The derivation of an algorithm for program specialisation

Prior approaches based on characteristic trees failed to preserve characteristic trees upon generalization: two atoms with identical specialization behavior may be generalized by one with a completely different specialization behavior.

“First, they failed to preserve the characteristic trees upon generalization: two atoms with identical specialization behavior may be generalized by one with a completely different specialization behavior.”

Prior characteristic-tree approaches have always been limited by an ad hoc depth bound, possibly leading to very undesirable specialization results.

“Second, the characteristic trees have always been limited by some ad hoc depth bound, possibly leading to very undesirable specialization results (as we will show later in the article).”

In those cases Algorithm 3.4.3, as well as all earlier approaches based on characteristic trees, terminates at the cost of imposing an ad hoc depth bound on characteristic trees.

“In those cases Algorithm 3.4.3,as well as all earlier approaches based on characteristic trees [Gallagher 1991;Gallagher and Bruynooghe 1991;Leuschel and De Schreye 1998], terminates at the cost of imposing an ad hoc depth bound on characteristic trees.”

Prior characteristic-tree approaches have always been limited by an ad hoc depth bound, possibly leading to very undesirable specialization results.

“Second, the characteristic trees have always been limited by some ad hoc depth bound, possibly leading to very undesirable specialization results (as we will show later in the article).”

In Example 4.1.1, unfolding, including determinate and well-founded unfolding, produces an infinite number of different characteristic atoms, all with a different characteristic tree.

“As can be noticed in Figure 4, unfolding (determinate [Gallagher 1991;Gallagher Bruynooghe [1991]; Leuschel and De Schreye 1998] and well founded [Bruynooghe et al. 1992;Martens and De Schreye 1996;Martens et al. 1994], among others) produces an infinite number of different characteristic atoms, all with a different characteristic tree.”

Prior approaches based on characteristic trees failed to preserve characteristic trees upon generalization: two atoms with identical specialization behavior may be generalized by one with a completely different specialization behavior.

“First, they failed to preserve the characteristic trees upon generalization: two atoms with identical specialization behavior may be generalized by one with a completely different specialization behavior.”

In those cases Algorithm 3.4.3, as well as all earlier approaches based on characteristic trees, terminates at the cost of imposing an ad hoc depth bound on characteristic trees.

“In those cases Algorithm 3.4.3,as well as all earlier approaches based on characteristic trees [Gallagher 1991;Gallagher and Bruynooghe 1991;Leuschel and De Schreye 1998], terminates at the cost of imposing an ad hoc depth bound on characteristic trees.”

The partial deduction method of Gallagher [1991] was extended by de Waal [1994] by adorning characteristic trees with a depth-k abstraction of the corresponding atom component.

“the partial deduction method of Gallagher [1991] was extended by de Waal [1994] by adorning characteristic trees with a depth-k abstraction of the corresponding atom component.”

For SP, the nontermination symbol means real nontermination; for MIXTUS, heap overflow after 20 minutes; for PADDY, a thorough system crash after 2 minutes.

“-⊥, SP: this means”

Partial evaluation of ITE-Prolog can be situated somewhere between partial deduction of pure logic programs and partial evaluation of full Prolog.

“In summary, partial evaluation of ITE-Prolog, can be situated somewhere between partial deduction of pure logic programs (see [60,31,10,69,68] and systems like sP [30,29], sAGE [34,33] or more recently ECCE [50,51,57]) and partial evaluation of full Prolog (e.g. MIXTUs [83,82] or PADDY [76–78]).”