Concepts inProofs by structural induction using partial evaluation
Higher-order function
In mathematics and computer science, a higher-order function (also functional form, functional or functor) is a function that does at least one of the following: take one or more functions as an input output a function All other functions are first order functions. In mathematics higher-order functions are also known as operators or functionals. The derivative in calculus is a common example, since it maps a function to another function.
more from Wikipedia
A program transformation is any operation that takes a computer program and generates another program. In many cases the transformed program is required to be semantically equivalent to the original, relative to a particular formal semantics and in fewer cases the transformations result in programs that semantically differ from the original in predictable ways.
more from Wikipedia
Structural induction
Structural induction is a proof method that is used in mathematical logic (e.g. , in the proof of Łoś' theorem), computer science, graph theory, and some other mathematical fields. It is a generalization of mathematical induction. Structural recursion is a recursion method bearing the same relationship to structural induction as ordinary recursion bears to ordinary mathematical induction.
more from Wikipedia
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms. The derivation of a theorem is often interpreted as a proof of the truth of the resulting expression, but different deductive systems can yield other interpretations, depending on the meanings of the derivation rules.
more from Wikipedia