Okay, is *this* monadic?

Question

I'm putting a security layer in front of a document-oriented and I needed a reasonably abstract way for the application to define what new documents and what updates to existing documents are legal for a particular user.

The particular issues are -- The documents are defined (at least in transit) as JSON objects, so the rules may be hierarchical and so the rule-engine has to work recursively. For example, the Employee object may have a sub-object called Compensation and that sub-object has a field called PayPeriod that must be one of 'weekly', 'biweekly', or 'monthly'. -- it runs Node.js and some rules need to read from input (for example, to read more user data from a database) , so it has to run in continuation style.

So what I came up with is this: each rule is a function that takes the current value, the proposed new value, and a callback that is invoked with the value to be used. That value can be one of the two inputs or some third value calculated by the rule. Here's one rule:

var nonEmpty = function(proposedValue, existingValue, callback) {
    callback( (proposedValue.length > 0) ? proposedValue : existingValue);
};

This rule would only allow you to set or replaces this field with a non-zero-length value. Of course, that only makes sense for string values (ignore lists for the moment, so we need a rule to enforce string-ness):

var isString = function(proposedValue, existingValue, callback) {
    callback( ( typeof(proposedValue) === 'string') ? proposedValue : existingValue);
};

In fact, that seems like a common sort of problem, so I wrote a rule generator:

var ofType = function(typeName) {
    return function(proposedValue, existingValue, callback) {
    callback( ( typeof(proposedValue) === typeName) ? proposedValue : existingValue);
    };
};

var isString = ofType('string')

but I need a way to string rules together:

var and = function(f1, f2) {
    return function(proposedValue, existingValue, callback) {
    f1(proposedValue, existingValue, 
       function(newProposedValue) {
           f2(newProposedValue, existingValue, callback);
       });
    };
};

var nonEmptyString = and(isString, nonEmpty);

So the rule for an adminstrator to update an Employee record might be:

limitedObject({
   lastName : nonEmptyString,
   firstName : nonEmptyString,
   compensation : limitedObject({
      payPeriod : oneOf('weekly', 'biweekly', 'monthly'),
      pay : numeric
  }
}) 

limitedObject (like ofType) is a rule-generating function, and it that only allows the fields specified in its argument and applies the given rule to the values of those fields.

So I wrote all this, and it works like a charm. All my bugs turned out to be errors in the unit tests! Well, almost all of them. Anyway, if you've read this far, here is my question:

I've been febrilely studying monads and my reading inspired me to solve the problem this way. But, is this truly monadic?

(Possible answers: "Yes", "No, but that's okay because monads aren't really the right approach for this problem", and "No, and here's what needs to change". Fourth possibilities also welcome.)

Answer 1

No, this does not appear to be monadic. What you've defined appears to be a mini-DSL of rule combinators, where you have simple rules like ofType(typeName) and ways of combining rules into bigger rules like and(rule1, rule2).

In order to have a monad, you need some notion of context in which you can put any value. You also need the following operations:

1. A function wrap(x) for putting any value into some default context.
2. A function map(f, m) for applying a function f to transform the value within m without altering the context.
3. A function flatten(mm) for flattening two layers of context into one.

These operations must satisfy certain "obvious" laws:

1. Adding a layer of context on the outside and collapsing gives you back what you started with.

   flatten(wrap(m)) == m
   

2. Adding a layer of context on the inside and collapsing gives you back what you started with.

   flatten(map(wrap, m)) == m
   

3. If you have a value with three layers of context, it does not matter whether you collapse the two inner or the two outer layers first.

   flatten(flatten(mmm)) == flatten(map(flatten, mmm))
   

It is also possible to define a monad in terms of wrap as above and another operation bind, however this is equivalent to the above, as you can define bind in terms of map and flatten, and vice versa.

function bind(f, m) { return flatten(map(f, m)); }

# or

function map(f, m) { return bind(function(x) { return wrap(f(x)); }, m); }
function flatten(mm) { return bind(function(x) { return x; }, mm); }

It is not clear what the notion of context would be here, how you would turn any value into a rule. Thus the question of how to flatten two layers of rules makes even less sense.

I don't think a monad is a suitable abstraction here.

However there it is easy to see that your and does form a monoid with the always-succeeding rule (shown below) as the identity element.

function anything(proposedValue, existingValue, callback) {
    callback(proposedValue);
}