Programming Language Theory Concept

Compiler

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Mathematically, denote $\begin{array}{l} m a t h c a l P_{S} \end{array}$ as the set of programs in the source language and $\begin{array}{l} m a t h c a l P_{T} \end{array}$ as the set of programs in the target language. Then, a compiler is a function $\begin{array}{l} C : \\ m a t h c a l P_{S} \\ t o \\ m a t h c a l P_{T} \end{array}$

Mathematically, denote $𝒫_{S}$ as the set of programs in the source language and $𝒫_{T}$ as the set of programs in the target language. Then, a compiler is a function $C : 𝒫_{S} \to 𝒫_{T}$ .