Emacs: Pattern Matching with pcase

This is a tutorial on how to use the pcase macro in modern flavors of GNU Emacs.

Exact matches

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")

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 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 logical pattern (see next section), the part of the value being matched at that position is bound to a local variable of the same name.

Logical and literal patterns

To master pcase, there are two types of patterns you must know: Logical patterns, and literal, or quoted, patterns. Logical patterns describe the kind of data we’d like to match against, and other special actions to take when it matches; and quoted patterns are the “literal” aspect, stating the exact form of a particular match.

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

pcase matches against a list of logical patterns, so to use a literal pattern, we must quote it, unless it consists entirely of self-quoting atoms:

(pcase value
  ('sym (message "Matched the symbol `sym'"))
  ((1 2) (message "Matched the list (1 2)")))

Literal patterns may also be introduced using a backquote, in which case commas may be used to place logical patterns within them, in exactly the same way that quoting and anti-quoting works for macros. For example:

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

More on logical patterns

There are many special logical patterns. 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 (1 2)")))


When performing a match, if a symbol occurs within a logical pattern, 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 PAT ...) and (and PAT ...)

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

(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. See above for examples.

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 exists.

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 code:

(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 logical pattern.

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 logical pattern 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 can be thought of as a more expressive form of destructuring-bind.

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 logical pattern, 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 than the current match.