How can a time function exist in functional progra

Question

I've to admit that I don't know much about functional programming. I read about it from here and there, and so came to know that in functional programming, a function returns the same output, for same input, no matter how many times the function is called. It's exactly like a mathematical function which evaluates to the same output for the same value of the input parameters which involves in the function expression.

For example, consider this:

f(x,y) = x*x + y; // It is a mathematical function

No matter how many times you use f(10,4), its value will always be 104. As such, wherever you've written f(10,4), you can replace it with 104, without altering the value of the whole expression. This property is referred to as referential transparency of an expression.

As Wikipedia says (link),

Conversely, in functional code, the output value of a function depends only on the arguments that are input to the function, so calling a function f twice with the same value for an argument x will produce the same result f(x) both times.

Can a time function (which returns the current time) exist in functional programming?

• If yes, then how can it exist? Does it not violate the principle of functional programming? It particularly violates referential transparency which is one of the property of functional programming (if I correctly understand it).

• Or if no, then how can one know the current time in functional programming?

Answer 1

I am surprised that none of the answers or comments mention coalgebras or coinduction. Usually, coinduction is mentioned when reasoning about infinite data structures, but it is also applicable to an endless stream of observations, such as a time register on a CPU. A coalgebra models hidden state; and coinduction models observing that state. (Normal induction models constructing state.)

This is a hot topic in Reactive Functional Programming. If you're interested in this sort of stuff, read this: http://digitalcommons.ohsu.edu/csetech/91/ (28 pp.)

Answer 2

Most functional programming languages are not pure, i.e. they allow functions to not only depend on their values. In those languages it is perfectly possible to have a function returning the current time. From the languages you tagged this question with this applies to Scala and F# (as well as most other variants of ML).

In languages like Haskell and Clean, which are pure, the situation is different. In Haskell the current time would not be available through a function, but a so-called IO action, which is Haskell's way of encapsulating side effects.

In Clean it would be a function, but the function would take a world value as its argument and return a fresh world value (in addition to the current time) as its result. The type system would make sure that each world value can be used only once (and each function which consumes a world value would produces a new one). This way the time function would have to be called with a different argument each time and thus would be allowed to return a different time each time.

Answer 3

Yes, a getting time function can exist in functional programming using a slightly modified version on functional programming known as impure functional programming (the default or the main one is pure functional programming).

In case of getting the time (or reading file, or launching missile) the code needs to interact with the outer world to get the job done and this outer world is not based on the pure foundations of functional programming. To allow a pure functional programming world to interact with this impure outside world, people have introduced impure functional programming. After all, software which doesn't interact with the outside world isn't any useful other than doing some mathematical computations.

Few functional programming programming languages have this impurity feature inbuilt in them such that it is not easy to separate out which code is impure and which is pure (like F#, etc.) and some functional programming languages make sure that when you do some impure stuff that code is clearly stand out as compared to pure code, like Haskell.

Another interesting way to see this would be that your get time function in functional programming would take a "world" object which has the current state of the world like time, number of people living in the world, etc. Then getting time from which world object would be always pure i.e you pass in the same world state you will always get the same time.

Answer 4

In Haskell one uses a construct called monad to handle side effects. A monad basically means that you encapsulate values into a container and have some functions to chain functions from values to values inside a container. If our container has the type:

data IO a = IO (RealWorld -> (a,RealWorld))

we can safely implement IO actions. This type means: An action of type IO is a function, that takes a token of type RealWorld and returns a new token, together with a result.

The idea behind this is that each IO action mutates the outside state, represented by the magical token RealWorld. Using monads, one can chain multiple functions that mutate the real world together. The most important function of a monad is >>=, pronounced bind:

(>>=) :: IO a -> (a -> IO b) -> IO b

>>= takes one action and a function that takes the result of this action and creates a new action out of this. The return type is the new action. For instance, let's pretend there is a function now :: IO String, which returns a String representing the current time. We can chain it with the function putStrLn to print it out:

now >>= putStrLn

Or written in do-Notation, which is more familiar to an imperative programmer:

do currTime <- now
   putStrLn currTime

All this is pure, as we map the mutation and information about the world outside to the RealWorld token. So each time, you run this action, you get of course a different output, but the input is not the same: the RealWorld token is different.

Answer 5

Another way to explain it is this: no function can get the current time (since it keeps changing), but an action can get the current time. Let's say that getClockTime is a constant (or a nullary function, if you like) which represents the action of getting the current time. This action is the same every time no matter when it is used so it is a real constant.

Likewise, let's say print is a function which takes some time representation and prints it to the console. Since function calls cannot have side effects in a pure functional language, we instead imagine that it is a function which takes a timestamp and returns the action of printing it to the console. Again, this is a real function, because if you give it the same timestamp, it will return the same action of printing it every time.

Now, how can you print the current time to the console? Well, you have to combine the two actions. So how can we do that? We cannot just pass getClockTime to print, since print expects a timestamp, not an action. But we can imagine that there is an operator, >>=, which combines two actions, one which gets a timestamp, and one which takes one as argument and prints it. Applying this to the actions previously mentioned, the result is... tadaaa... a new action which gets the current time and prints it. And this is incidentally exactly how it is done in Haskell.

Prelude> System.Time.getClockTime >>= print
Fri Sep  2 01:13:23 東京 (標準時) 2011

So, conceptually, you can view it in this way: A pure functional program does not perform any I/O, it defines an action, which the runtime system then executes. The action is the same every time, but the result of executing it depends on the circumstances of when it is executed.

I don't know if this was any clearer than the other explanations, but it sometimes helps me to think of it this way.

Answer 6

You're broaching a very important subject in functional programming, that is, performing I/O. The way many pure languages go about it is by using embedded domain-specific languages, e.g., a sublanguage whose task it is to encode actions, which can have results.

The Haskell runtime for example expects me to define an action called main that is composed of all actions that make up my program. The runtime then executes this action. Most of the time, in doing so it executes pure code. From time to time the runtime will use the computed data to perform I/O and feeds back data back into pure code.

You might complain that this sounds like cheating, and in a way it is: by defining actions and expecting the runtime to execute them, the programmer can do everything a normal program can do. But Haskell's strong type system creates a strong barrier between pure and "impure" parts of the program: you cannot simply add, say, two seconds to the current CPU time, and print it, you have to define an action that results in the current CPU time, and pass the result on to another action that adds two seconds and prints the result. Writing too much of a program is considered bad style though, because it makes it hard to infer which effects are caused, compared to Haskell types that tell us everything we can know about what a value is.

Example: clock_t c = time(NULL); printf("%d\n", c + 2); in C, vs. main = getCPUTime >>= \c -> print (c + 2*1000*1000*1000*1000) in Haskell. The operator >>= is used to compose actions, passing the result of the first to a function resulting in the second action. This looking quite arcane, Haskell compilers support syntactic sugar that allows us to write the latter code as follows:

type Clock = Integer -- To make it more similar to the C code

-- An action that returns nothing, but might do something
main :: IO ()
main = do
    -- An action that returns an Integer, which we view as CPU Clock values
    c <- getCPUTime :: IO Clock
    -- An action that prints data, but returns nothing
    print (c + 2*1000*1000*1000*1000) :: IO ()

The latter looks quite imperative, doesn't it?