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Converting a mapping into a well-defined function

Dear Mathematica User Friends:

I need to build a module that takes a non-empty set A
(whose elements are 2-tuples), and appends (or not) those 2-tuples
to a set B  according to the following criteria:

(1.) if the abscissa of a 2-tuple in A is unique (among the abscissas
of all the other 2-tuples in A), then the module appends that 2-tuple
to the set B.

(2.) if there are n 2-tuples in A that share the same abscissa, then
the module appends the first of those 2-tuples to B ("first" here means
the first of such n 2-tuple encountered, as you read A from left to
right),but does not append the rest to B.

(3.) the module does not attempt to sort the set B, after the appending
process is completed.


If A = {{a,5},{b,27},{a,14},{c,4},{e,94},{b,6},{d,9},{e,4}}



Another way to re-phrase the above example;

if A defines a mapping:

A(a)=5, A(b)=27, A(a)=14, A(c)=4, A(e)=94, A(b)=6, A(d)=9, A(e)=4

them the module converts the mapping A into a well-defined function:

A(a)=5, A(b)=27, A(c)=4, A(d)=9, A(e)=94.

Thank you for your help!

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