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Girardian turnstyle
I don't know whether this is "the official" macro, but this is
the one I used in my TCS survey paper (Vol. 110, No 2), and I think
it gives a pretty good approximation of the Girardian turnstyle:
\def\joinrelm{\mathrel{\mkern-3mu}}
\def\relbar{\mathrel{\smash-}}
\def\tailpiece{\vrule height 1ex width 0.3ex depth -.1ex}
\def\seqsym{\mathrel{\tailpiece\joinrelm\relbar}}
\def\sequent#1#2{#1 \seqsym #2}
Example:
$$\sequent{\Gamma}{\Delta}$$
-- Jean Gallier