A computer program, prog, is seen as a mapping of input data into output data:
, the static data, is the part of the input data known at compile time.
The partial evaluator transforms into by precomputing all static input at compile time. is called the "residual program" and should run more efficiently than the original program. The act of partial evaluation is said to "residualize" to .
If Istatic is source code designed to run inside said interpreter, then partial evaluation of the interpreter with respect to this data/program produces prog*, a version of the interpreter that only runs that source code, is written in the implementation language of the interpreter, does not require the source code to be resupplied, and runs faster than the original combination of the interpreter and the source. In this case prog* is effectively a compiled version of Istatic.
This technique is known as the first Futamura projection, of which there are three:
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