We’ve barely scratched the surface of matching as implemented in Eq. We now need to digg into the subject by following a tiny example. I’ve not yet implemented a modulo operator in the language, so it’s a nice occasion to implement one ourselves.
Let’s write our modulo in the most straightforward way. .. command-output:: cat docexample/modulo101.txt
Here we have written a loop within the modintern function, the condition of the loop is symbolized by the first argument, unifying to a boolean. The rest can be seen as a local variable, as for the num. We remove the modulo while the rest is still greater than it. So, now let’s try it.
$ eq eval -f docexample/modulo101.txt; true
No function definition match the parameters
modintern(n < p, n, p)
No function definition match the parameters
modintern(rest - num < num, rest - num, num)
2
We got two errors we some cryptic messages (yes it’s in my <strong>`TODO`</strong> list to ameliorate them). But what the OMGWTFBBQ!!!!111!!!ELEVEN!!! has happenned? the problem is :=
The := operator let you set the value of a variable. The right and side of the operator (3 here), is evaluated at the definition site.
modintern( false, rest, num ) := modintern( rest - num < num, rest - num, num );
The first arrise when we use the second definition of the function. We already have defined a part of the function. As the := operator evaluate it’s right part, it tries to match ( rest - num < num, rest - num, num ) As those variables are not yet defined, they cannot be reduced to a boolean. And as you can imagine true =~= (rest - num < num, rest - num, num) is false. (I use =~= as a shorthand for matching, don’t try to use it, it doesn’t exist, yet). In the same way the difinition of the modulo function can only fail.
So, new program :
$ cat docexample/modulo606.txt
modintern( true, rest, num ) :> rest;
modintern( false, rest, num ) :> modintern( rest - num < num, rest - num, num );
modulo( n, p ) :> modintern( n < p, n, p );
modulo( 18, 4 )
Notice the new :> operator.
$ eq eval -f docexample/modulo606.txt
2
The :> operator is the Lazy attribute operator. It has exactly the same function as :=, but it doesn’t evaluate it’s right side. It kept it’s right side frozen, the right side is unfrozen when the function is called. All the functions in the standard library are defined with the Lazy operator to avoid problem at definition site.
$ eq eval "x - 3 = x - 3"
3 + x = 3 + x
The = is thought to compare equality on value, but some times you want to check deep equality, like in the previous sample. The two sub-tree are identical, you could try to write some weird function deconstructing the two subexpression to provide equality. Or you can try a very simple trick.
$ eq eval "equal( a, a ) :> true; equal( a, b ) :> false; equal( x - 3, x - 3)"
true
equal( a, a ) does all the job, the first argument match himself with the variable, and then a is substituted by the first argument in the argument list and in the function body. Then the second argument has a complex tree to match to. If it does, the first equation is chosen, giving a deep equality check. Otherwise, the all accepting clause equal( a, b ) is selected and reject the equality.