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==Specialization with compilation==

The specialized algorithm has to be represented in a form that can be interpreted.

In many situations, usually when <math>\mathit{alg}_A(B)</math> is to be computed on many values of <math>B</math> in a row, <math>\mathit{alg}_A</math> can be written as machine code instructions for a special [[abstract machine]], and it is typically said that <math>A</math> is ''compiled''. The code itself can then be additionally optimized by answer-preserving transformations that rely only on the semantics of instructions of the abstract machine.

The instructions of the abstract machine can usually be represented as [[Record (computer science)|record]]s. One field of such a record, an ''instruction identifier'' (or ''instruction tag''), would identify the instruction type, e.g. an [[Integer (computer science)|integer]] field may be used, with particular integer values corresponding to particular instructions. Other fields may be used for storing additional parameters of the instruction, e.g. a [[Pointer (computer programming)|pointer]] field may point to another instruction representing a label, if the semantics of the instruction require a jump. All instructions of the code can be stored in a traversable [[data structure]] such as an [[Array (data type)|array]], [[linked list]], or [[Tree (abstract data type)|tree]].

''Interpretation'' (or ''execution'') proceeds by fetching instructions in some order, identifying their type, and executing the actions associated with said type.

In many programming languages, such as [[C (programming language)|C]] and [[C++]], a simple [[Switch statement|<code>switch</code> statement]] may be used to associate actions with different instruction identifiers. Modern compilers usually compile a <code>switch</code> statement with constant (e.g. integer) labels from a narrow range by storing the address of the statement corresponding to a value <math>i</math> in the <math>i</math>-th cell of a special array, as a means of efficient optimisation. This can be exploited by taking values for instruction identifiers from a small interval of values.