  Constructor-Based Conditional Rewriting Logic is a general framework for
integrating first-order functional and logic programming which gives an
algebraic semantics for non-deterministic functional-logic programs. In the
context of this formalism, we introduce a simple notion of program module as an
open program which can be extended together with several mechanisms to combine
them. These mechanisms are based on a reduced set of operations. However, the
high expressiveness of these operations enable us to model typical constructs
for program modularization like hiding, export/import,
genericity/instantiation, and inheritance in a simple way. We also deal with
the semantic aspects of the proposal by introducing an immediate consequence
operator, and studying several alternative semantics for a program module,
based on this operator, in the line of logic programming: the operator itself,
its least fixpoint (the least model of the module), the set of its
pre-fixpoints (term models of the module), and some other variations in order
to find a compositional and fully abstract semantics wrt the set of operations
and a natural notion of observability.
