[zby]

I am happy with you with all that mathy stuff and I agree that it is cool - but it does not address my point which was that functions are black boxes. Once you have 'f' you can compose it whatever you want - but you cannot change its parts - ala universal design pattern (yet another too long Yegge rant: http://steve-yegge.blogspot.com/2008/10/universal-design-pat...).

Sure composing can somehow work for these case, just like a Turing Machine would work, after all it is all equivalent - but we really tend to think about reality in terms of prototypes - a pony is like a horse only small, a goose is like a duck only bigger and white, etc. - this is what makes this inheritance and overriding so convenient. And if you argue that it is not as clean as pure function composition, that it can quickly get into a tangled mass where pure functions are pure and easy to reason about (but it is all equivalent - so you can actually write the same tangled mess code in a pure functional language - by carrying the state around like the burlaks on Volga) - then yeah I agree - engineering is always about trade-offs. I am only trying to explain one of the sides of that trade off.

[sixbrx]

Why would you need to change its parts, it can be parameterized over the parts that change, by passing in other functions as arguments. It's also cheap conceptually and syntactically to create new ones, if an existing one doesn't fit the bill.

[zby]

I don't really know - I've never extensively programmed in functional way (beside studies) - but the point about overriding is that you do it post-hoc you get a library class and you change it. The original author does not need to imagine all the ways you'd like to modify it - and yet by doing some basic structural design and putting stuff into methods he gives you the opportunity to override. Also I imagine that this level of parametrizing - that is if every function in a package is a parameter to another function in that package then it gets messy, but with subclassing/overriding you can change any method and it changes for all other methods.