[lmm]

> A complicated function may be made of a bunch of statements where each statement makes sense easily. The entire function may still be complicated.

Statement yes, but I avoid them where possible - the complexity comes from their interactions because their interactions are unmanaged, implicit and arbitrary. If you make each function an expression made up of expressions and functions, then I think it becomes true that if each expression makes sense easily then the whole will also make sense easily.

[mannykannot]

As far as the complexity of programs are concerned, there is a similarity between statements at one level of abstraction and functions at a higher level. I have seen many cases where small functions have been assembled into complicated programs. These programs often have a proliferation of 'helper' classes and functions, where you have to trace through long series of calls to get to where the work is done. They often seem to come from a poor design that has been repeatedly patched instead of fixed, or from programmers who write functions because they think they will be part of the solution, but not backing out and replacing them them when they find a complication they had not anticipated.

Using small functions is a necessary, but not sufficient, condition for making understandable code.

[lmm]

I think what you're describing is a case where you can't understand what those helpers do, and therefore can't understand what the function that calls them does. I maintain that if each individual function makes sense then the whole will too.

[pshc]

This holds if the small functions are built around a coherent top-down design, respecting each other's invariants. Once the project is too large to fit in one's head, it is no longer sufficient for each function to be 'correct' in a local sense.

[mannykannot]

Sensible, understandable functions can be assembled into complicated, incomprehensible programs in exactly the same way that the sensible, understandable operators of a programming language can.