Futamura Projections[Y. Futamura, ``Partial Evaluation of Computation Process -- An Approach to a Compiler-Compiler'', Systems, Computers, Controls, 2(5):45-50, 1971. The presentation here follows Jones et al.]

Partial evaluation is a powerful unifying technique that describes many operations in computer science.

We use the notation [![ P ]!] _L to denote running a program P in language L. Suppose that int is an interpreter for a language S and source is a program written in S. Then:

• output	=	[![ source ]!] s [ input ]
  	=	[![ int ]!] [ source, input]
  	=	[![ [![ mix ]!] [ int, source] ]!] [ input]
  	=	[![ target ]!] [ input ]

  Therefore, target = [![ mix ]!] [ int, source] .

• target	=	[![ mix ]!] [ int, source]
  	=	[![ [![ mix ]!] [ mix, int ] ]!] [ source]
  	=	[![ compiler ]!] [ source ]

  Thus, compiler = [![ mix ]!] [ mix, int ] = [![ cogen ]!] [ int ]
  

• Finally, cogen = [![ mix ]!] [ mix, mix ] = [![ cogen ]!] [ mix ]
  is a compiler generator, i.e., a program that transforms interpreters into compilers.