Abstract
The concept of imbedding a programming language L into a formal system is introduced and used as the basis of defining the semantics Θ of the language. Θ is an operator which maps a program p in L onto a function. The pair (L, Θ) is called a programming system. If (L, Θ) and (L,' Θ') are two programming systems, a mapping Γ from L into L' is called a compiler. A compiler is said to be correct if Θ'(Γ(p)) = Θ(p) for p in L. These ideas are illustrated in terms of two programming systems, one for recursive functions and the other for Turing machines.
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