What is the difference between functional programming and declarative programming?

Question

I would like understand the difference between functional, and declarative programming.

Can you show me an example where the code is declarative, but not yet functional?
Is it possible to be functional but not declarative, i.e. imperative?

Answer 1

A non-functional declarative language is PROLOG. Programming in PROLOG is stating a number of facts, and then ask questions, which the system tries to verify or deny.

Example:

human(socrates).       // "Socrates is a human."
mortal(X) :- human(X). // "If X is a human, then X is mortal" or
                       // "All humans are mortal."

? mortal(socrates)     // Is Socrates mortal?
Yes.
? mortal(X)            // Who is mortal?
socrates               
? mortal(pythagoras). 
No.                    // since system doesn't know about any human except Socrates

Another well known language that is declarative, but not functional, is SQL.

Note that there are not only no functions as first class values. In the PROLOG example, there are no functions at all! To be sure, both SQL and PROLOG have some built-in functions, but have no way to let you write your own functions. One could think that the rule

mortal(X) :- human(X).

is a function, but it isn't, it is an inference rule. Hence, declarative, non-functional languages.

For the second part of your question: it is certainly possible to write imperative code in functional programming languages. Simon Peyton Jones once stated that he thinks that Haskell is the finest imperative programming language in the world. (And this was only a half joke.)

Example:

 main = do
      print "Enter a number"
      line <- getLine
      print (succ (read line :: Int))