What's in an Emacs Lambda

There was recently some interesting discussion about correctly using backquotes to express a mixture of data and code. Since lambda expressions seem to evaluate to themselves, what’s the difference? For example, an association list of operations:

'((add . (lambda (a b) (+ a b)))
  (sub . (lambda (a b) (- a b)))
  (mul . (lambda (a b) (* a b)))
  (div . (lambda (a b) (/ a b))))

It looks like it would work, and indeed it does work in this case. However, there are good reasons to actually evaluate those lambda expressions. Eventually invoking the lambda expressions in the quoted form above are equivalent to using eval. So, instead, prefer the backquote form:

`((add . ,(lambda (a b) (+ a b)))
  (sub . ,(lambda (a b) (- a b)))
  (mul . ,(lambda (a b) (* a b)))
  (div . ,(lambda (a b) (/ a b))))

There are a lot of interesting things to say about this, but let’s first reduce it to two very simple cases:

(lambda (x) x)

'(lambda (x) x)

What’s the difference between these two forms? The first is a lambda expression, and it evaluates to a function object. The other is a quoted list that looks like a lambda expression, and it evaluates to a list — a piece of data.

A naive evaluation of these expressions in *scratch* (C-x C-e) suggests they are are identical, and so it would seem that quoting a lambda expression doesn’t really matter:

(lambda (x) x)
;; => (lambda (x) x)

'(lambda (x) x)
;; => (lambda (x) x)

However, there are two common situations where this is not the case: byte compilation and lexical scope.

Lambda under byte compilation

It’s a little trickier to evaluate these forms byte compiled in the scratch buffer since that doesn’t happen automatically. But if it did, it would look like this:

;;; -*- lexical-binding: nil; -*-

(lambda (x) x)
;; => #[(x) "\010\207" [x] 1]

'(lambda (x) x)
;; => (lambda (x) x)

The #[...] is the syntax for a byte-code function object. As discussed in detail in my byte-code internals article, it’s a special vector object that contains byte-code, and other metadata, for evaluation by Emacs’ virtual stack machine. Elisp is one of very few languages with readable function objects, and this feature is core to its ahead-of-time byte compilation.

The quote, by definition, prevents evaluation, and so inhibits byte compilation of the lambda expression. It’s vital that the byte compiler does not try to guess the programmer’s intent and compile the expression anyway, since that would interfere with lists that just so happen to look like lambda expressions — i.e. any list containing the lambda symbol.

There are three reasons you want your lambda expressions to get byte compiled:

While it’s common for personal configurations to skip byte compilation, Elisp should still generally be written as if it were going to be byte compiled. General rule of thumb: Ensure your lambda expressions are actually evaluated.

Lambda in lexical scope

As I’ve stressed many times, you should always use lexical scope. There’s no practical disadvantage or trade-off involved. Just do it.

Once lexical scope is enabled, the two expressions diverge even without byte compilation:

;;; -*- lexical-binding: t; -*-

(lambda (x) x)
;; => (closure (t) (x) x)

'(lambda (x) x)
;; => (lambda (x) x)

Under lexical scope, lambda expressions evaluate to closures. Closures capture their lexical environment in their closure object — nothing in this particular case. It’s a type of function object, making it a valid first argument to funcall.

Since the quote prevents the second expression from being evaluated, semantically it evaluates to a list that just so happens to look like a (non-closure) function object. Invoking a data object as a function is like using eval — i.e. executing data as code. Everyone already knows eval should not be used lightly.

It’s a little more interesting to look at a closure that actually captures a variable, so here’s a definition for constantly, a higher-order function that returns a closure that accepts any number of arguments and returns a particular constant:

(defun constantly (x)
  (lambda (&rest _) x))

Without byte compiling it, here’s an example of its return value:

(constantly :foo)
;; => (closure ((x . :foo) t) (&rest _) x)

The environment has been captured as an association list (with a trailing t), and we can plainly see that the variable x is bound to the symbol :foo in this closure. Consider that we could manipulate this data structure (e.g. setcdr or setf) to change the binding of x for this closure. This is essentially how closures mutate their own environment. Moreover, closures from the same environment share structure, so such mutations are also shared. More on this later.

Semantically, closures are distinct objects (via eq), even if the variables they close over are bound to the same value. This is because they each have a distinct environment attached to them, even if in some invisible way.

(eq (constantly :foo) (constantly :foo))
;; => nil

Without byte compilation, this is true even when there’s no lexical environment to capture:

(defun dummy ()
  (lambda () t))

(eq (dummy) (dummy))
;; => nil

The byte compiler is smart, though. As an optimization, the same closure object is reused when possible, avoiding unnecessary work, including multiple object allocations. Though this is a bit of an abstraction leak. A function can (ab)use this to introspect whether it’s been byte compiled:

(defun have-i-been-compiled-p ()
  (let ((funcs (vector nil nil)))
    (dotimes (i 2)
      (setf (aref funcs i) (lambda ())))
    (eq (aref funcs 0) (aref funcs 1))))

;; => nil

(byte-compile 'have-i-been-compiled-p)

;; => t

The trick here is to evaluate the exact same non-capturing lambda expression twice, which requires a loop (or at least some sort of branch). Semantically we should think of these closures as being distinct objects, but, if we squint our eyes a bit, we can see the effects of the behind-the-scenes optimization.

Don’t actually do this in practice, of course. That’s what byte-code-function-p is for, which won’t rely on a subtle implementation detail.


I mentioned before that one of the potential gotchas of not byte compiling your lambda expressions is overcapturing closure variables in the interpreter.

To evaluate lisp code, Emacs has both an interpreter and a virtual machine. The interpreter evaluates code in list form: cons cells, numbers, symbols, etc. The byte compiler is like the interpreter, but instead of directly executing those forms, it emits byte-code that, when evaluated by the virtual machine, produces identical visible results to the interpreter — in theory.

What this means is that Emacs contains two different implementations of Emacs Lisp, one in the interpreter and one in the byte compiler. The Emacs developers have been maintaining and expanding these implementations side-by-side for decades. A pitfall to this approach is that the implementations can, and do, diverge in their behavior. We saw this above with that introspective function, and it comes up in practice with advice.

Another way they diverge is in closure variable capture. For example:

;;; -*- lexical-binding: t; -*-

(defun overcapture (x y)
  (when y
    (lambda () x)))

(overcapture :x :some-big-value)
;; => (closure ((y . :some-big-value) (x . :x) t) nil x)

Notice that the closure captured y even though it’s unnecessary. This is because the interpreter doesn’t, and shouldn’t, take the time to analyze the body of the lambda to determine which variables should be captured. That would need to happen at run-time each time the lambda is evaluated, which would make the interpreter much slower. Overcapturing can get pretty messy if macros are introducing their own hidden variables.

On the other hand, the byte compiler can do this analysis just once at compile-time. And it’s already doing the analysis as part of its job. It can avoid this problem easily:

(overcapture :x :some-big-value)
;; => #[0 "\300\207" [:x] 1]

It’s clear that :some-big-value isn’t present in the closure.

But… how does this work?

How byte compiled closures are constructed

Recall from the internals article that the four core elements of a byte-code function object are:

  1. Parameter specification
  2. Byte-code string (opcodes)
  3. Constants vector
  4. Maximum stack usage

While a closure seems like compiling a whole new function each time the lambda expression is evaluated, there’s actually not that much to it! Namely, the behavior of the function remains the same. Only the closed-over environment changes.

What this means is that closures produced by a common lambda expression can all share the same byte-code string (second element). Their bodies are identical, so they compile to the same byte-code. Where they differ are in their constants vector (third element), which gets filled out according to the closed over environment. It’s clear just from examining the outputs:

(constantly :a)
;; => #[128 "\300\207" [:a] 2]

(constantly :b)
;; => #[128 "\300\207" [:b] 2]

constantly has three of the four components of the closure in its own constant pool. Its job is to construct the constants vector, and then assemble the whole thing into a byte-code function object (#[...]). Here it is with M-x disassemble:

0       constant  make-byte-code
1       constant  128
2       constant  "\300\207"
4       constant  vector
5       stack-ref 4
6       call      1
7       constant  2
8       call      4
9       return

(Note: since byte compiler doesn’t produce perfectly optimal code, I’ve simplified it for this discussion.)

It pushes most of its constants on the stack. Then the stack-ref 5 (5) puts x on the stack. Then it calls vector to create the constants vector (6). Finally, it constructs the function object (#[...]) by calling make-byte-code (8).

Since this might be clearer, here’s the same thing expressed back in terms of Elisp:

(defun constantly (x)
  (make-byte-code 128 "\300\207" (vector x) 2))

To see the disassembly of the closure’s byte-code:

(disassemble (constantly :x))

The result isn’t very surprising:

0       constant  :x
1       return

Things get a little more interesting when mutation is involved. Consider this adder closure generator, which mutates its environment every time it’s called:

(defun adder ()
  (let ((total 0))
    (lambda () (cl-incf total))))

(let ((count (adder)))
  (funcall count)
  (funcall count)
  (funcall count))
;; => 3

;; => #[0 "\300\211\242T\240\207" [(0)] 2]

The adder essentially works like this:

(defun adder ()
  (make-byte-code 0 "\300\211\242T\240\207" (vector (list 0)) 2))

In theory, this closure could operate by mutating its constants vector directly. But that wouldn’t be much of a constants vector, now would it!? Instead, mutated variables are boxed inside a cons cell. Closures don’t share constant vectors, so the main reason for boxing is to share variables between closures from the same environment. That is, they have the same cons in each of their constant vectors.

There’s no equivalent Elisp for the closure in adder, so here’s the disassembly:

0       constant  (0)
1       dup
2       car-safe
3       add1
4       setcar
5       return

It puts two references to boxed integer on the stack (constant, dup), unboxes the top one (car-safe), increments that unboxed integer, stores it back in the box (setcar) via the bottom reference, leaving the incremented value behind to be returned.

This all gets a little more interesting when closures interact:

(defun fancy-adder ()
  (let ((total 0))
    `(:add ,(lambda () (cl-incf total))
      :set ,(lambda (v) (setf total v))
      :get ,(lambda () total))))

(let ((counter (fancy-adder)))
  (funcall (plist-get counter :set) 100)
  (funcall (plist-get counter :add))
  (funcall (plist-get counter :add))
  (funcall (plist-get counter :get)))
;; => 102

;; => (:add #[0 "\300\211\242T\240\207" [(0)] 2]
;;     :set #[257 "\300\001\240\207" [(0)] 3]
;;     :get #[0 "\300\242\207" [(0)] 1])

This is starting to resemble object oriented programming, with methods acting upon fields stored in a common, closed-over environment.

All three closures share a common variable, total. Since I didn’t use print-circle, this isn’t obvious from the last result, but each of those (0) conses are the same object. When one closure mutates the box, they all see the change. Here’s essentially how fancy-adder is transformed by the byte compiler:

(defun fancy-adder ()
  (let ((box (list 0)))
    (list :add (make-byte-code 0 "\300\211\242T\240\207" (vector box) 2)
          :set (make-byte-code 257 "\300\001\240\207" (vector box) 3)
          :get (make-byte-code 0 "\300\242\207" (vector box) 1))))

The backquote in the original fancy-adder brings this article full circle. This final example wouldn’t work correctly if those lambdas weren’t evaluated properly.

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Chris Wellons