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$e = x \mid \lambda x\!:\!\tau.e \mid e \, e \mid c$

So, what is $\mid$ in this example of simply typed lambda calculus?

The syntax of the simply typed lambda calculus is essentially that of the lambda calculus itself. (Wikipedia, simply typed lambda calculus)

I wasn't able to see $\mid$ in untyped lambda calculus.. How is $\mid$ used in lambda calculus?

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Where did you come across this? –  Harald Hanche-Olsen Feb 24 '13 at 15:48
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If I interpret your question correctly, the $\mid$ simply means an alternative in the syntax: an expression $e$ is either a variable ($x$), a $\lambda$ term ($\lambda x: \tau. e$), a function application ($ee$) or a constant ($c$). See en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form. –  Johannes Kloos Feb 24 '13 at 16:01
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@JohannesKloos Please consider converting your comment into an answer, so that this question gets removed from the unanswered list. If you do so, it is helpful to post it to this chat room to make people aware of it (and attract some upvotes). For further reading on the issue of too many unanswered questions, see here, here or here. –  Lord_Farin Oct 8 '13 at 13:52
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1 Answer 1

If I interpret your question correctly, the ∣ simply means an alternative in the syntax: an expression e is either a variable (x), a λ term (λx:τ.e), a function application (ee) or a constant (c)

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