Partial evaluation

In computing, partial evaluation is a technique for several different types of program optimization by specialization. The most straightforward application is to produce new programs that run faster than the originals while being guaranteed to behave in the same way.

A computer program prog is seen as a mapping of input data into output data:

${\displaystyle prog:I_{\text{static}}\times I_{\text{dynamic}}\to O,}$

where ${\displaystyle I_{\text{static}}}$, the static data, is the part of the input data known at compile time.

The partial evaluator transforms ${\displaystyle \langle prog,I_{\text{static}}\rangle }$ into ${\displaystyle prog^{*}:I_{\text{dynamic}}\to O}$ by precomputing all static input at compile time. ${\displaystyle prog^{*}}$ is called the "residual program" and should run more efficiently than the original program. The act of partial evaluation is said to "residualize" ${\displaystyle prog}$ to ${\displaystyle prog^{*}}$.