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

@article{Wirth1994ACA, title={A Constructor-Based Approach to Positive/Negative-Conditional Equational Specifications}, author={Claus-Peter Wirth and Bernhard Gramlich}, journal={J. Symb. Comput.}, year={1994}, volume={17}, pages={51-90} }

We study algebraic specifications given by finite sets R of positive/negative-conditional equations (i.e. universally quantified first-order implications with a single equation in the succedent and a conjunction of positive and negative (i.e. negated) equations in the antecedent). The class of models of such a specification R does not contain in general a minimum model in the sense that it can be mapped to any other model by some homomorphism. We present a constructor-based approach for…

## 21 Citations

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…

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.

Theorem Proving in Hierarchical Causal Specifications

- Mathematics, Computer ScienceAdvances in Algorithms, Languages, and Complexity
- 1997

An algebraic specification language that allows for sufficient expessiveness, admits a well-defined se-mantics, and allows for formal proofs is interested, and clausal specifications over built-in algebras over Horn clause specifications are studied.

Conditional Equational Specifications of Data Types with Partial Operations for Inductive Theorem Proving

- Computer ScienceRTA
- 1997

This work develops admissibility conditions that guarantee the unique existence of a distinguished data model and provides an effectively testable confluence criterion which does not presuppose termination.

Syntactic Confluence Criteria for Positive/Negative-Conditional Term Rewriting Systems

- LinguisticsArXiv
- 2009

Criteria for level confluence are presented that are not criteria forshallow confluence actually and the severe requirement of normality is weakened in the criteria for shallow confluence of noetherian and non-noetherian conditional systems to the easily satisfied requirement of quasi-normality.

Basics of Term Rewriting

- Computer ScienceHandbook of Formal Languages
- 1997

Term rewriting can be seen as a generalization of string rewriting as studied early in this century by Axel Thue, and thereby introduced the idea of a universal algebra and the free algebra over sets of equations.

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.

Operational Specifications with Built-Ins

- Computer ScienceSTACS
- 1994

An order-sorted approach is used to suitably assign semantics to equational specifications in a denotational as well as an operational way, which enables the operationalization to generalize some basic results from classical rewrite theory.

On Termination and Confluence of Conditional Rewrite Systems

- Computer ScienceCTRS
- 1994

Any conditional TRS (CTRS) which is an innermost terminating overlay system such that all (conditional) critical pairs are joinable is complete, i.e., terminating and confluent.

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