This paper describes 20BJ, a tactic-based generic theorem prover that encodes object logics into equational logic via an abstract data type of object logic sentences and proofs. 20BJ is built upon OBJ3, a term rewriting implementation of (order sorted conditional) equational logic. Because object logic proofs are explicitly represented, 20BJ can not only reason with them, but also about them, a...

A hierarchy of institutions ranging form equational logic to partial conditional existence-equational logic with relations is built. The diierent levels of the hierarchy can be separated by properties of pa-rameterized abstract data types. A sample parameterized abstract data type, bounded stacks, is located within the hierarchy.

Equational Reasoning is a feature of Functional Programming much envied by Logic Programmers. We argue that logic programmers should not shy away from adopting equational reasoning because of perceived pitfalls, but rather embrace it to indulge in its many benefits. We propose and illustrate two approaches: a cumbersome indirection via Haskell and a more insightful approach directly in Prolog.

ions, that the set of success patterns of a logic program P with respect to an abstraction α is tantamount to the success set of the equational logic program where Eα is an equality theory induced by α. Therefore, either the fixpoint semantics or the procedural semantics defined for equational logic programs can be used to compute success patterns of logic programs. From this observation, the s...

Extra variables in a clause are variables which occur in the body but not in the head. It has been argued that extra variables are necessary and contribute to the expressive power of logic languages. In the first part of this paper, we show that this is not true in general. For this purpose, we provide a simple syntactic transformation of each logic program into a logic program without extra va...

Maude is a high-level language and a high-performance system supporting exe-cutable speciication and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational speciication and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that ha...

Extra variables in a clause are variables which occur in the body but not in the head. It has been argued that extra variables are necessary and contribute to the expressive power of logic languages. In the rst part of this paper, we show that this is not true in general. For this purpose, we provide a simple syntactic transformation of each logic program into a logic program without extra vari...

This research exploits the view of constraint programming as computation in a logical system, namely constraint logic. The basic ingredients of constraint logic are: constraint models for the semantics (they form a comma-category over a fixed model of “built-ins”), generalized polynomials in the rôle of basic syntactic ingredient, and a constraint satisfaction relation between semantics and syn...

In modern functional logic languages like Curry or Toy, programs are possibly non-confluent and nonterminating rewrite systems, defining possibly non-deterministic non-strict functions. Therefore, equational reasoning is not valid for deriving properties of such programs. In a previous work we showed how a mapping from CRWL –a well known logical framework for functional logic programming– into ...