In order to define a new environment using \left and \right, I need to know how those macros are defined.

Unfortunately, both \show\left and \show\right return an error. My last resort was to scan latex.ltx for the definitions of \left and \right, to no avail.

Where are \left and \right defined?

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    with \show you don't get an error it just shows the definition (not very informative definition for primitives) show output is formatted very similar to error output. Jun 12 '13 at 19:19

\left and \right are TeX primitives.

If you write \show\left, you will obtain:

> \left=\left.

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