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

The notation [[ P ]] _L denotes 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.

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