we define, the factor algebra of the ground term algebra modulo the congruence of this reduction relation is a minimal model which is (beyond that) the minimum of all models that do not identify more constructor ground terms than necessary.

## 29 Citations

A Constructor-Based Approach to Positive/Negative-Conditional Equational Specifications

- Computer Science, MathematicsJ. Symb. Comput.
- 1994

This work presents a constructor-based approach for assigning appropriate semantics to algebraic specifications given by finite sets R of positive/negative-conditional equations with universally quantified first-order implications with a single equation in the succedent and a conjunction of positive and negative equations.

Constructor-Based Inductive Validity in Positive/Negative-Conditional Equational Specifications

- Mathematics
- 1993

We study algebraic speciications given by nite sets R of positive/negative-conditional equations (i. e. universally quantiied rst-order implications with a single equation in the succedent and a…

Semantics for Positive/Negative Conditional Rewrite Systems

- Computer ScienceCTRS
- 1992

Two approaches to define the semantics for positive/negative conditional rewrite systems are presented and a well-founded ordering and a set of predefined inequations leads to an initial model semantics provided the inequations are interpreted in a non-standard way.

A Constructor-Based Approach toPositive / Negative-ConditionalEquational

- Computer Science, Mathematics
- 1994

Several kinds of compatibility of R with a reduction ordering for achieving decidability of reducibility, and several criteria for the connuence of the reduction relation are presented.

A Framework for Operational Equational Specifications with Pre-defined Structures

- Computer ScienceJ. Symb. Comput.
- 1999

A general framework for studying equational specifications with pre-defined structures is presented and a semantically enriched notion of term rewriting is introduced in order to enable functional-style computations.

Writing Positive/Negative-Conditional Equations Conveniently

- Computer ScienceArXiv
- 2009

Based on the presented macroADruleADconstruct, positive/negativeAD Conditional equational specifiADcations can be written on a higher level because a rewrite system translates the macroAD ruleADconstructsinto positive/ negativeADconditional equations.

On Notions of Inductive Validity for First-Oder Equational Clauses

- MathematicsCADE
- 1994

We define and discuss various conceivable notions of inductive validity for first-order equational clauses. This is done within the framework of constructor-based positive/negative conditional…

Partial Functions in Clausal Speci cations ?

- Computer Science, Mathematics
- 1996

This paper deene three types of semantics for such a hierarchical speciication: model-theoretic, operational, and rewrite-based semantics, and shows that all these semantics coincide, provided some restrictions are met.

Inductive theorem proving in theories specified by positive/negative-conditional equations

- Computer Science
- 1999

The proposed inference system provides explicit induction hypotheses and can be instantiated with various wellfounded induction orderings and is well-suited for inductive theorem proving in the presence of partially defined functions.

Consistency of Recursive Definitions via Shallow Confluence of Non-Orthogonal Non-Terminating Conditional Term Rewriting Systems with any kind of Extra Variables

- Mathematics
- 2005

Recursive definitions can be adequately and conveniently modeled with left-linear conditional term rewriting systems, provided that non-termination, non-trivial critical pairs, and extra variables…

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