Approaches to currying in JavaScript

August 21, 2010

JavaScript’s dynamic nature makes it hard to straightforwardly apply many functional programming idioms. One example of this is currying: any function may be passed an arbitrary number of arguments, making it impossible to write a truly general currying function.

To recap, currying is a technique for transforming a function which accepts n parameters into a nest of partially applicable functions. Consider the function f = λxyz.M, which has three parameters, x, y and z. By currying, we obtain a new function f* = λx.(λy.(λz.M)).

One simple example is currying an add function which accepts 2 parameters and returns the result of adding them together.

var add = function(a, b) {
    return a + b;
};

var curriedAdd = function(a) {
    return function(b) {
        return a + b;
    };
};

A function which returns the result of evaluating a quadratic expression demonstrates more clearly the ‘nesting’ of functions which currying produces.

var quadratic = function(a, b, c, x) {
    return a * x * x + b * x + c;
};

var curriedQuadratic = function(a) {
    return function(b) {
        return function(c) {
            return function(x) {
                return a * x * x + b * x + c;
            };
        };
    };
};

Given a pattern like this, the obvious question is how to generalise it. Ideally, we would write a curry function to automatically transform functions like quadratic into ones like curriedQuadratic. The simplest approach is to make curried functions always return a single wrapping function:

var naiveCurry = function(f) {
    var args = Array.prototype.slice.call(arguments, 1);
    
    return function() {
        var largs = Array.prototype.slice.call(arguments, 0);
        return f.apply(this, args.concat(largs));
    };
};

Clearly this is not true currying, except for functions of arity 2. We cannot use it to perform the transformation from quadratic to curriedQuadratic.

A cleverer approach would be to detect the arity of the function we wish to curry. To do this, we can use the length property of the function, which returns the number of named arguments the function accepts. Math.tan.length is 1, while parseInt.length is 2.

var curryByLength = function(f) {
    var arity = f.length,
        args  = Array.prototype.slice.call(arguments, 1),
    
    accumulator = function() {
        var largs = args;
        
        if (arguments.length > 0) {
            // We must be careful to copy the `args` array with `concat` rather
            // than mutate it; otherwise, executing curried functions can have
            // strange non-local effects on other curried functions.
            largs = largs.concat(Array.prototype.slice.call(arguments, 0));
        }
        
        if (largs.length >= arity) {
            return f.apply(this, largs);
        } else {
            return curryByLength.apply(this, [f].concat(largs));
        }
    };
    
    return args.length >= arity ? accumulator() : accumulator;
};

However, the length property of any given JavaScript function can easily mislead. To begin with, we often find it useful to define functions with optional parameters.

var someFunction = function(a, flag) {
    if (flag) {
        // Some computation involving a
    } else {
        // Some other computation involving a
    }
};

Now consider a variadic function, like Math.max, which returns the largest number amongst its arguments. Despite the fact that it can in fact be called with any number of arguments, including 0 and 1, it has a length property of 2. Consequently, our ‘smarter’ curry function will only work with Math.max up to a point. This will throw a type error, even though Math.max will accept three arguments quite happily:

curryByLength(Math.max)(1)(2)(3);

Currying Math.max limits its utility to discriminating between two numbers, not n numbers. We can easily think of similar examples—other variadic functions, functions with optional arguments, and similarly clever abuses of JavaScript’s dynamic arguments to create complex APIs. jQuery’s bind method could be considered an example of this: the event handler can be passed to the method as either the second or the third argument, depending on whether the user wishes to use the optional eventData parameter or not.

It is easy to see that there is no general way of resolving this issue: currying is essentially at odds with variadic functions and the ability to change the number of arguments a function accepts at runtime. However, one’s choices are not limited simply to the approaches discussed above; there are alternatives, even if they do not fully dispose of the problem of dynamic arity.

Firstly, one can simply leave things as they are, with the curry function having a known limitation around functions with dynamic arity. The burden is placed on the user to ensure they take care when currying.

Alternatively, one could make the arity an explicit component of the curry function. This differs from the implicit detection of the arity via the curried function’s length property (however, the implementation is almost identical).

var curryWithExplicitArity = function(f, n) {
    var args = Array.prototype.slice.call(arguments, 2),
    
    accumulator = function() {
        var largs = args;
        
        if (arguments.length > 0) {
            largs = largs.concat(Array.prototype.slice.call(arguments, 0));
        }
        
        if (largs.length >= n) {
            return f.apply(this, largs);
        } else {
            return curryByLength.apply(this, [f].concat(largs));
        }
    };
    
    return args.length >= n ? accumulator() : accumulator;
};

Finally, one could have entirely different curry functions for each arity. This has the benefit of being explicit, and while it doesn’t solve the problem of functions with dynamic arity, it does mean that one doesn’t have to specify the arity of the function one wishes to curry each time as an additional parameter. Instead of writing curry(f, 3), one can simply write curry3(f).

In fact, there is a way to combine these last two approaches, by writing a function which generates curry functions for any given arity.

var ncurry = function(n) {
    var _curry = function(f) {
        var args = Array.prototype.slice.call(arguments, 1),
        
        return function() {
            var largs = args.concat(Array.prototype.slice.call(arguments, 0));
            
            if (largs.length < n) {
                largs.unshift(f);
                return _curry.apply(null, largs);
            } else {
                return f.apply(null, largs);
            }
        };
    };
    
    return _curry;
};

For common use cases such as functions which accept 2 or 3 arguments, one can write simple aliases using ncurry, while one can always use ncurry ‘inline’ where necessary.

var curry  = ncurry(2),
    curry3 = ncurry(3);

// Presumably `f7` is a function which accepts 7 arguments
var fc7 = ncurry(7)(f7);

However, oftentimes something along the lines of curryByLength is preferable. If the library of functions one is working with consists of a set of functions with well-defined lists of parameters, then implicit rather than explicit conversion can be more convenient and more natural; it is, after all, rather nicer to be able to write curry(f) than curry(f, n) or even ncurry(n)(f).

Ultimately which approach one decides to take must be based on understanding of the properties of the functions one is working with. A choice of currying function will then arise naturally—and after all, one can always use several. Both of these approaches are available in Udon, my library for functional programming in JavaScript, as Udon.curry and Udon.ncurry.

Extralogical

Approaches to currying in JavaScript

Further reading & prior art