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"Banana" brackets are used to denote catamorphisms:

Another notation found in the literature is (!|f|!).

These symbols are very similar to the composition of a $($ and a $|$, is this similarity more than coincidence? I.e. is there some motivation where they represent the same as $|...|$ followed by $(...)$ ?

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The earliest reference I can find to "banana brackets" is in:

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Where they are clearly crescent-moon/banana shaped symbols: ⦅...⦆.

The later style using $($ and $|$ seems to be a typographic practicality, and is used by Malcolm himself in another publication the same year:

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