#10063: State a law for foldMap -------------------------------------+------------------------------------- Reporter: ekmett | Owner: ekmett Type: feature | Status: new request | Milestone: 7.12.1 Priority: low | Version: 7.10.1-rc1 Component: Core | Operating System: Unknown/Multiple Libraries | Type of failure: Documentation Keywords: | bug Architecture: | Blocked By: Unknown/Multiple | Related Tickets: Test Case: | Blocking: | Differential Revisions: | -------------------------------------+------------------------------------- After being prodded by /u/random_crank on reddit, I realized there is a law we can state for `foldMap`: A monoid homomorphism `g` is a function such that {{{#!hs g mempty = mempty g (mappend a b) = mappend (g a) (g b) }}} holds. For any monoid homomorphism `g`: {{{#!hs foldMap (g . f) = g . foldMap f }}} This isn't strictly a free theorem as it relies on the `Monoid` laws, but it is true and has the same general flavor as the equally complicated free theorem for `foldr`. This law is a bit technical, but is a nice tool for equational reasoning, and gives rise to a much nicer `foldMap`-based version of the "banana split" theorem for `foldr`. {{{#!hs foldMap f &&& foldMap g = foldMap (f &&& g) }}} -- Ticket URL: http://ghc.haskell.org/trac/ghc/ticket/10063 GHC http://www.haskell.org/ghc/ The Glasgow Haskell Compiler