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This is the answer to the following question:

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)

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)!

Note

If you got this right, you should really be using Pyke!

More:

Literal Patterns

Explanation of literal patterns.

Pattern Variables

Explanation of pattern variables.

Tuple Patterns

Explanation of tuple patterns.

Matching Two Patterns

Explanation of matching two patterns together, vs matching a pattern to data.