Can functional programming be used to develop a full enterprise application

The usual way to go about state changes in a pure language like Haskell is to model them as functions that take the old state and return a modified version. Even for complex objects, this is efficient because of Haskell's lazy evaluation strategy - even though you are syntactically creating a new object, it is not copied in its entirety; each field is evaluated only when it is needed.

If you have more than a few local state changes, things can become clumsy, which is where monads come in. The monad paradigm can be used to encapsulate a state and its changes; the textbook example is the State monad that comes with a standard Haskell install. Note, however, that a monad is nothing special: it's just a data type that exposes two methods (>>= and return), and meets a few expectations (the 'monad laws'). Under the hood, the State monad does exactly the same: take the old state and return a modified state; only the syntax is nicer.

What you are really asking about here is how to do Polymorphism in functional languages, i.e. how to create functions that behave differently based on their arguments.

Note the first argument to a function is typically equivalent to the "object" in OOP, but in functional languages you usually want to separate functions from data, so the "object" is likely to be a pure (immutable) data value.

Functional languages in general provide various options for achieving polymorphism:

• Something like multimethods which call a different function based on examining the arguments provided. This can be done on the type of the first argument (which is effectively equal to the behaviour of most OOP languages), but could also be done on other attributes of the arguments.
• Prototype / object-like data structures which contain first-class functions as members. So you could embed a "say" function inside your dog and cat data structures. Effectively you have made the code part of the data.
• Pattern matching - where pattern matching logic is built into the function definition, and ensures different behaviours for different parameters. Common in Haskell.
• Branching / conditions - equivalent to if / else clauses in OOP. Might not be highly extensible, but can still be appropriate in many cases when you have a limited set of possible values (e.g. was the function passed a number or a string or null?)

As an example, here's a Clojure implementation of your problem using multimethods:

;; define a multimethod, that dispatched on the ":type" keyword
(defmulti say :type)  

;; define specific methods for each possible value of :type. You can add more later
(defmethod say :cat [animal what] (println (str "Car purrs: " what)))
(defmethod say :dog [animal what] (println (str "Dog barks: " what)))
(defmethod say :default [animal what] (println (str "Unknown noise: " what)))

(say {:type :dog} "ruff")
=> Dog barks: ruff

(say {:type :ape} "ook")
=> Unknown noise: ook

Note that this behaviour doesn't require any explicit classes to be defined: regular maps work fine. The dispatch function (:type in this case) could be any arbitrary function of the arguments.