Editing Referential transparency (section)

== History ==
The concept originated in [[Alfred North Whitehead]] and [[Bertrand Russell]]'s ''[[Principia Mathematica]]'' (1910–1913):<ref name="whitehead1927" />
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A proposition as the vehicle of truth or falsehood is a particular occurrence, while a proposition considered factually is a class of similar occurrences. It is the proposition considered factually that occurs in such statements as “''A'' believes ''p''“ and “''p'' is about ''A''.”

Of course it is possible to make statements about the particular fact “Socrates is Greek.” We may say how many centimetres long it is; we may say it is black; and so on. But these are not the statements that a philosopher or logician is tempted to make.

When an assertion occurs, it is made by means of a particular fact, which is an instance of the proposition asserted. But this particular fact is, so to speak, “transparent”; nothing is said about it, but by means of it something is said about something else. It is this “transparent” quality that belongs to propositions as they occur in truth-functions. This belongs to ''p'' when ''p'' is asserted, but not when we say “''p'' is true.”
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It was adopted in analytic philosophy in [[Willard Van Orman Quine]]'s ''[[Word and Object]]'' (1960):<ref name="quine1960" />
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When a singular term is used in a sentence purely to specify its object, and the sentence is true of the object, then certainly the sentence will stay true when any other singular term is substituted that designates the same object. Here we have a criterion for what may be called ''purely referential position'': the position must be subject to the ''substitutivity of identity''.

[…]

Referential transparency has to do with constructions (§ 11); modes of containment, more specifically, of singular terms or sentences in singular terms or sentences. I call a mode of containment {{mvar|φ}} referentially transparent if, whenever an occurrence of a singular term {{mvar|t}} is purely referential in a term or sentence {{math|''ψ''(''t'')}}, it is purely referential also in the containing term or sentence {{math|''φ''(''ψ''(''t''))}}.
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The term appeared in its contemporary computer science usage in the discussion of [[Variable (computer science)|variable]]s in [[programming language]]s in [[Christopher Strachey]]'s seminal set of lecture notes ''[[Fundamental Concepts in Programming Languages]]'' (1967):<ref name="strachey1967" />
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One of the most useful properties of expressions is that called by Quine [4] ''referential transparency''. In essence this means that if we wish to find the value of an expression which contains a sub-expression, the only thing we need to know about the sub-expression is its value. Any other features of the sub-expression, such as its internal structure, the number and nature of its components, the order in which they are evaluated or the colour of the ink in which they are written, are irrelevant to the value of the main expression.
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