Pathological Answer

Pathological Question

What is the bound value of pattern variable $y after matching the following two tuple patterns:

Tuple pattern A:

((ho, $_, ($a, $a)), ($a, $a, $b), ($a, *$b))

Tuple pattern B:

($x, $x, $y)

Answer

Let's take this step by step, matching each element of the two tuple patterns in turn.

1. Match (ho, $_, ($a, $a)) to $x.

   This succeeds with the following binding:

   $x:

   (ho, $_, ($a, $a))

2. Match ($a, $a, $b) to $x.

   Because $x is bound to a value, this becomes the same as matching:

   • ($a, $a, $b) to
   • (ho, $_, ($a, $a))

   Which succeeds, binding:

   $a:

   ho

   $b:

   ($a, $a)

   $_ is an anonymous variable, so it is not bound (or bound to).

3. Match ($a, *$b) to $y.

   Because both $a and $b have bound values, this becomes the same as matching:

   • (ho, ho, ho) to
   • $y

   Which succeeds, binding:

   $y:

   (ho, ho, ho)

So the overall match succeeds with the following bindings:

$x:

(ho, $_, ($a, $a))

$a:

ho

$b:

($a, $a)

$y:

(ho, ho, ho)

And so $y is (ho, ho, ho)!