Function level programs as mathematical objects

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Abstract
Most programs written today are “object-level” programs. That is, programs describe how to combine various “objects” (i.e., numbers, symbols, arrays, etc.) to form other objects until the final “result objects” have been formed. New objects are constructed from existing ones by the application of various object-to-object functions such as + or matrix inversion. Conventional, von Neumann programs are object level; “expressions” on the right side of assignment statements are exclusively concerned with building an object that is then to be stored. Lambda calculus based languages, such as LISP and ISWIM [Landin 66], are also, in practice, object level languages, although they have the means to be more.

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