Bird–Meertens formalism
The Bird–Meertens formalism is a calculus for deriving programs from specifications (in a functional-programming setting) by a process of equational reasoning. It was devised by Richard Bird and Lambert Meertens as part of their work within IFIP Working Group 2.1.
It is sometimes referred to in publications as BMF, as a nod to Backus–Naur form. Facetiously it is also referred to as Squiggol, as a nod to ALGOL, which was also in the remit of WG 2.1, and because of the "squiggly" symbols it uses. A less-used variant name, but actually the first one suggested, is SQUIGOL.
Map is a well-known second-order function that applies itself to every element of a list; in BMF, it is written :
Likewise, reduce is a function that collapses a list into a single value by repeated application of a binary operator. It is written / in BMF. Taking as a suitable binary operator with neutral element e, we have
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