  Constraint logic programming emerged in the late 80's as a highly declarative
class of programming languages based on first-order logic and theories with
decidable constraint languages, thereby subsuming Prolog restricted to equality
constraints over the Herbrand's term domain. This approach has proven extremely
successfull in solving combinatorial problems in the industry which quickly led
to the development of a variety of constraint solving libraries in standard
programming languages. Later came the design of a purely declarative front-end
constraint-based modeling language, MiniZinc, independent of the constraint
solvers, in order to compare their performances and create model benchmarks.
Beyond that purpose, the use of a high-level modeling language such as MiniZinc
to develop complete applications, or to teach constraint programming, is
limited by the impossibility to program search strategies, or new constraint
solvers, in a modeling language, as well as by the absence of an integrated
development environment for both levels of constraint-based modeling and
constraint solving. In this paper, we propose to solve those issues by taking
Prolog with its constraint solving libraries, as a unified relation-based
modeling and programming language. We present a Prolog library for high-level
constraint-based mathematical modeling, inspired by MiniZinc, using subscripted
variables (arrays) in addition to lists and terms, quantifiers and iterators in
addition to recursion, together with a patch of constraint libraries in order
to allow array functional notations in constraints. We show that this approach
does not come with a significant computation time overhead, and presents
several advantages in terms of the possibility of focussing on mathematical
modeling, getting answer constraints in addition to ground solutions,
programming search or constraint solvers if needed, and debugging models within
a unique modeling and programming environment.
