On 17.02.2007 20:47, Jon Harrop wrote:
> I recently got engaged in a thread on comp.lang.functional about ML and
> Lisp. I posted some simple but efficient OCaml code that is difficult to
> translate into Lisp:
> 
> let rec ( +: ) f g = match f, g with
>   | `Q n, `Q m -> `Q (n +/ m)
>   | `Q (Int 0), e | e, `Q (Int 0) -> e
>   | f, `Add(g, h) -> f +: g +: h
>   | f, g -> `Add(f, g)
> 
> let rec ( *: ) f g = match f, g with
>   | `Q n, `Q m -> `Q (n */ m)
>   | `Q (Int 0), e | e, `Q (Int 0) -> `Q (Int 0)
>   | `Q (Int 1), e | e, `Q (Int 1) -> e
>   | f, `Mul(g, h) -> f *: g *: h
>   | f, g -> `Mul(f, g)
> 
> let rec simplify = function
>   | `Q _ | `Var _ as e -> e
>   | `Add(f, g) -> simplify f +: simplify g
>   | `Mul(f, g) -> simplify f *: simplify g;;
> 
> This code does some simple rearrangements of symbolic expressions to
> simplify them, e.g. 2+1*x+0 -> 2+x. It works with arbitrary-precision
> rational arithmetic.
> 
> Does Ruby have pattern matching? If so, what does the above look like in
> Ruby? If not, how else can you express this elegantly in Ruby?

Not that I am aware of.  Even a quick search on RAA doesn't reveal 
anything: http://raa.ruby-lang.org/search.rhtml?search=pattern

I guess the major issue here between Ruby and Lisp is that you do not 
have access to Ruby expressions natively the same way as you have in 
Lisp.  There are no macros that integrate nicely with the language as 
Lisp macros do.

The Ruby solution would likely involve creating a parser for the 
expressions you want to simplify, then simplifying the syntax tree and 
outputting it again.  For getting at the Ruby parse tree there are 
indeed libraries, so that parse should not be too hard.  In any case I 
guess the solution will only be half as elegant as the other two you 
presented. :-)

Side note: the feature that comes closest to pattern matching is the 
assignment grouping of expressions:

irb(main):014:0> a,(b,(c,d),e)=1,[2,[3,4],5]
=> [1, [2, [3, 4], 5]]
irb(main):015:0> a
=> 1
irb(main):016:0> b
=> 2
irb(main):017:0> c
=> 3
irb(main):018:0> d
=> 4
irb(main):019:0> e
=> 5

> Lisp doesn't have pattern matching but Pascal Constanza wrote quite an
> elegant solution in Lisp using dynamic method dispatch:
> 
> (defstruct add x y)
> (defstruct mul x y)
> 
> (defgeneric simplify-add (x y)
>    (:method ((x number) (y number)) (+ x y))
>    (:method ((x (eql 0)) y) y)
>    (:method (x (y (eql 0))) x)
>    (:method (x (y add))
>     (simplify-add (simplify-add x (add-x y)) (add-y y)))
>    (:method (x y) (make-add :x x :y y)))
> 
> (defgeneric simplify-mul (x y)
>    (:method ((x number) (y number)) (* x y))
>    (:method ((x (eql 0)) y) 0)
>    (:method (x (y (eql 0))) 0)
>    (:method ((x (eql 1)) y) y)
>    (:method (x (y (eql 1))) x)
>    (:method (x (y mul))
>     (simplify-mul (simplify-mul x (mul-x y)) (mul-y y)))
>    (:method (x y) (make-mul :x x :y y)))
> 
> (defgeneric simplify (exp)
>    (:method (exp) exp)
>    (:method ((exp add))
>     (simplify-add (simplify (add-x exp)) (simplify (add-y exp))))
>    (:method ((exp mul))
>     (simplify-mul (simplify (mul-x exp)) (simplify (mul-y exp)))))
> 
> This has the advantage that Lisp optimises the above so that it is only 10x
> slower than the OCaml. Unlike the OCaml, it can be extended and
> automatically reoptimised at run-time.

I have to admit that I am only familiar with very basic Lisp.  But it 
does look elegant. :-)

Kind regards

	robert