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Re: The poor state of documentation of pcase like things.

From: John Wiegley
Subject: Re: The poor state of documentation of pcase like things.
Date: Thu, 17 Dec 2015 16:42:13 -0800
User-agent: Gnus/5.130014 (Ma Gnus v0.14) Emacs/24.5 (darwin)

>>>>> Kaushal Modi <address@hidden> writes:

> I would welcome a short tutorial on how (and why) to use pcase.

The following is a brief pcase tutorial. I welcome any edits and comments.
Also, I wonder if anyone would be willing to hammer this into a form better
suited to the Emacs Lisp manual. I'm not familiar enough with the "language"
of that document at the moment to emulate it, though I could do some reading
next week if no one else is interested in word-smithing.


                         Pattern Matching with pcase

All data fits into some kind of pattern. The most explicit pattern is a
description of the data itself. Let's consider the following value as a
running example:

    '(1 2 (4 . 5) "Hello")

# Exact matches

Explicitly stated, this is a list of four elements, where the first two
elements are the integers 1 and 2, the third is a cons consisting of a car of
4 and a cdr of 5, and the fourth is the string "Hello". This states an
explicit pattern that we can match against using an equality test:

    (equal value '(1 2 (4 . 5) "Hello"))

# Pattern matches

Where patterns become useful is when we want to generalize a bit. Let's say we
want to do a similar equality test, but we don't care what the final string's
contents are, only that it's a string. Even though it's simply state, this
becomes quite difficult using an equality test:

    (and (equal (subseq value 0 3) '(1 2 (4 .5)))
         (stringp (nth 3 value)))

What we would prefer is a more direct language for encoding our description of
the *family of values we'd like to match against*. The way we said in English
was: the first three elements exactly so, and the last element, any string.
This is how we'd phrase that using `pcase':

    (pcase value
      (`(1 2 (4 . 5) ,(pred stringp))
        (message "It matched!")))

Think of `pcase' as a form of `cond', where instead of evaluating each test
for non-nil, it compares a series of *patterns* against the value under
consideration (often called the "scrutinee" in the literature). There can be
many patterns, and the first one wins, as with cond.

# Capturing matches

But `pcase' can go one step further: Not only can we compare a candidate value
against a family of possible values described by their pattern, we can also
"capture" sub-values from that pattern for later use. Continuing from the last
example, let's say we want to print the string that match, even though we
didn't care about the contents of the string for the sake of the match:

    (pcase value
      (`(1 2 (4 . 5) ,(and (pred stringp) foo))
        (message "It matched, and the string was %s" foo)))

Whenever a naked symbol like `foo' occurs as a UPattern (see next section),
the part of the value being matched at that position is bound to a local
variable of the same name.

# QPatterns and UPatterns

To master `pcase', there are two types of patterns you must know: UPatterns
and QPatterns. UPatterns are the "logical" aspect of pattern matching, where
we describe the kind of data we'd like to match against, and other special
actions to take when it matches; and QPatterns are the "literal" aspect,
stating the exact form of a particular match.

QPatterns are by far the easiest to think about. To match against any atom,
string, or list of the same, the corresponding QPattern is that exact value.
So the QPattern "foo" matches the string "foo", 1 matches the atom 1, etc.

`pcase' matches against a list of UPatterns, so to use a QPattern, we must
backquote it:

    (pcase value
      (`1 (message "Matched a 1"))
      (`2 (message "Matched a 2"))
      (`"Hello" (message "Matched the string Hello")))

The only special QPattern is the anti-quoting pattern, `,foo`, which allows
you to use UPatterns within QPatterns! The analogy to macro expansion is
direct, so you can think of them similarly.  For example:

    (pcase value
      (`(1 2 ,(or `3 `4))
       (message "Matched either the list (1 2 3) or (1 2 4)")))

# More on UPatterns

There are many special UPatterns, and their variety makes this the hardest
aspect to master. Let's consider them one by one.

## Underscore `_'

To match against anything whatsoever, no matter its type or value, use
underscore. Thus to match against a list containing anything at all at its
head, we'd use:

    (pcase value
      (`(_ 1 2)
       (message "Matched a list of anything followed by (2 3)")))

## Self-quoting

If an atom is self-quoting, we don't need to use backquotes to match against
it. This means that the QPattern `1 is identical to the UPattern 1:

    (pcase value
      (1 (message "Matched a 1"))
      (2 (message "Matched a 2"))
      ("Hello" (message "Matched the string Hello")))

## Symbol

When performing a match, if a symbol occurs within a UPattern, it binds
whatever was found at that position to a local symbol of the same name. Some
examples will help to make this clearer:

    (pcase value
      (`(1 2 ,foo 3)
       (message "Matched 1, 2, something now bound to foo, and 3"))
       (message "Match anything at all, and bind it to foo!"))
      (`(,the-car . ,the-cdr))
       (message "Match any cons cell, binding the car and cdr locally"))

The reason for doing this is two-fold: Either to refer to a previous match
later in the pattern (where it is compared using `eq'), or to make use of a
matched value within the related code block:

    (pcase value
      (`(1 2 ,foo ,foo 3)
       (message "Matched (1 2 %s %s 3)" foo)))

## `(or UPAT ...)` and `(and UPAT ...)

We can express boolean logic within a pattern match using the `or` and `and`

    (pcase value
      (`(1 2 ,(or 3 4)
         ,(and (pred stringp)
               (pred (string> "aaa"))
               (pred (lambda (x) (> (length x) 10)))))
       (message "Matched 1, 2, 3 or 4, and a long string "
                "that is lexically greater than 'aaa'")))

## `pred' predicates

Arbitrary predicates can be applied to matched elements, where the predicate
will be passed the object that matched. As in the previous example, lambdas
can be used to form arbitrarily complex predicates, with their own logic.

## guard expressions

At any point within a match, you may assert that something is true by
inserting a guard. This might consult some other variable to confirm the
validity of a pattern at a given time, or it might reference a local symbol
that was earlier bound by the match itself, as described above:

    (pcase value
      (`(1 2 ,foo ,(guard (and (not (numberp foo)) (/= foo 10)))
       (message "Matched 1, 2, anything, and then anything again, "
                "but only if the first anything wasn't the number 10"))))

Note that in this example, the guard occurs at a match position, so even
though the guard doesn't refer to what is being matched, if it passes, then
whatever occurs at that position (the fourth element of the list), would be an
unnamed successful matched. This is rather bad form, so we can be more
explicit about the logic here:

    (pcase value
      (`(1 2 ,(and foo (guard (and (not (numberp foo)) (/= foo 10)))) _)
       (message "Matched 1, 2, anything, and then anything again, "
                "but only if the first anything wasn't the number 10"))))

This means the same, but associates the guard with the value it tests, and
makes it clear that we don't care what the fourth element is, only that it

## Pattern let bindings

Within a pattern we can match sub-patterns, using a special form of let that
has a meaning specific to `pcase':

    (pcase value
      (`(1 2 ,(and foo (let 3 foo)))
       (message "A weird way of matching (1 2 3)")))

This example is a bit contrived, but it allows us to build up complex guard
patterns that might match against values captured elsewhere in the surrounding

    (pcase value1
      (`(1 2 ,foo)
       (pcase value2
         (`(1 2 ,(and (let (or 3 4) foo) bar))
          (message "A nested pcase depends on the results of the first")))))

Here the third value of `value2' -- which must be a list of exactly three
elements, starting with 1 and 2 -- is being bound to the local variable `bar',
but only if foo was a 3 or 4. There are many other ways this logic could be
expressed, but this gives you a test of how flexibly you can introduce
arbitrary pattern matching of other values within any UPattern.

# `pcase-let' and `pcase-let*'

That's all there is to know about `pcase'! The other two utilities you might
like to use are `pcase-let` and `pcase-let*`, which do similar things to their
UPattern counter-part `let', but as regular Lisp forms:

    (pcase-let ((`(1 2 ,foo) value1)
                (`(3 4 ,bar) value2))
      (message "value1 is a list of (1 2 %s); value2 ends with %s"
               foo bar))

Note that `pcase-let' does not fail, and always executes the correspond forms
unless there is a type error. That is, `value1' above is not required to fit
the form of the match exactly. Rather, every binding that can paired is bound
to its corresponding element, but every binding that cannot is bound to nil:

    (pcase-let ((`(1 2 ,foo) '(10)))
      (message "foo = %s" foo))   => prints "foo = nil"

    (pcase-let ((`(1 2 ,foo) 10))
      (message "foo = %s" foo))   => Lisp error, 10 is not a list

    (pcase-let ((`(1 2 ,foo) '(3 4 10)))
      (message "foo = %s" foo))   => prints "foo = 10"

Thus, `pcase-let' could be thought of as a more expressive form of

The `pcase-let*' variant, like `let*', allows you to reference bound local
symbols from prior matches.

    (pcase-let* ((`(1 2 ,foo) '(1 2 3))
                 (`(3 4 ,bar) (list 3 4 foo)))
      (message "foo = %s, bar = %s" foo bar))  => foo = 3, bar = 3

However, if you name a symbol with same name in a later UPattern, it is not
used as an `eq' test, but rather shadows that symbol:

    (pcase-let* ((`(1 2 ,foo) '(1 2 3))
                 (`(3 4 ,foo) '(3 4 5)))
      (message "1 2 %s" foo))

This prints out "1 2 5", rather current match.

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