# equational logic

## equational logic

(logic)
First-order equational logic consists of quantifier-free terms of ordinary first-order logic, with equality as the only predicate symbol. The model theory of this logic was developed into Universal algebra by Birkhoff et al. [Birkhoff, Gratzer, Cohn]. It was later made into a branch of category theory by Lawvere ("algebraic theories").
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In practice, most equational logic programs are constructor-based; symbols, called constructors, that construct data terms are distinguished from those, called defined functions or operations, that operate on data terms (see, e.
Unification modulo an equality theory for equational logic programming.
For recent notable work, I focus on some significant theorem-proving systems: the geometry theorem provers of Chou (Chou, Gao, and Zhang 1994; Chou 1988); the Boyer and Moore (1988) interactive theorem prover NQTHM and its successor ACL2 (Kaufmann and Moore 1996); the rewrite rule laboratory (RRL) of Kaput and Zhang (1995); the resolution prover OTTER (McCune and Otter 1997; McCune 1994) and the equational logic prover EQP by McCune (1996); the interactive higher-order logic provers NUPRL (Constable et al.
Rewriting-based automated deduction systems often work with equational logics using oriented equations, or rewrite rules.
Incremental constraint satisfaction for equational logic programming.
But it seems that the complexity of the equational logic of nondeterminism exceeds by far the complexity of classical equational reasoning.
In summary, the declarative control architecture implements, with an equational logic formalism, a combination of planning, inference and feedback control principles.
PIM is an equational logic designed to function as a "transformational toolkit" for compilers and other programming tools that analyze and manipulate imperative languages.
This article is an effort to contribute to a better understanding of these issues by presenting a formal account of properties of an equational logic called PIM [Field 1992].
1987] present (implicitly) a completeness result for an equational logic that PIM resembles in some respects.
PIM is an equational logic, rather than, for example, a sequent calculus such as that of Mason and Talcott [1989] or Selke [1989a; 1989b], the latter system of which, like PIM, was based on the work of Cartwright and Felleisen [1989].
We assume some familiarity on the part of the reader with equational logic and initial-algebra semantics.

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