I'd like to learn more about lisp macros and I want to create a simple implementation of the defun macro.
I'm also interested in lisp's source code in all the implementations.
This is a tricky question, because of bootstrapping: defun does a lot of things (iow, calls a lot of functions), but to define those functions one needs a working defun. Thus there are three(3!) definitions of defun in clisp/src/init.lisp: at lines
228
1789
1946
The very basic definition of defun could be this:
(defmacro defun (fname lambda-list &rest body)
`(setf (fdefinition ',fname)
(lambda ,lambda-list
(block ,fname ,#body))))
In fact, this is the first definition of defun in CLISP (line 228), except that there is no defmacro and no backquote at that moment yet, so the actual code looks a lot uglier.
See also Is defun or setf preferred for creating function definitions in common lisp and why? where I discuss macroexpansions of defuns.
You can easily check how your particular CL implementation, implemented defun by running
(macroexpand '(defun add2 (x) (+ x 2)))
On SBCL it expands to:
(PROGN
(EVAL-WHEN (:COMPILE-TOPLEVEL) (SB-C:%COMPILER-DEFUN 'ADD2 NIL T))
(SB-IMPL::%DEFUN 'ADD2
(SB-INT:NAMED-LAMBDA ADD2
(X)
(BLOCK ADD2 (+ X 2)))
(SB-C:SOURCE-LOCATION)))
T
To see the particular source code that implemented the I would use (on Emacs) the M-. key binding and then I will write defun and hit enter. Then Emacs will get to the source code:
(sb!xc:defmacro defun (&environment env name lambda-list &body body)
#!+sb-doc
"Define a function at top level."
[...]
I am not going to paste the whole macro as it is rather long. If you are not on Emacs, you can try searching in the repos as most implementations are open source.
BTW defun is not so special. You can implement much of it with setf-inf a symbol-function to a lambda. E.g.:
(setf (symbol-function 'ADD3) #'(lambda (x) (+ x 3)))
; => #<FUNCTION (LAMBDA (X)) {1006E94EBB}>
(add3 4)
; => 7
Related
In this post, I ask tangentially why when I declare in SBCL
(defun a (&rest x)
x)
and then check what the function cell holds
(describe 'a)
COMMON-LISP-USER::A
[symbol]
A names a compiled function:
Lambda-list: (&REST X)
Derived type: (FUNCTION * (VALUES LIST &OPTIONAL))
Source form:
(LAMBDA (&REST X) (BLOCK A X))
I see this particular breakdown of the original function. Could someone explain what this output means? I'm especially confused by the last line
Source form:
(LAMBDA (&REST X) (BLOCK A X))
This is mysterious because for some reason not clear to me Lisp has transformed the original function into a lambda expression. It would also be nice to know the details of how a function broken down like this is then called. This example is SBCL. In Elisp
(symbol-function 'a)
gives
(lambda (&rest x) x)
again, bizarre. As I said in the other post, this is easier to understand in Scheme -- but that created confusion in the answers. So once more I ask, Why has Lisp taken a normal function declaration and seemingly stored it as a lambda expression?
I'm still a bit unclear what you are confused about, but here is an attempt to explain it. I will stick to CL (and mostly to ANSI CL), because elisp has a lot of historical oddities which just make things hard to understand (there is an appendix on elisp). Pre-ANSI CL was also a lot less clear on various things.
I'll try to explain things by writing a macro which is a simple version of defun: I'll call this defun/simple, and an example of its use will be
(defun/simple foo (x)
(+ x x))
So what I need to do is to work out what the expansion of this macro should be, so that it does something broadly equivalent (but simpler than) defun.
The function namespace & fdefinition
First of all I assume you are comfortable with the idea that, in CL (and elisp) the namespace of functions is different than the namespace of variable bindings: both languages are lisp-2s. So in a form like (f x), f is looked up in the namespace of function bindings, while x is looked up in the namespace of variable bindings. This means that forms like
(let ((sin 0.0))
(sin sin))
are fine in CL or elisp, while in Scheme they would be an error, as 0.0 is not a function, because Scheme is a lisp-1.
So we need some way of accessing that namespace, and in CL the most general way of doing that is fdefinition: (fdefinition <function name>) gets the function definition of <function name>, where <function name> is something which names a function, which for our purposes will be a symbol.
fdefinition is what CL calls an accessor: this means that the setf macro knows what to do with it, so that we can mutate the function binding of a symbol by (setf (fdefinition ...) ...). (This is not true: what we can access and mutate with fdefinition is the top-level function binding of a symbol, we can't access or mutate lexical function bindings, and CL provides no way to do this, but this does not matter here.)
So this tells us what our macro expansion needs to look like: we want to set the (top-level) definition of the name to some function object. The expansion of the macro should be like this:
(defun/simple foo (x)
x)
should expand to something involving
(setf (fdefinition 'foo) <form which makes a function>)
So we can write this bit of the macro now:
(defmacro defun/simple (name arglist &body forms)
`(progn
(setf (fdefinition ',name)
,(make-function-form name arglist forms))
',name))
This is the complete definition of this macro. It uses progn in its expansion so that the result of expanding it is the name of the function being defined, which is the same as defun: the expansion does all its real work by side-effect.
But defun/simple relies on a helper function, called make-function-form, which I haven't defined yet, so you can't actually use it yet.
Function forms
So now we need to write make-function-form. This function is called at macroexpansion time: it's job is not to make a function: it's to return a bit of source code which will make a function, which I'm calling a 'function form'.
So, what do function forms look like in CL? Well, there's really only one such form in portable CL (this might be wrong, but I think it is true), which is a form constructed using the special operator function. So we're going to need to return some form which looks like (function ...). Well, what can ... be? There are two cases for function.
(function <name>) denotes the function named by <name> in the current lexical environment. So (function car) is the function we call when we say (car x).
(function (lambda ...)) denotes a function specified by (lambda ...): a lambda expression.
The second of these is the only (caveats as above) way we can construct a form which denotes a new function. So make-function-form is going to need to return this second variety of function form.
So we can write an initial version of make-function-form:
(defun make-function-form (name arglist forms)
(declare (ignore name))
`(function (lambda ,arglist ,#forms)))
And this is enough for defun/simple to work:
> (defun/simple plus/2 (a b)
(+ a b))
plus/2
> (plus/2 1 2)
3
But it's not quite right yet: one of the things that functions defined by defun can do is return from themselves: they know their own name and can use return-from to return from it:
> (defun silly (x)
(return-from silly 3)
(explode-the-world x))
silly
> (silly 'yes)
3
defun/simple can't do this, yet. To do this, make-function-form needs to insert a suitable block around the body of the function:
(defun make-function-form (name arglist forms)
`(function (lambda ,arglist
(block ,name
,#forms))))
And now:
> (defun/simple silly (x)
(return-from silly 3)
(explode-the-world x))
silly
> (silly 'yes)
3
And all is well.
This is the final definition of defun/simple and its auxiliary function.
Looking at the expansion of defun/simple
We can do this with macroexpand in the usual way:
> (macroexpand '(defun/simple foo (x) x))
(progn
(setf (fdefinition 'foo)
#'(lambda (x)
(block foo
x)))
'foo)
t
The only thing that's confusing here is that, because (function ...) is common in source code, there's syntactic sugar for it which is #'...: this is the same reason that quote has special syntax.
It's worth looking at the macroexpansion of real defun forms: they usually have a bunch of implementation-specific stuff in them, but you can find the same thing there. Here's an example from LW:
> (macroexpand '(defun foo (x) x))
(compiler-let ((dspec::*location* '(:inside (defun foo) :listener)))
(compiler::top-level-form-name (defun foo)
(dspec:install-defun 'foo
(dspec:location)
#'(lambda (x)
(declare (system::source-level
#<eq Hash Table{0} 42101FCD5B>))
(declare (lambda-name foo))
x))))
t
Well, there's a lot of extra stuff in here, and LW obviously has some trick around this (declare (lambda-name ...)) form which lets return-from work without an explicit block. But you can see that basically the same thing is going on.
Conclusion: how you make functions
In conclusion: a macro like defun, or any other function-defining form, needs to expand to a form which, when evaluated, will construct a function. CL offers exactly one such form: (function (lambda ...)): that's how you make functions in CL. So something like defun necessarily has to expand to something like this. (To be precise: any portable version of defun: implementations are somewhat free to do implementation-magic & may do so. However they are not free to add a new special operator.)
What you are seeing when you call describe is that, after SBCL has compiled your function, it's remembered what the source form was, and the source form was exactly the one you would have got from the defun/simple macro given here.
Notes
lambda as a macro
In ANSI CL, lambda is defined as a macro whose expansion is a suitable (function (lambda ...)) form:
> (macroexpand '(lambda (x) x))
#'(lambda (x) x)
t
> (car (macroexpand '(lambda (x) x)))
function
This means that you don't have to write (function (lambda ...)) yourself: you can rely on the macro definition of lambda doing it for you. Historically, lambda wasn't always a macro in CL: I can't find my copy of CLtL1, but I'm pretty certain it was not defined as one there. I'm reasonably sure that the macro definition of lambda arrived so that it was possible to write ISLisp-compatible programs on top of CL. It has to be in the language because lambda is in the CL package and so users can't portably define macros for it (although quite often they did define such a macro, or at least I did). I have not relied on this macro definition above.
defun/simple does not purport to be a proper clone of defun: its only purpose is to show how such a macro can be written. In particular it doesn't deal with declarations properly, I think: they need to be lifted out of the block & are not.
Elisp
Elisp is much more horrible than CL. In particular, in CL there is a well-defined function type, which is disjoint from lists:
> (typep '(lambda ()) 'function)
nil
> (typep '(lambda ()) 'list)
t
> (typep (function (lambda ())) 'function)
t
> (typep (function (lambda ())) 'list)
nil
(Note in particular that (function (lambda ())) is a function, not a list: function is doing its job of making a function.)
In elisp, however, an interpreted function is just a list whose car is lambda (caveat: if lexical binding is on this is not the case: it's then a list whose car is closure). So in elisp (without lexical binding):
ELISP> (function (lambda (x) x))
(lambda (x)
x)
And
ELISP> (defun foo (x) x)
foo
ELISP> (symbol-function 'foo)
(lambda (x)
x)
The elisp intepreter then just interprets this list, in just the way you could yourself. function in elisp is almost the same thing as quote.
But function isn't quite the same as quote in elisp: the byte-compiler knows that, when it comes across a form like (function (lambda ...)) that this is a function form, and it should byte-compile the body. So, we can look at the expansion of defun in elisp:
ELISP> (macroexpand '(defun foo (x) x))
(defalias 'foo
#'(lambda (x)
x))
(It turns out that defalias is the primitive thing now.)
But if I put this definition in a file, which I byte compile and load, then:
ELISP> (symbol-function 'foo)
#[(x)
"\207"
[x]
1]
And you can explore this a bit further: if you put this in a file:
(fset 'foo '(lambda (x) x))
and then byte compile and load that, then
ELISP> (symbol-function 'foo)
(lambda (x)
x)
So the byte compiler didn't do anything with foo because it didn't get the hint that it should. But foo is still a fine function:
ELISP> (foo 1)
1 (#o1, #x1, ?\C-a)
It just isn't compiled. This is also why, if writing elisp code with anonymous functions in it, you should use function (or equivalently #'). (And finally, of course, (function ...) does the right thing if lexical scoping is on.)
Other ways of making functions in CL
Finally, I've said above that function & specifically (function (lambda ...)) is the only primitive way to make new functions in CL. I'm not completely sure that's true, especially given CLOS (almost any CLOS will have some kind of class instances of which are functions but which can be subclassed). But it does not matter: it is a way and that's sufficient.
DEFUN is a defining macro. Macros transform code.
In Common Lisp:
(defun foo (a)
(+ a 42))
Above is a definition form, but it will be transformed by DEFUN into some other code.
The effect is similar to
(setf (symbol-function 'foo)
(lambda (a)
(block foo
(+ a 42))))
Above sets the function cell of the symbol FOO to a function. The BLOCK construct is added by SBCL, since in Common Lisp named functions defined by DEFUN create a BLOCK with the same name as the function name. This block name can then be used by RETURN-FROM to enable a non-local return from a specific function.
Additionally DEFUN does implementation specific things. Implementations also record development information: the source code, the location of the definition, etc.
Scheme has DEFINE:
(define (foo a)
(+ a 10))
This will set FOO to a function object.
I am trying to make a list of callback functions, which could look like this:
(("command1" . 'callback1)
("command2" . 'callback2)
etc)
I'd like it if I could could do something like:
(define-callback callback1 "command1" args
(whatever the function does))
Rather than
(defun callback1 (args)
(whatever the function does))
(add-to-list 'callback-info ("command1" . 'callback1))
Is there a convenient way of doing this, e.g., with macros?
This is a good example of a place where it's nice to use a two-layered approach, with an explicit function-based layer, and then a prettier macro layer on top of that.
Note the following assumes Common Lisp: it looks just possible from your question that you are asking about elisp, in which case something like this can be made to work but it's all much more painful.
First of all, we'll keep callbacks in an alist called *callbacks*:
(defvar *callbacks* '())
Here's a function which clears the alist of callbacks
(defun initialize-callbacks ()
(setf *callbacks* '())
(values)
Here is the function that installs a callback. It does this by searching the list to see if there is a callback with the given name, and if there is then replacing it, and otherwise installing a new one. Like all the functions in the functional layer lets us specify the test function which will let us know if two callback names are the same: by default this is #'eql which will work for symbols and numbers, but not for strings. Symbols are probably a better choice for the names of callbacks than strings, but we'll cope with that below.
(defun install-callback (name function &key (test #'eql))
(let ((found (assoc name *callbacks* :test test)))
(if found
(setf (cdr found) function)
(push (cons name function) *callbacks*)))
name)
Here is a function to find a callback, returning the function object, or nil if there is no callback with that name.
(defun find-callback (name &key (test #'eql))
(cdr (assoc name *callbacks* :test test)))
And a function to remove a named callback. This doesn't tell you if it did anything: perhaps it should.
(defun remove-callback (name &key (test #'eql))
(setf *callbacks* (delete name *callbacks* :key #'car :test test))
name)
Now comes the macro layer. The syntax of this is going to be (define-callback name arguments ...), so it looks a bit like a function definition.
There are three things to know about this macro.
It is a bit clever: because you can know at macro-expansion time what sort of thing the name of the callback is, you can decide then and there what test to use when installing the callback, and it does this. If the name is a symbol it also wraps a block named by the symbol around the body of the function definition, so it smells a bit more like a function defined by defun: in particular you can use return-from in the body. It does not do this if the name is not a symbol.
It is not quite clever enough: in particular it does not deal with docstrings in any useful way (it ought to pull them out of the block I think). I am not sure this matters.
The switch to decide the test uses expressions like '#'eql which reads as (quote (function eql)): that is to avoid wiring in functions into the expansion because functions are not externalisable objects in CL. However I am not sure I have got this right: I think what is there is safe but it may not be needed.
So, here it is
(defmacro define-callback (name arguments &body body)
`(install-callback ',name
,(if (symbolp name)
`(lambda ,arguments
(block ,name
,#body))
`(lambda ,arguments
,#body))
:test ,(typecase name
(string '#'string=)
(symbol '#'eql)
(number '#'=)
(t '#'equal))))
And finally here are two different callbacks being defined:
(define-callback "foo" (x)
(+ x 3))
(define-callback foo (x)
(return-from foo (+ x 1)))
These lists are called assoc lists in Lisp.
CL-USER 120 > (defvar *foo* '(("c1" . c1) ("c2" . c2)))
*FOO*
CL-USER 121 > (setf *foo* (acons "c0" `c1 *foo*))
(("c0" . C1) ("c1" . C1) ("c2" . C2))
CL-USER 122 > (assoc "c1" *foo* :test #'equal)
("c1" . C1)
You can write macros for that, but why? Macros are advanced Lisp and you might want to get the basics right, first.
Some issues with you example you might want to check out:
what are assoc lists?
what are useful key types in assoc lists?
why you don't need to quote symbols in data lists
variables are not quoted
data lists need to be quoted
You can just as easy create such lists for callbacks without macros. We can imagine a function create-callback, which would be used like this:
(create-callback 'callback1 "command1"
(lambda (arg)
(whatever the function does)))
Now, why would you use a macro instead of a plain function?
In the end, assisted by the responders above, I got it down to something like:
(defmacro mk-make-command (name &rest body)
(let ((func-sym (intern (format "mk-cmd-%s" name))))
(mk-register-command name func-sym)
`(defun ,func-sym (args &rest rest)
(progn
,#body))))
I am trying to emulate the single namespace of scheme within common lisp, with a macro (based on Doug Hoyte's) that expands to a lambda, where every use of an f! symbol (similar to Doug Hoyte's o! and g! symbols) in the function position expands to the same expression, but with funcall added in the function position of each invocation. For example:
(fplambda (f!z x) (f!z x x))
would expand to:
(LAMBDA (F!Z X) (FUNCALL F!Z X X))
The macro currently looks like this:
(defmacro fplambda (parms &body body)
(let ((syms (remove-duplicates
(remove-if-not #'f!-symbol-p
(flatten body)))))
`(lambda ,parms
(macrolet ,(mapcar
(lambda (f)
`(,f (&rest parmlist) `(funcall ,',f ',#parmlist)))
syms))
,#body)))
but given the above input, it expands (as far as I can see) to this:
(LAMBDA (F!F X)
(MACROLET ((F!F (&REST PARMLIST) `(FUNCALL ,'F!F ',#PARMLIST))))
(F!F X X))
In the macrolet definition, F!F should not be quoted or unquoted, and parmlist should just be unquoted. What is going on?
Thanks in advance!
Your definition is mostly right. You just made two pretty simple mistakes. The first one being a mismatched paren. The macrolet does not include the body (in the output the macrolet and the body are at the same level of indentation).
As for the nested backquote, the only mistake is the quote before parmlist. Other than that everything else is correct. The comma and quote before F!F is actually correct. From the hyperspec:
"An implementation is free to interpret a backquoted form F1 as any form F2 that, when evaluated, will produce a result that is the same under equal as the result implied by the above definition". Since the inner backquote has not been expanded yet, it does not have to be free of quotes and unquotes. The expression `(,'x) is actually the same as `(x).
Nested backquotes are notoriously complicated. What is probably the easiest way to understand them is to read Steele's explanation of them.
Edit:
The answer to your question about whether it is possible to use a fplambda expression in the function position is no. From the part of the hyperspec that deals with the evaluation of code: "If the car of the compound form is not a symbol, then that car must be a lambda expression, in which case the compound form is a lambda form.". Since the car of the form, (fplambda ...), is not a lambda expression, your code is no longer valid Common Lisp code.
There is a workaround to this that I figured out, but it's kind of ugly. You can define a reader macro that will allow you to write something like ([fplambda ...] ...) and have it read as
((LAMBDA (&REST #:G1030) (APPLY (FPLAMBDA ...) #:G1030)) ...)
which would do what you want. Here is code that will allow you to do that:
(set-macro-character #\[ 'bracket-reader)
(set-macro-character #\] (get-macro-character #\)))
(defun bracket-reader (stream char)
"Read in a bracket."
(declare (ignore char))
(let ((gargs (gensym)))
`(lambda (&rest ,gargs)
(apply ,(read-delimited-list #\] stream t)
,gargs))))
The only other solution I can think of would be to use some sort of code walker (I can't help you there).
I am working on a genetic programming hobby project.
I have a function/macro setup that, when evaluated in a setq/setf form, will generate a list that will look something like this.
(setq trees (make-trees 2))
==> (+ x (abs x))
Then it will get bound out to a lambda function #<FUNCTION :LAMBDA (X) ... > via strategic use of functions/macros
However, I want to get a bit more effective with this than manually assigning to variables, so I wrote something like this:
(setq sample
(let* ((trees (make-trees 2))
(tree-bindings (bind-trees trees))
(evaluated-trees (eval-fitness tree-bindings))))
(list (trees tree-bindings evaluated-trees)))
However, I get EVAL: trees has no value when I place this in a let form. My suspicion is that the macro expansions don't get fully performed in a LET as compared to a SETF, but that doesn't make sense to me.
What is the cause of this issue?
--- edit: yanked my code and put the whole file in a pastebin ---
Supposing that I decide that a setq isn't going to do it for me and I write a simple function to do it:
(defun generate-sample ()
(let ((twiggs (make-trees 2)))
(let ((tree-bindings (bind-trees twiggs)))
(let ((evaluated-trees (eval-fitness tree-bindings)))
(list twiggs tree-bindings evaluated-trees)))))
This yields an explosion of ...help file error messages (??!?)... and "eval: variable twiggs has no value", which stems from the bind-trees definition on SLIME inspection.
I am reasonably sure that I've completely hosed my macros. http://pastebin.org/673619
(Setq make-trees 2) sets the value of the variable make-trees to 2, then returns 2.
I do not see a reason for a macro in what you describe. Is it true that your make-trees creates a single random tree, which can be interpreted as a program? Just define this as a function with defun. I am thinking of something like this:
(defun make-tree (node-number)
(if (= node-number 1)
(make-leaf)
(cons (get-random-operator)
(mapcar #'make-tree
(random-partition (- node-number 1))))))
Let and setq do totally different things. Setq assigns a value to an existing variable, while let creates a new lexical scope with a number of lexical bindings.
I think that you should present more of your code; currently, your question does not make a lot of sense.
Update:
I will fix your snippet's indentation to make things clearer:
(setq sample
(let* ((trees (make-trees 2))
(tree-bindings (bind-trees trees))
(evaluated-trees (eval-fitness tree-bindings))))
(list (trees tree-bindings evaluated-trees)))
Now, as written before, let* establishes lexical bindings. These
are only in scope within its body:
(setq sample
(let* ((trees (make-trees 2))
(tree-bindings (bind-trees trees))
(evaluated-trees (eval-fitness tree-bindings)))
;; here trees, tree-bindings, and evaluated-trees are bound
) ; end of let* body
;; here trees, tree-bindings, and evaluated trees are not in scope anymore
(list (trees tree-bindings evaluated-trees)))
That last line is spurious, too. If those names were bound, it would
return a list of one element, which would be the result of evaluating
the function trees with tree-bindings and evaluated-trees as
arguments.
You might get what you want like this:
(setq sample
(let* ((trees (make-trees 2))
(tree-bindings (bind-trees trees))
(evaluated-trees (eval-fitness tree-bindings)))
(list trees tree-bindings evaluated-trees)))
Another update:
The purpose of macros is to eliminate repeated code when that elimination is not possible with functions. One frequent application is when dealing with places, and you also need them to define new control constructs. As long as you do not see that something cannot work as a function, do not use a macro for it.
Here is some code that might help you:
(defun make-tree-lambda (depth)
(list 'lambda '(x)
(new-tree depth)))
(defun make-tree-function (lambda-tree)
(eval lambda-tree))
(defun eval-fitness (lambda-form-list input-output-list)
"Determines how well the lambda forms approach the wanted function
by comparing their output with the wanted output in the supplied test
cases. Returns a list of mean quadratic error sums."
(mapcar (lambda (lambda-form)
(let* ((actual-results (mapcar (make-tree-function lambda-form)
(mapcar #'first input-output-list)))
(differences (mapcar #'-
actual-results
(mapcar #'second input-output-list)))
(squared-differences (mapcar #'square
differences)))
(/ (reduce #'+ squared-differences)
(length squared-differences))))
lambda-form-list))
(defun tree-fitness (tree-list input-output-list)
"Creates a list of lists, each inner list is (tree fitness). Input
is a list of trees, and a list of test cases."
(mapcar (lambda (tree fitness)
(list tree fitness))
tree-list
(eval-fitness (mapcar #'make-tree-lambda tree-list)
input-output-list)))
I have an s-expression bound to a variable in Common Lisp:
(defvar x '(+ a 2))
Now I want to create a function that when called, evaluates the expression in the scope in which it was defined. I've tried this:
(let ((a 4))
(lambda () (eval x)))
and
(let ((a 4))
(eval `(lambda () ,x)))
But both of these create a problem: EVAL will evaluate the code at the top level, so I can't capture variables contained in the expression. Note that I cannot put the LET form in the EVAL. Is there any solution?
EDIT: So if there is not solution to the EVAL problem, how else can it be done?
EDIT: There was a question about what exactly I am try to do. I am writing a compiler. I want to accept an s-expression with variables closed in the lexical environment where the expression is defined. It may indeed be better to write it as a macro.
You need to create code that has the necessary bindings. Wrap a LET around your code and bind every variable you want to make available in your code:
(defvar *x* '(+ a 2))
(let ((a 4))
(eval `(let ((a ,a))
,*x*)))
CLISP implements an extension to evaluate a form in the lexical environment. From the fact that it is an extension, I suspect you can't do that in a standard-compliant way.
(ext:eval-env x (ext:the-environment))
See http://clisp.cons.org/impnotes.html#eval-environ.
What is the actual problem that you want to solve? Most likely, you're trying to tackle it the wrong way. Lexical bindings are for things that appear lexically within their scope, not for random stuff you get from outside.
Maybe you want a dynamic closure? Such a thing doesn't exist in Common Lisp, although it does in some Lisp dialects (like Pico Lisp, as far as I understand).
Note that you can do the following, which is similar:
(defvar *a*)
(defvar *x* '(+ *a* 2)) ;'
(let ((a 10))
;; ...
(let ((*a* a))
(eval *x*)))
I advise you to think hard about whether you really want this, though.
In Common Lisp you can define *evalhook* Which allows you to pass an environment to (eval ...). *evalhook* is platform independent.
It is possible to use COMPILE to compile the expression into function and then use PROGV to FUNCALL the compiled function in the environment where variables are dynamically set. Or, better, use COMPILE to compile the expression into function that accepts variables.
Compile accepts the function definition as a list and turns it into function. In case of SBCL, this function is compiled into machine code and will execute efficiently.
First option (using compile and progv):
(defvar *fn* (compile nil '(lambda () (+ a 2)))
(progv '(a) '(4) (funcall *fn*))
=>
6
Second option:
(defvar *fn* (compile nil '(lambda (a) (+ a 2))))
(funcall *fn* 4)
=>
6