Truly declarative language?

Does anyone know of a truly declarative language? The behavior I'm looking for is kind of what Excel does, where I can define variables and formulas, and have the formula's result change when the input changes (without having set the answer again myself)

The behavior I'm looking for is best shown with this pseudo code:

X = 10     // define and assign two variables
Y = 20;

Z = X + Y  // declare a formula that uses these two variables

X = 50     // change one of the input variables

?Z         // asking for Z should now give 70 (50 + 20)

I've tried this in a lot of languages like F#, python, matlab etc, but every time I tried this they come up with 30 instead of 70. Which is correct from an imperative point of view, but I'm looking for a more declarative behavior if you know what I mean.

And this is just a very simple calculatio开发者_运维知识库n. When things get more difficult it should handle stuff like recursion and memoization automagically.

The code below would obviously work in C# but it's just so much code for the job, I'm looking for something a bit more to the point without all that 'technical noise'

class BlaBla{
    public int X {get;set;}  // this used to be even worse before 3.0
    public int Y {get;set;}
    public int Z {get{return X + Y;}}
}

static void main(){
   BlaBla bla = new BlaBla();
   bla.X = 10;
   bla.Y = 20;
   // can't define anything here
   bla.X = 50; // bit pointless here but I'll do it anyway. 
   Console.Writeline(bla.Z);// 70, hurray!
}

This just seems like so much code, curly braces and semicolons that add nothing.

Is there a language/ application (apart from Excel) that does this? Maybe I'm no doing it right in the mentioned languages, or I've completely missed an app that does just this.

I prototyped a language/ application that does this (along with some other stuff) and am thinking of productizing it. I just can't believe it's not there yet. Don't want to waste my time.

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Any Constraint Programming system will do that for you. Examples of CP systems that have an associated language are ECLiPSe, SICSTUS Prolog / CP package, Comet, MiniZinc, ...

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It looks like you just want to make Z store a function instead of a value. In C#:

var X = 10;    // define and assign two variables
var Y = 20;

Func<int> Z = () => X + Y;  // declare a formula that uses these two variables

Console.WriteLine(Z());

X = 50;     // change one of the input variables

Console.WriteLine(Z());

So the equivalent of your ?-prefix syntax is a ()-suffix, but otherwise it's identical. A lambda is a "formula" in your terminology.

Behind the scenes, the C# compiler builds almost exactly what you presented in your C# conceptual example: it makes X into a field in a compiler-generated class, and allocates an instance of that class when the code block is entered. So congratulations, you have re-discovered lambdas! :)

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In Mathematica, you can do this:

x = 10;     (* # assign 30 to the variable x *)
y = 20;     (* # assign 20 to the variable y *)
z := x + y; (* # assign the expression x+y to the variable z *)
Print[z];
(* # prints 30 *)
x = 50;
Print[z];
(* # prints 70 *)

The operator := (SetDelayed) is different from = (Set). The former binds an unevaluated expression to a variable, the latter binds an evaluated expression.

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Wanting to have two definitions of X is inherently imperative. In a truly declarative language you have a single definition of a variable in a single scope. The behavior you want from Excel corresponds to editing the program.

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Have you seen Resolver One? It's like Excel with a real programming language behind it.

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Here is Daniel's example in Python, since I noticed you said you tried it in Python.

x = 10
y = 10

z = lambda: x + y

# Output: 20
print z()

x = 20

# Output: 30
print z()

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Two things you can look at are the cells lisp library, and the Modelica dynamic modelling language, both of which have relation/equation capabilities.

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There is a Lisp library with this sort of behaviour:

http://common-lisp.net/project/cells/

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JavaFX will do that for you if you use bind instead of = for Z

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react is an OCaml frp library. Contrary to naive emulations with closures it will recalculate values only when needed

        Objective Caml version 3.11.2

# #use "topfind";;
# #require "react";;
# open React;;
# let (x,setx) = S.create 10;;
val x : int React.signal = <abstr>
val setx : int -> unit = <fun>
# let (y,sety) = S.create 20;;
val y : int React.signal = <abstr>
val sety : int -> unit = <fun>
# let z = S.Int.(+) x y;;
val z : int React.signal = <abstr>
# S.value z;;
- : int = 30
# setx 50;;
- : unit = ()
# S.value z;;
- : int = 70

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You can do this in Tcl, somewhat. In tcl you can set a trace on a variable such that whenever it is accessed a procedure can be invoked. That procedure can recalculate the value on the fly.

Following is a working example that does more or less what you ask:

proc main {} {
    set x 10
    set y 20
    define z {$x + $y}

    puts "z (x=$x): $z"
    set x 50
    puts "z (x=$x): $z"
}


proc define {name formula} {
    global cache
    set cache($name) $formula
    uplevel trace add variable $name read compute
}

proc compute {name _ op} {
    global cache
    upvar $name var
    if {[info exists cache($name)]} {
        set expr $cache($name)
    } else {
        set expr $var
    }
    set var [uplevel expr $expr]
}

main

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Groovy and the magic of closures.

def (x, y) = [ 10, 20 ]

def z = { x + y }

assert 30 == z()

x = 50

assert 70 == z()

def f = { n -> n + 1 }  // define another closure

def g = { x + f(x) }    // ref that closure in another

assert 101 == g()       // x=50, x + (x + 1)

f = { n -> n + 5 }     // redefine f()

assert 105 == g()      // x=50, x + (x + 5)

It's possible to add automagic memoization to functions too but it's a lot more complex than just one or two lines. http://blog.dinkla.net/?p=10

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In F#, a little verbosily:

let x = ref 10
let y = ref 20

let z () = !x + !y

z();;
y <- 40
z();;

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You can mimic it in Ruby:

x = 10
y = 20
z = lambda { x + y }
z.call    # => 30
z = 50
z.call    # => 70

Not quite the same as what you want, but pretty close.

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not sure how well metapost (1) would work for your application, but it is declarative.

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Lua 5.1.4 Copyright (C) 1994-2008 Lua.org, PUC-Rio

x = 10
y = 20
z = function() return x + y; end
x = 50
= z()
70

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It's not what you're looking for, but Hardware Description Languages are, by definition, "declarative".

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This F# code should do the trick. You can use lazy evaluation (System.Lazy object) to ensure your expression will be evaluated when actually needed, not sooner.

let mutable x = 10;
let y = 20;

let z = lazy (x + y);
x <- 30;

printf "%d" z.Value