Partial evaluators can be separated into two classes: offline specializers, which make all of their reduce/residualize decisions before specialization, and online specializers, which make such decisions during specialization. The choice of which method to use is driven by a tradeoff between the efficiency of the specializer and the quality of the residual programs that it produces. Existing research describes some of the inefficiencies of online specializers, and how these are avoided using offline methods, but fails to address the price paid in specialization quality. This paper motivates research in online specialization by describing two fundamental limitations of the offline approach, and explains why the online approach does not encounter the same difficulties.

Program specializers improve the speed of programs by performing some of the programs' reductions at specialization time rather than at runtime. This specialization process can be time-consuming; one common technique for improving the speed of the specialization of a particular program is to specialize the specializer itself on that program, creating a custom specializer, or program generator, for that particular program.

: We have developed techniques for obtaining and using type information during program specialization (partial evaluation). Computed along with every residual expression and every specialized program is type information that bounds the possible values that the specialized program will compute at run time. The three keystones of this research are symbolic values that represent both the set of values that might be computed at runtime and the code for creating the runtime value, generalization of symbolic values, and the use of online fixed-point iterations for computing the type of values returned by specialized recursive functions. This work differs from previous specializers in computing type information for all residual expressions, including residual if expressions, and residual calls to specialized user functions. The specializer exploits the type information it computes to increase the efficiency of specialized functions. In particular, this research allows the class of recursive d...