Partial evaluation

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title: "Partial evaluation" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["compiler-optimizations", "evaluation-strategy"] description: "Technique for program optimization" topic_path: "general/compiler-optimizations" source: "https://en.wikipedia.org/wiki/Partial_evaluation" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Technique for program optimization ::

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 \texttt{prog} is seen as a mapping of input data into output data:

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

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

The partial evaluator transforms \langle \texttt{prog}, I_\text{static}\rangle into \texttt{prog}^* : I_\text{dynamic} \to O by precomputing all static input at compile time. \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" \texttt{prog} to \texttt{prog}^*.

Futamura projections

A particularly interesting example of the use of partial evaluation, first described in the 1970s by Yoshihiko Futamura, is when \texttt{prog} is an interpreter for a programming language.

If I_\text{static} is source code designed to run inside that interpreter, then partial evaluation of the interpreter with respect to this data/program produces \texttt{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 \texttt{prog}^ is effectively a compiled version of I_\text{static}.

This technique is known as the first Futamura projection, of which there are three:

1. Specializing an interpreter for given source code, yielding an executable.
2. Specializing the specializer for the interpreter (as applied in #1), yielding a compiler.
3. Specializing the specializer for itself (as applied in #2), yielding a tool that can convert any interpreter to an equivalent compiler.

They were described by Futamura in Japanese in 1971{{citation | title=Partial Evaluation of Computation Process --- An approach to a Compiler-Compiler | volume=54-C | journal=Transactions of the Institute of Electronics and Communications Engineers of Japan | pages=721–728 | year=1971}} and in English in 1983.

PyPy's RPython and GraalVM's Truffle framework are examples of real-world JIT compilers that implement Futamura's first projection.

References

General references

References

1. "Professor Yoshihiko Futamura".
2. Futamura, Y.. (1983). "RIMS Symposia on Software Science and Engineering". Springer.

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::