Improved tupling for optimizing multi-paradigm declarative programs

This paper investigates the optimization by fold/unfold of declarative programs that integrate the best features from both functional and logic programming. Transformation sequences are guided by a mixed strategy which, in three low-level transformation phases. successfully combines two well-known heuristics -composition and tupling-, thus avoiding the construction of intermediate data structures and redundant. sub-computations. In particular, whereas composition is able to produce a single function definition for some nested (composed) functions. the tupling method merges non-nested functions calls into a new, function definition called eureka. We solve the non trivial problem of discovering the set of calls to be tupled in an incremental way.. i.e. chaining different eureka definitions where only non-nested calls sharing common variables are taken into account. Moreover, by appropriately combining both strategies, together with a simplification pre-process based on a kind of normalization, we automatically optimize a wide range of programs (with nested and/or non-nested function calls) at a very low cost.