In this paper we formalise CSP solving as an inference process. Based on the notion of Computational Systems we associate actions with rewriting rules and control with strategies that establish the order of application of the inferences. The main contribution of this work is to lead the way to the design of a formalism allowing to better understand constraint solving and to apply in the domain of CSP the knowledge already developed in Automated Deduction. Keywords: Constraint Satisfaction Problems, Computational Systems, Rewriting Logic. 1 Introduction In the last twenty years many work has been done on solving Constraint Satisfaction Problems, CSP. The solvers used by constraint solving systems can be seen as encapsulated in black boxes. In this work we formalise CSP solving as an inference process. We are interested in description of constraint solving using rule-based algorithms because of the explicit distinction made in this approach between deduction rules and control. We associ...

ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the so-called lambda-abstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. \x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous function-valued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with rstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordina...

ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the so-called lambda-abstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. "x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous function-valued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with firstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordinary...