Friday, September 23, 2011

EQ 2: Textual Replacement

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E [x := R] or $$E _{R} ^{x}$$ denotes an expression that is the same as E, but with all the occurrences of x replaced by "(R)". Unnecessary parentheses maybe removed after substitution.

e.g: (z + y) [z := 5] becomes ((5) + y) becomes (by removing unnecessary parentheses) (5 + y)

If x is a list of *distinct* $$x_1, x_2,...x_n$$ of variables and R a list $$R_1\ , R_2 , ... R_n$$ of expressions then $$E _{R} ^{x}$$ denotes the *simultaneous* replacement in E of the variables of x by corresponding expressions of R, each expression being enclosed by parentheses.

(z + y) [z,y := 5,6] becomes ((5) + (6)) becomes (by removing unnecessary parentheses) (5 + 6)

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