Runtime pattern matching in Racket - macros

If Racket's match macro were a function I could do this:
(define my-clauses (list '[(list '+ x y) (list '+ y x)]
'[_ 42]))
(on-user-input
(λ (user-input)
(define expr (get-form-from-user-input user-input)) ; expr could be '(+ 1 2), for example.
(apply match expr my-clauses)))
I think there are two very different ways to do this. One is to move my-clauses into macro world, and make a macro something like this (doesn't work):
(define my-clauses (list '[(list '+ x y) (list '+ y x)]
'[_ 42]))
(define-syntax-rule (match-clauses expr)
(match expr my-clauses)) ; this is not the way it's done.
; "Macros that work together" discusses this ideas, right? I'll be reading that today.
(on-user-input
(λ (user-input)
(define expr (get-form-from-user-input user-input)) ; expr could be '(+ 1 2), for example.
(match-clauses expr)))
The alternative, which might be better in the end because it would allow me to change my-clauses at runtime, would be to somehow perform the pattern matching at runtime. Is there any way I can use match on runtime values?
In this question Ryan Culpepper says
It's not possible to create a function where the formal parameters and body are given as run-time values (S-expressions) without using eval.
So I guess I'd have to use eval, but the naive way won't work because match is a macro
(eval `(match ,expr ,#my-clauses) (current-namespace))
I got the desired result with the following voodoo from the guide
(define my-clauses '([(list'+ x y) (list '+ y x)]
[_ 42]))
(define-namespace-anchor a)
(define ns (namespace-anchor->namespace a))
(eval `(match '(+ 1 2) ,#my-clauses) ns) ; '(+ 2 1)
Is the pattern matching happening at runtime now? Is it a bad idea?

To answer the first part of your question (assuming you don't necessarily need the match clauses to be supplied at runtime):
The key is to:
Define my-clauses for compile time ("for syntax").
Reference that correctly in the macro template.
So:
(begin-for-syntax
(define my-clauses (list '[(list '+ x y) (list '+ y x)]
'[_ 42])))
(define-syntax (match-clauses stx)
(syntax-case stx ()
[(_ expr) #`(match expr #,#my-clauses)]))

The pattern matching is happening at runtime in the last example.
One way to check is to look at the expansion:
> (syntax->datum
(expand '(eval `(match '(+ 1 2) ,#my-clauses) ns)))
'(#%app eval (#%app list* 'match ''(+ 1 2) my-clauses) ns)
Whether is a good idea...
Using eval is rather slow, so if you call it often it might be better to find another solution. If you haven't seen it already you might want to read "On eval in dynamic languages generally and in Racket specifically." on the Racket blog.

Thank you both very much, your answers gave me much food for thought. What I am trying to do is still not very well defined, but I seem to be learning a lot in the process, so that's good.
The original idea was to make an equation editor that is a hybrid between paredit and a computer algebra system. You enter an initial math s-expression, e.g. (+ x (* 2 y) (^ (- y x) 2). After that the program presents you with a list of step transformations that you would normally make by hand: substitute a variable, distribute, factor, etc. Like a CAS, but one step at a time. Performing a transformation would happen when the user presses the corresponding key combination, although one possibility is to just show a bunch of possible results, and let the user choose the new state of the expression amongst them. For UI charterm will do for now.
At first I thought I would have the transformations be clauses in a match expression, but now I think I'll make them functions that take and return s-expressions. The trouble with choosing compile time vs runtime is that I want the user to be able to add more transformations, and choose his own keybindings. That could mean that they write some code which I require, or they require mine, before the application is compiled, so it doesn't force me to use eval. But it may be best if I give the user a REPL so he has programmatic control of the expression and his interactions with it as well.
Anyway, today I got caught up reading about macros, evaluation contexts and phases. I'm liking racket more and more and I'm still to investigate about making languages... I will switch to tinkering mode now and see if I get some basic form of what I'm describing to work before my head explodes with new ideas.

Related

Lisp - "list 'if x y nil" what is usage of the tick (') symbol and "list" function here?

I am taking a programming language principle class where the professor talks about macro using Lisp (Precisly, Elisp). However, he didn't teach us how to write this language. As a result, I am trying to learn myself.
However, there are something that I just can't understand regarding the use of "tick" (') in Lisp. I do, however, understand the basic use. For example, if we have (cdr '(a b c)) it will give us a list (b c). Without the tick symbol, (a b c) would be evaluated as a function.
In the code written by my professor, I have noticed a strange use of "tick" symbol that I can't really understand the usage:
; not sure why there is a "'" in front of if and it is being added to a list ??
(defmacro myand(x y) (list 'if x y nil))
; Another example. Tick symbol before "greater than" symbol ? and made into a list?
(list 'if (list '> x y))
The uses of list and tick symbol just doesn't really make sense to me. Can anyone explain what is going on here? I suppose this is something special to Lisp
The 'tick symbol' is ': '<x> is syntactic sugar for (quote <x>) for any <x>. And (quote <x>) is simply <x> for any object <x>.
quote is needed in Lisp because programs in Lisp often want to reason about things which would have meaning as parts of Lisp programs, and need to say 'this isn't part of this program: it's data'. So, for instance, if I have a list of the form
((a . 1) (b . 2) ... (x . 26)) and I want to look up a symbol in it, I might write a function like this:
(defun ass (key alist)
(if (null? alist)
'()
(if (eql (car (car alist)) key)
(car alist)
(ass key (cdr alist)))))
Then when I wanted to look up, say x, I would have to say (ass (quote x) ...) because if I said (ass x ...) then x would be treated as a variable, and I don't want that: I want the symbol x.
In your example you are looking at programs which write Lisp programs – macros in other words – and these programs need to spend a lot of their time manipulating what will be Lisp source code as data. So in your myand macro, what you want is that
(myand x y)
should be rewritten as
(if x y nil)
Which is the same thing. So to construct this you need a list of four elements: the symbol if, the two variables and the symbol nil. Well you can make a list with list:
(list 'if x y 'nil)
Except that it turns out that the value of the symbol nil is just itself (nil is rather special in many Lisps in fact), so you can not bother quoting that: (list 'if x y nil) (I personally would have quoted it in this case, to make it clear what was literal and what was being evaluated, but that's probably not common).

What is the difference between define vs define-syntax and let vs let-syntax when value is syntax-rules?

I'm in a process of implementing Hygienic macros in my Scheme implementation, I've just implemented syntax-rules, but I have this code:
(define odd?
(syntax-rules ()
((_ x) (not (even? x)))))
what should be the difference between that and this:
(define-syntax odd?
(syntax-rules ()
((_ x) (not (even? x)))))
from what I understand syntax-rules just return syntax transformer, why you can't just use define to assign that to symbol? Why I need to use define-syntax? What extra stuff that expression do?
Should first also work in scheme? Or only the second one?
Also what is the difference between let vs let-syntax and letrec vs letrec-syntax. Should (define|let|letrec)-syntax just typecheck if the value is syntax transformer?
EDIT:
I have this implementation, still using lisp macros:
;; -----------------------------------------------------------------------------
(define-macro (let-syntax vars . body)
`(let ,vars
,#(map (lambda (rule)
`(typecheck "let-syntax" ,(car rule) "syntax"))
vars)
,#body))
;; -----------------------------------------------------------------------------
(define-macro (letrec-syntax vars . body)
`(letrec ,vars
,#(map (lambda (rule)
`(typecheck "letrec-syntax" ,(car rule) "syntax"))
vars)
,#body))
;; -----------------------------------------------------------------------------
(define-macro (define-syntax name expr)
(let ((expr-name (gensym)))
`(define ,name
(let ((,expr-name ,expr))
(typecheck "define-syntax" ,expr-name "syntax")
,expr-name))))
This this code correct?
Should this code works?
(let ((let (lambda (x) x)))
(let-syntax ((odd? (syntax-rules ()
((_ x) (not (even? x))))))
(odd? 11)))
This question seems to imply some deep confusion about macros.
Let's imagine a language where syntax-rules returns some syntax transformer function (I am not sure this has to be true in RnRS Scheme, it is true in Racket I think), and where let and let-syntax were the same.
So let's write this function:
(define (f v)
(let ([g v])
(g e (i 10)
(if (= i 0)
i
(e (- i 1))))))
Which we can turn into this, of course:
(define (f v n)
(v e (i n)
(if (<= i 0)
i
(e (- i 1)))))
And I will tell you in addition that there is no binding for e or i in the environment.
What is the interpreter meant to do with this definition? Could it compile it? Could it safely infer that i can't possibly make any sense since it is used as a function and then as a number? Can it safely do anything at all?
The answer is that no, it can't. Until it knows what the argument to the function is it can't do anything. And this means that each time f is called it has to make that decision again. In particular, v might be:
(syntax-rules ()
[(_ name (var init) form ...)
(letrec ([name (λ (var)
form ...)])
(name init))]))
Under which the definition of f does make some kind of sense.
And things get worse: much worse. How about this?
(define (f v1 v2 n)
(let ([v v1])
(v e (i n)
...
(set! v (if (eq? v v1) v2 v1))
...)))
What this means is that a system like this wouldn't know what the code it was meant to interpret meant until, the moment it was interpreting it, or even after that point, as you can see from the second function above.
So instead of this horror, Lisps do something sane: they divide the process of evaluating bits of code into phases where each phase happens, conceptually, before the next one.
Here's a sequence for some imagined Lisp (this is kind of close to what CL does, since most of my knowledge is of that, but it is not intended to represent any particular system):
there's a phase where the code is turned from some sequence of characters to some object, possibly with the assistance of user-defined code;
there's a phase where that object is rewritten into some other object by user- and system-defined code (macros) – the result of this phase is something which is expressed in terms of functions and some small number of primitive special things, traditionally called 'special forms' which are known to the processes of stage 3 and 4;
there may be a phase where the object from phase 2 is compiled, and that phase may involve another set of user-defined macros (compiler macros);
there is a phase where the resulting code is evaluated.
And for each unit of code these phases happen in order, each phase completes before the next one begins.
This means that each phase in which the user can intervene needs its own set of defining and binding forms: it needs to be possible to say that 'this thing controls what happens at phase 2' for instance.
That's what define-syntax, let-syntax &c do: they say that 'these bindings and definitions control what happens at phase 2'. You can't, for instance, use define or let to do that, because at phase 2, these operations don't yet have meaning: they gain meaning (possibly by themselves being macros which expand to some primitive thing) only at phase 3. At phase 2 they are just bits of syntax which the macro is ingesting and spitting out.

Is there a way to get a macro to do an extra evaluation before returning its result?

I’m trying to get get my macro to do an extra evaluation of its result before returning it. Can this be done without eval?
I'm trying to solve the problem in exercise 4 below:
Define a macro nth-expr that takes an integer n and an arbitrary number of expressions, evaluates the nth expression and returns its value. This exercise is easy to solve, if you assume that the first argument is a literal integer.
4. As exercise 3, but assume that the first argument is an expression to be evaluated.
It's easy to get the macro to pick the right expression:
(defmacro nth-expr% (n &rest es)
`(nth ,n ',es))
CL-USER> (defvar i 1)
I
CL-USER> (nth-expr% (1+ i) (+ 2 3) (- 4 3) (+ 3 1))
(+ 3 1)
The expression (+ 3 1) is the one we want, but we want the macro to evaluate it to 4 before returning it.
It can of course be done with eval:
(defmacro nth-expr%% (n &rest es)
`(eval (nth ,n ',es)))
CL-USER> (nth-expr%% (1+ i) (+ 2 3) (- 4 3) (+ 3 1))
4
But is there another way?
It feels like the solution should be to put the body of nth-expr% in a helper macro and have the top level macro only contain an unquoted call to this helper:
(defmacro helper (n es)
`(nth ,n ',es))
(defmacro nth-expr (n &rest es) ; doesn't work!
(helper n es))
The idea is that the call to helper would return (+ 3 1), and this would then be the expansion of the call to nth-expr, which at run-time would evaluate to 4. It blows up, of course, because N and ES get treated like literals.
That's not that easy.
Using eval is not good, since eval does not evaluate the code in the local lexical environment.
Remember, if we allow an expression to be evaluated to determine the number of another expression to execute, then we don't know this number at macro expansion time - since the expression could be based on a value that needs to be computed - for example based on some variable:
(nth-expression
foo
(bar)
(baz))
So we might want to think about code which does that:
(case foo
(0 (bar))
(1 (baz)))
CASE is evaluating foo and then uses the result to find a clause which has the same value in its head. The consequent forms of that clause then will be evaluated.
Now we need to write code which expands the former into the latter.
This would be a very simple version:
(defmacro nth-expression (n-form &body expressions)
`(case ,n-form
,#(loop for e in expressions
and i from 0
collect `(,i ,e))))
Question: what might be drawbacks of using CASE like that?
Knuto: Rainer Joswig may be asking you to think about how the case statement works. Namely, that after evaluating the keyform (ie, the first argument), it will be compared sequentially to the key in each clause until a match is found. The comparisons could be time consuming if there are many clauses. You can discover this by carefully reading the entry for case in the Hyperspec (as he more than once has insisted I do):
The keyform or keyplace is evaluated to produce the test-key. Each of
the normal-clauses is then considered in turn.
Also note that constructing many case clauses will add to the time to expand and compile the macro at compile time.
Regarding your use of eval in nth-expr%%, you can still achieve the effect of an eval by switching to apply:
(defmacro nth-expr%% (n &rest es)
`(let ((ne (nth ,n ',es)))
(apply (car ne) (cdr ne))))
But see Plugging the Leaks at http://www.gigamonkeys.com/book/macros-defining-your-own.html about a more robust treatment.
In general, a more efficient way to process the expressions is as a simple vector, rather than a list. (The problem statement does not rule out a vector representation.) While nth and case involve searching through the expressions one-by-one, a function like aref or svref can directly index into it. Assuming a vector of expressions is passed to the macro along with an index, perhaps first requiring (coerce expressions 'simple-vector) if a list, then the result can be computed in constant time no matter how many expressions there are:
(defmacro nth-expr%%% (n es)
`(let ((ne (svref ',es ,n)))
(apply (car ne) (cdr ne))))
so that now
(defvar i 1)
(nth-expr%%% (1+ i) #((+ 2 3) (- 4 3) (+ 3 1))) -> 4

Standard way for breaking out of recursion in scheme

I am writing my first program in scheme. I get pretty deep into recursion because I basically interpret a program for a simple robot which can have nested procedure calls.
If I find a violation I need to stop interpreting the program and return the last valid state.
I've solved it by declaring a global variable (define illegalMoveFlag 0) and then setting it via set!.
It works fine, but I guess my tutor won't like it (because it's not functional approach I guess)
Other approach I've thought about is to add an error parameter to every function I call recursively in the program. I don't quite like it because it would make my code far less readable, but I guess it's more 'functional'.
Is there maybe a third way I didn't think about? And can my approach be justified in this paradigm, or is it basically a code smell?
Since this was your first Scheme program, you probably just need to introduce a conditional expression, cond, in order to avoid further recursion when you reach the end. For example:
; sum : natural -> natural
; compute the sum 0+1+...+max
(define (sum max)
(define (sum-helper i sum-so-far)
(if (> i max)
sum-so-far
(sum-helper (+ i 1) (+ sum-so-far i))))
(sum-helper 0 0))
(display (sum 10))
(newline)
However, if you need a traditional return to return like longjmp in C, you will need to store and use an escape continuation. This can be done like this:
(define (example)
(let/ec return
(define (loop n)
(if (= n 100000)
(return (list "final count: " n))
(loop (+ n 1))))
(loop 0)))
(display (example))
If let/ec is not defined in your Scheme implementation, then prefix your program with:
(define-syntax let/ec
(syntax-rules ()
[(_ return body ...)
(call-with-current-continuation
(lambda (return)
body ...))]))
UPDATE:
Note that cond has an => variant:
(cond
[(call-that-can-fail)
=> (lambda (a) <use-a-here>))]
[else <do-something-else>])
If the call succeeds then the first, clause is
taken and the result is bound to a. If the call fails,
then the else clause is used.
The usual way to stop recursing is, well, to stop recursing. i.e., don't call the recursive function any longer. :-)
If that is too hard to do, the other way to break out of something is to capture a continuation at the top level (before you start recursing), then invoke the continuation when you need to "escape". Your instructor may not like this approach, though. ;-)
You might want to use the built-in procedure error, like so:
(error "Illegal move") ; gives ** Error: Illegal move
This will raise an exception and stop interpreting the program (though I suspect this may not be what you are looking for).
You can also provide additional arguments, like this:
(error "Illegal move: " move) ; gives ** Error: Illegal move: <move>
You can exit of a recursion (or from any other process) using a continuation. Without knowing more specifics, I'd recommend you take a look at the documentation of your interpreter.
Make illegalMoveFlag a paramter in the function instead of a global variable
I'll give you a simple example with factorials
ie:
0! = 1
n! = n * (n - 1)! when n (1 ... infinity)
lets call this a recursive factorial
(define (fact-r n)
(if
[eq? n 0]
1
(* n (fact-r (- n 1)))
)
)
An alternative would be to use a parameter to the function to end the recursion
Lets call it iterative factorial
(define (fact-i n total)
(if
(eq? n 0)
total
(fact-i (- n 1) (* n total))
)
)
total needs to start at 1 so we should make another function to make using it nicer
(define (nice-fact n)
(fact-i n 1))
You could do something similar with illegalMoveFlag to avoid having a global variable
As far as avoiding using set! goes, we'll probably need more information.
In some cases its still rather hard to avoid using it. Scheme is fully turing complete without the use of set! however when it comes to accessing an external source of information such as a database or a robot set! can become the only practical solution...

Scheme macro triggered by keyword which is not the head of a list

Suppose I want to trigger a Scheme macro on something other than the first item in an s-expression. For example, suppose that I wanted to replace define with an infix-style :=, so that:
(a := 5) -> (define a 5)
((square x) := (* x x)) -> (define (square x) (* x x))
The actual transformation seems to be quite straightforward. The trick will be getting Scheme to find the := expressions and macro-expand them. I've thought about surrounding large sections of code that use the infix syntax with a standard macro, maybe: (with-infix-define expr1 expr2 ...), and having the standard macro walk through the expressions in its body and perform any necessary transformations. I know that if I take this approach, I'll have to be careful to avoid transforming lists that are actually supposed to be data, such as quoted lists, and certain sections of quasiquoted lists. An example of what I envision:
(with-infix-define
((make-adder n) := (lambda (m) (+ n m)))
((foo) :=
(add-3 := (make-adder 3))
(add-6 := (make-adder 6))
(let ((a 5) (b 6))
(+ (add-3 a) (add-6 b))))
(display (foo))
(display '(This := should not be transformed))
So, my question is two-fold:
If I take the with-infix-define route, do I have to watch out for any stumbling blocks other than quote and quasiquote?
I feel a bit like I'm reinventing the wheel. This type of code walk seems like exactly what standard macro expanding systems would have to do - the only difference is that they only look at the first item in a list when deciding whether or not to do any code transformation. Is there any way I can just piggyback on existing systems?
Before you continue with this, it's best to think things over thoroughly -- IME you'd often find that what you really want a reader-level handling of := as an infix syntax. That will of course mean that it's also infix in quotations etc, so it would seem bad for now, but again, my experience is that you end up realizing that it's better to do things consistently.
For completeness, I'll mention that in Racket there's a read-syntax hack for infix-like expressions: (x . define . 1) is read as (define x 1). (And as above, it works everywhere.)
Otherwise, your idea of a wrapping macro is pretty much the only thing you can do. This doesn't make it completely hopeless though, you might have a hook into your implementation's expander that can allow you to do such things -- for example, Racket has a special macro called #%module-begin that wraps a complete module body and #%top-interaction that wraps toplevel expressions on the REPL. (Both of these are added implicitly in the two contexts.) Here's an example (I'm using Racket's define-syntax-rule for simplicity):
#lang racket/base
(provide (except-out (all-from-out racket/base)
#%module-begin #%top-interaction)
(rename-out [my-module-begin #%module-begin]
[my-top-interaction #%top-interaction]))
(define-syntax infix-def
(syntax-rules (:= begin)
[(_ (begin E ...)) (begin (infix-def E) ...)]
[(_ (x := E ...)) (define x (infix-def E) ...)]
[(_ E) E]))
(define-syntax-rule (my-module-begin E ...)
(#%module-begin (infix-def E) ...))
(define-syntax-rule (my-top-interaction . E)
(#%top-interaction . (infix-def E)))
If I put this in a file called my-lang.rkt, I can now use it as follows:
#lang s-exp "my-lang.rkt"
(x := 10)
((fib n) :=
(done? := (<= n 1))
(if done? n (+ (fib (- n 1)) (fib (- n 2)))))
(fib x)
Yes, you need to deal with a bunch of things. Two examples in the above are handling begin expressions and handling function bodies. This is obviously a very partial list -- you'll also want bodies of lambda, let, etc. But this is still better than some blind massaging, since that's just not practical as you can't really tell in advance how some random piece of code will end up. As an easy example, consider this simple macro:
(define-syntax-rule (track E)
(begin (eprintf "Evaluating: ~s\n" 'E)
E))
(x := 1)
The upshot of this is that for a proper solution, you need some way to pre-expand the code, so that you can then scan it and deal with the few known core forms in your implmenetation.
Yes, all of this is repeating work that macro expanders do, but since you're changing how expansion works, there's no way around this. (To see why it's a fundamental change, consider something like (if := 1) -- is this a conditional expression or a definition? How do you decide which one takes precedence?) For this reason, for languages with such "cute syntax", a more popular approach is to read and parse the code into plain S-expressions, and then let the actual language implementation use plain functions and macros.
Redefining define is a little complicated. See #Eli's excellent explanation.
If on the other hand, you are content with := to use set! things are a little simpler.
Here is a small example:
#lang racket
(module assignment racket
(provide (rename-out [app #%app]))
(define-syntax (app stx)
(syntax-case stx (:=)
[(_ id := expr)
(identifier? #'id)
(syntax/loc stx (set! id expr))]
[(_ . more)
(syntax/loc stx (#%app . more))])))
(require 'assignment)
(define x 41)
(x := (+ x 1))
(displayln x)
To keep the example to a single file, I used submodules (available in the prerelease version of Racket).