Pattern matching

[Jon Harrop]

Hi!

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?

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.

 

[Robert Klemme]

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

 

[Phil Tomson]

Hi!

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?

check out this article on artima by Topher Cyl:
http://www.artima.com/rubycs/articles/patterns_sexp_dsls.html


Phil

 

[Jon Harrop]

check out this article on artima by Topher Cyl:
http://www.artima.com/rubycs/articles/patterns_sexp_dsls.html

Great article. Thanks.