The pretentious view that Haskell's core is a mathematical structure familiar to mathematicians is wrong.
Haskell borrows concepts from category theory (a "field" so abstract from most math that most mathematicians don't need but a handful of its concepts) to label typeclasses, and those typeclasses don't always follow from their namesake.
Monads, functors, arrows, etc. are more aesthetic than fundamental to the core nature of Haskell. They're just a bookish (and sometimes bureaucratic, IMO) design choice. What I mean by that, is that the language designers took a concept (referential transparency) and built an understandable structure, but beside and aside from this, made a bunch of nested, derived typeclasses of dubious value or purpose. Sometimes I look at a Haskell library and have a more academic version of the, "Why the fuck is this a class?" moment.
I'd like to comment tangentially that Haskell is almost the OOP/Java of the 2010's - the programming community claims that it makes your code "safer", and in some sense it very much does, but its features are being perverted and overhyped while its caveats are being forgotten.
Haskell borrows concepts from category theory (a "field" so abstract from most math that most mathematicians don't need but a handful of its concepts) to label typeclasses, and those typeclasses don't always follow from their namesake.
Further, Haskell could exist and keep its property of referential transparency without the the 'mathematical' structures or their names. Here's a version of Haskell without monads: http://donsbot.wordpress.com/2009/01/31/reviving-the-gofer-s...
Monads, functors, arrows, etc. are more aesthetic than fundamental to the core nature of Haskell. They're just a bookish (and sometimes bureaucratic, IMO) design choice. What I mean by that, is that the language designers took a concept (referential transparency) and built an understandable structure, but beside and aside from this, made a bunch of nested, derived typeclasses of dubious value or purpose. Sometimes I look at a Haskell library and have a more academic version of the, "Why the fuck is this a class?" moment.
I'd like to comment tangentially that Haskell is almost the OOP/Java of the 2010's - the programming community claims that it makes your code "safer", and in some sense it very much does, but its features are being perverted and overhyped while its caveats are being forgotten.