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 {\displaystyle {\texttt {prog}}} is seen as a mapping of input data into output data: prog : I static × I dynamic → O , {\displaystyle {\texttt {prog}}:I_{\text{static}}\times I_{\text{dynamic}}\to O,} where I static {\displaystyle I_{\text{static}}} , the static data, is the part of the input data known at compile time. The partial evaluator transforms ⟨ prog , I static ⟩ {\displaystyle \langle {\texttt {prog}},I_{\text{static}}\rangle } into prog ∗ : I dynamic → O {\displaystyle {\texttt {prog}}^{*}:I_{\text{dynamic}}\to O} by precomputing all static input at compile time. prog ∗ {\displaystyle {\texttt {prog}}^{*}} is called the "residual program" and should run more efficiently than the original program. The act of partial evaluation is said to "residualize" prog {\displaystyle {\texttt {prog}}} to prog ∗ {\displaystyle {\texttt {prog}}^{*}} .
Source: “Yoshihiko Futamura”, English Wikipedia (CC BY-SA 4.0), excerpt