Here’s a function that fails a static type check, but has no runtime type error:
(defun foo ()
(sqrt (if (static-type-check? #’foo)
"bogus"
2.0))
I suspect most people that favor static types will argue that this sort of program doesn’t count for some reason or other. I think this is more an example (albeit contrived) of the limitations of static type checking.
Many years ago I worked on a language called REBOL. REBOL was notable in that it used a variation of Polish notation. Function names came first, followed by the arguments in left to right order. Parentheses were generally not needed as the subexpression boundaries could be deduced from the arguments. It’s a bit complicated to explain, but pretty easy to code up.
An interpreter environment will be a lists of frames, and each frame is an association list of variable bindings.
(defun lookup (environment symbol)
(cond ((consp environment)
(let ((probe (assoc symbol (car environment))))
(if probe
(cdr probe)
(lookup (cdr environment) symbol))))
((null environment) (error "Unbound variable."))
(t (error "Bogus environment."))))
(defun extend-environment (environment formals values)
(cons (map ’list #’cons formals values) environment))
define mutates the topmost frame of the environment.
(defun environment-define! (environment symbol value)
(cond ((consp environment)
(let ((probe (assoc symbol (car environment))))
(if probe
(setf (cdr probe) value)
(setf (car environment) (acons symbol value (car environment))))))
((null environment) (error "No environment."))
(t (error "Bogus environment."))))
We’ll use Lisp procedures to represent REBOL primitives. The initial environment will have a few built-in primitives:
(defun initial-environment ()
(extend-environment
nil
’(add
lessp
mult
print
sub
sub1
zerop)
(list #’+
#’<
#’*
#’print
#’-
#’1-
#’zerop)))
A closure is a three-tuple
(defclass closure () ((arguments :initarg :arguments :reader closure-arguments) (body :initarg :body :reader closure-body) (environment :initarg :environment :reader closure-environment)))
An applicable object is either a function or a closure.
(deftype applicable () ’(or closure function))
We need to know how many arguments a function takes. We keep a table of the argument count for the primitives
(defparameter +primitive-arity-table+ (make-hash-table :test #’eq))
(eval-when (:load-toplevel :execute)
(setf (gethash #’* +primitive-arity-table+) 2)
(setf (gethash #’< +primitive-arity-table+) 2)
(setf (gethash #’+ +primitive-arity-table+) 2)
(setf (gethash #’- +primitive-arity-table+) 2)
(setf (gethash #’1- +primitive-arity-table+) 1)
(setf (gethash #’print +primitive-arity-table+) 1)
(setf (gethash #’zerop +primitive-arity-table+) 1)
)
(defun arity (applicable)
(etypecase applicable
(closure (length (closure-arguments applicable)))
(function (or (gethash applicable +primitive-arity-table+)
(error "Unrecognized function.")))))
REBOL-EVAL-ONE takes a list of REBOL expressions and
returns two values: the value of the leftmost expression in the
list, and the list of remaining expressions.
(defun rebol-eval-one (expr-list environment)
(if (null expr-list)
(values nil nil)
(let ((head (car expr-list)))
(etypecase head
((or number string) (values head (cdr expr-list)))
(symbol
(case head
(define
(let ((name (cadr expr-list)))
(multiple-value-bind (value tail) (rebol-eval-one (cddr expr-list) environment)
(environment-define! environment name value)
(values name tail))))
(if
(multiple-value-bind (pred tail) (rebol-eval-one (cdr expr-list) environment)
(values (rebol-eval-sequence (if (null pred)
(cadr tail)
(car tail))
environment)
(cddr tail))))
(lambda
(values (make-instance ’closure
:arguments (cadr expr-list)
:body (caddr expr-list)
:environment environment)
(cdddr expr-list)))
(otherwise
(let ((value (lookup environment head)))
(if (typep value ’applicable)
(rebol-eval-application value (cdr expr-list) environment)
(values value (cdr expr-list)))))))))))
If the leftmost symbol evaluates to something applicable, we find out how many arguments are needed, gobble them up, and apply the applicable:
(defun rebol-eval-n (n expr-list environment)
(if (zerop n)
(values nil expr-list)
(multiple-value-bind (value expr-list*) (rebol-eval-one expr-list environment)
(multiple-value-bind (values* expr-list**) (rebol-eval-n (1- n) expr-list* environment)
(values (cons value values*) expr-list**)))))
(defun rebol-eval-application (function expr-list environment)
(multiple-value-bind (arglist expr-list*) (rebol-eval-n (arity function) expr-list environment)
(values (rebol-apply function arglist) expr-list*)))
(defun rebol-apply (applicable arglist)
(etypecase applicable
(closure (rebol-eval-sequence (closure-body applicable)
(extend-environment (closure-environment applicable)
(closure-arguments applicable)
arglist)))
(function (apply applicable arglist))))
Evaluating a sequence is simply calling rebol-eval-one
over and over until you run out of expressions:
(defun rebol-eval-sequence (expr-list environment)
(multiple-value-bind (value expr-list*) (rebol-eval-one expr-list environment)
(if (null expr-list*)
value
(rebol-eval-sequence expr-list* environment))))
Let’s try it:
(defun testit ()
(rebol-eval-sequence
’(
define fib
lambda (x)
(if lessp x 2
(x)
(add fib sub1 x
fib sub x 2))
define fact
lambda (x)
(if zerop x
(1)
(mult x fact sub1 x))
define fact-iter
lambda (x answer)
(if zerop x
(answer)
(fact-iter sub1 x mult answer x))
print fib 7
print fact 6
print fact-iter 7 1
)
(initial-environment)))
CL-USER> (testit)
13
720
5040
This little interpreter illustrates how basic REBOL evaluation works. But this interpreter doesn’t support iteration. There are no iteration special forms and tail calls are not “safe for space”. Any iteration will run out of stack for a large enough number of repetition.
We have a few options:
do, repeat, loop, for, while, until etc.
To effectively support continuation passing style, you need tail recursion. This alone is a pretty compelling reason to support it.
But it turns out that this is easier said than done. Are you a cruel TA? Give your students this interpreter and ask them to make it tail recursive. The problem is that key recursive calls in the interpreter are not in tail position. These are easy to identify, but you’ll find that fixing them is like flattening a lump in a carpet. You’ll fix tail recursion in one place only to find your solution breaks tail recursion elsewhere.
If our interpreter is written in continuation passing style, it
will be syntactically tail recursive, but it won’t be
“safe for space” unless the appropriate continuations
are η-reduced. If we look at the continuation passing style
version of rebol-eval-sequence we’ll see a
problem:
(defun rebol-eval-sequence-cps (expr-list environment cont)
(rebol-eval-one-cps expr-list environment
(lambda (value expr-list*)
(if (null expr-list*)
(funcall cont value)
(rebol-eval-sequence-cps expr-list* environment cont)))))
We cannot η-reduce the continuation. We cannot make this “safe for space”.
But the continuation contains a conditional, and one arm of the
conditional simply invokes the containing continuation, so we can
η-convert this if we unwrap the conditional. We’ll do
this by passing two continuations to rebol-eval-one-cps
as follows
(defun rebol-eval-sequence-cps (expr-list environment cont)
(rebol-eval-one-cps expr-list environment
;; first continuation
(lambda (value expr-list*)
(rebol-eval-sequence-cps expr-list* environment cont))
;; second continuation, eta converted
cont))
rebol-eval-one-cps will call the first continuation if
there are any remaining expressions, and it will call the second
continuation if it is evaluating the final expression.
This intepreter, with the dual continuations
to rebol-eval-one-cps, is safe for space, and it will
interpret tail recursive functions without consuming unbounded stack
or heap.
But we still have a bit of an implementation problem. We’re allocating an extra continuation per function call. This doesn’t break tail recursion because we discard one of the continuations almost immediately. Our continuations are not allocated and deallocated in strict stack order anymore. We cannot easily convert ths back into a stack machine implementation.
To solve this problem, I rewrote the interpreter using Henry Baker’s Cheney on the M.T.A technique where the interpreter functions were a set of C functions that tail called each other and never returned. The stack would grow until it overflowed and then we’d garbage collect it and reset it. The return addresses pushed by the C function calls were ignored. Instead, continuation structs were stack allocated. These contained function pointers to the continuation. Essentially, we would pass two retun addresses on the stack, each in its own struct. Once the interpreter figured out which continuation to invoke, it would invoke the function pointer in the struct and pass a pointer to the struct as an argument. Thus the continuation struct would act as a closure.
This technique is pretty portable and not too bad to implement, but writing continuation passing style code in portable C is tedious. Even with macros to help, there is a lot of pointer juggling.
One seredipitous advatage of an implementation like this is that first-class continuations are essentially free. Now I’m not wedded to the idea of first-class continuations, but they make it much easier to implement error handling and advanced flow control, so if you get them for free, in they go.
With it’s Polish notation, tail recursion, and first-class continuations, REBOL was described as an unholy cross between TCL and Scheme. “The result of Outsterhout and Sussman meeting in a dark alley.”
Current versions of REBOL use a simplified interpreter that does not support tail recursion or first-class continuations.
Here’s a weird little success story involving Lisp. The code doesn’t rely on anything specific to Lisp. It could be rewritten in any language. Yet it wouldn’t have been written in the first place if it weren’t for Lisp.
I like to keep a Lisp REPL open in my Emacs for tinkering around with programming ideas. It only takes a moment to hook up a REST API or scrape some subprocess output, so I have a library of primitives that can talk to our internal build tools and other auxiliary tools such as GitHub or CircleCI. This comes in handy for random ad hoc scripting.
I found out that CircleCI is written in Clojure, and if you connect to your local CircleCI server, you can start a REPL and run queries on the internal CircleCI database. Naturally, I hooked up my local REPL to the Clojure REPL so I could send expressions over to be evaluated. We had multiple CircleCI servers running, so I could use my local Lisp to coordinate activity between the several CircleCI REPLs.
Then a need arose to transfer projects from one CircleCI server to another. My library had all the core capabilities, so I soon had a script for transferring projects. But after transferring a project, we had to fix up the branch protection in GitHub. The GitHub primitives came in handy. Of course our internal systems had to be informed that the project moved, but I had scripting primitives for that system as well.
More requirements arose: package the tool into a docker image, deploy it as a microservice, launch it as a kubernetes batch job, etc. At each point, the existing body of code was 90% of the solution, so it only required small changes to the code to handle the new requirements. As of now, the CircleCI migration tool is deployed as a service used by dozens of our engineers.
Now Lisp isn’t directly necessary for this project. It could easily (for some definitions of easy) be rewritten in another language. But the initial idea of connecting to a Clojure REPL from another Lisp is an obvious thing to try out and only takes moments to code up. If I were coding in another language, I could connect to the REPL, but then I’d have to translate between my other language and Lisp. It’s not an obvious thing to try out and would take a long time to code up. So while this project could be written in another language, it never would have been. And Lisp’s flexibility meant that there was never a reason for a rewrite, even as the requirements were changing.