My research interest is mainly concentrated in the area of functional logic programming. The aim of functional logic programming is to integrate the best features of both functional and logic programming. Logic programming provides the use of predicates and logical formulas. Logic programs have a great expressive power thanks to the ability of logic languages of computing using logical variables, partial data structures, and an operational mechanism that permits a  non deterministic search for answers. Functional programming are based on the concept of function. In a functional program functions are defined by means of equations. The deterministic evaluation of ground expressions increases the efficiency of functional programs. The concept of evaluation strategies, that also increase the efficiency of functional computations, relays on the existence and manipulation of nested terms. The combination of these features makes functional logic languages more expressive than functional languages and more efficient than traditional logic languages.

Actually, I am working along two lines:

• Narrowing Strategies
Functional logic languages  use term rewriting systems as programs and (some variant) of narrowing as  operational semantics. Narrowing extends the rewriting principle replacing pattern matching by unification, these two techniques coincide when they are applied on ground terms. Narrowing computes a suitable substitution which when is applied on a term it can be reduced on a rewriting step. Narrowing provides completeness in the sense of logic programming (computation of answers) and also in the sense of functional programming (computation of values or normal forms). Narrowing is a non determinist procedure, since there exists two levels of freedom: the choice of a reducible subterm and the choice of a rule which is used in the reduction. By this reason it generates a large search space. Many narrowing strategies have been defined in order to control the size of the search space, by erasing some useless derivations. A strategy is a position constraint that reduces the number of positions to be exploit.

My work in this area during the last years was centered in the formalization of a demand-driven narrowing strategy and the study of the formal relation between needed narrowing and this (not so lazy) demand-driven narrowing strategy
which is the basis for popular implementations of non-strict functional logic languages. Also, I am interested on implementation aspects of narrowing strategies and on extensions of narrowing (e.g. to non deterministic computations).
 

• Program Transformation and Partial Evaluation
The aim of program transformation is to derive a program semantically equivalent to the original program, but with a better behavior w.r.t. some determined properties (usually, we want that the transformed program may be executed more efficiently than the initial one). More accurately, given an initial program P, we want to obtain a new program P' which computes the same results and answers as P for any input term. From a theoretical point of view, the most important property of a transformation is its correctness. We say that a transformation is strongly sound when, given a term, the results and answers computed by P',  are exactly the same as the ones computed by the original program P for that term. On the other hand we say that a transformation is weakly sound when for each result and answer computed by P' there exists the same result but a more general computed answer in P. The definitions of (strong/weak) completeness are the reverse of the last concepts.

Partial evaluation is a program transformation technique, also known as program specialization, that aims to derive a specialized instance of a program w.r.t. a restricted set of inputs. Partial evaluation have been applied to all kind of programming languages, including  imperative languages (see here for a standard reference). Partial evaluation of functional logic languages was first formalized by Maria Alpuente and her fellows of the ELP group, I co-authored some of these papers.

Recently I have investigated a program transformation to improve non deterministic computations.

Also I am interested in the application of program transformation techniques in the context of narrowing implementations. The idea is to introduce transformation techniques inside the compilation process in order to improve the quality of the generated compiled code.