Warm-Up

stutter

(define (stutter ls)
  (cond
    ((empty? ls) '())
	(else (cons (car ls) (cons (car ls) (stutter (cdr ls)))))))

Quotes, vs. Quasi-quotes

A Quote

I was reading an article on combinators. Just a faaascinating story.

“So what traces are there of Moses Schönfinkel in Ekaterinoslav (AKA Dnipro) today? 132 years later it wasn’t so easy to find (especially during a pandemic)… but here’s a record of his birth: a certificate from the Ekaterinoslav Public Rabbi stating that entry 272 of the Birth Register for Jews from 1888 records that on September 7, 1888, a son Moses was born to the Ekaterinoslav citizen Ilya Schönfinkel and his wife Masha:”

  • Stephen Wolfram “Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel”

Remember that we Racketeers don’t need the closing quote. Why? Because ‘( … ) the matching close parenthesis tells us where the quote ends.

Quasiquotes and commas and patterns and pattern matching

“[H]ere’s a record of his birth:” an excited Wolfram writes, “a son Moses was born to the Ekaterinoslav citizen Ilya Schönfinkel and his wife Masha.”

This is not a quotation. Parts of it are the same, but there are some adjustments. The reporter (me) changed some parts of the original writing. So it’s sort-of a quotation. Or a quasi-quotation - “quasi” (approx) synonymous prefixes: pseudo, semi, demi.

Think of it as like a general “skeleton”, and we fill in the pieces.

We give the general skeleton, and fill in the particular pieces.

Why would we use it? It’s nice to see the structure, to see the shape of the data.

match – like cond, but w/patterns.

(match '(a b c)
  (?????    'yes)
  (else     'no))

Why? Because the structure is sometimes very nice.

'(define (length ls)
   (cond
     ((empty? ls) 0)
 	 (else (add1 (length (cdr ls))))))

(match expr
  (`(define (,name ,arg1) ,body) 'a-function) ;; I invite you to try this with `car`s and `cdr`s
  (else 'not-a-function))

The same kinds of programs, but differently.

stutter

(define (stutter ls)
  (match ls
    ('() '())
	(`(,a . ,d) `(,a ,a . ,(stutter d)))))

member?

(define (member? x ls)
  (match ls
    ('() #f)
	(`(,a . ,d)
	  (cond
	    ((equal? a x) #t)
		(else (member? x d))))))

You try

length

drop-first

Hungry for more?

With more firmly structured data we get more interesting programs. Here comes a new type of data, L. We’re going to get more sophisticated here. Whenever I use x or y in the description of L, that’s supposed to be a symbol. When I use the word lambda I mean it to be precisely that symbol—I’m using it as a constant. Whenever I use L, L1, L2, these are recursive positions.

L consists of x OR (lambda (x) L) OR (L1 L2)

So these are in L:

  • (a b)
  • z
  • (lambda (a) (lambda (z) a))
  • ((f h) (g h))
  • (t (lambda (h) v))
  • (lambda (lambda) lambda)

By contrast, these are not in L:

  • (lambda (z))
  • (a b c)
  • (t)
  • (5 z)
  • (lambda () (a b))

We want to write a function lambda->gamma that will take any L expression, and replace all uses of lambda in that constant position with gamma.

> (lambda->gamma '(lambda (a) (lambda (b) a)))
'(gamma (a) (gamma (b) a))
> (lambda->gamma '(b t))
'(b t)
> (lambda->gamma '((lambda (a) (a a)) (lambda (b) (b b))))
'((gamma (a) (a a)) (gamma (b) (b b)))
> (lambda->gamma '(lambda (lambda) lambda))
'(gamma (lambda) lambda)
> (lambda->gamma '(lambda lambda))
'(lambda  lambda)

Just Dessert.

This is not for the feint of heart or the uninitiated. If this stuff is generally new to you, stop here. This is one of those grimoires that are locked up in the Hogwarts library. But. Here we go.

You can nest quasiquoted expressions, of course. And you can mix them in with quotes in between.

> (quasiquote (unquote . unquote))
'(unquote . unquote)

> (quasiquote             (unquote (quote (unquote (+ 2 3)))))
',(+ 2 3)

> (quasiquote      (quote (unquote (quote (unquote (+ 2 3))))))
'',(+ 2 3)

> (quasiquote (quasiquote (unquote (quote (unquote (+ 2 3))))))
'`,'5

Explain the behavior of the first of these, and explain the behavior of the fourth in light of the second and the third.

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