Re: functional programming

Pascal J. Bourguignon wrote:

> So to make a list, first, the basic building block, the cons cell:
> 
> (class Cons
>  (attr_accessor :car)
>  (attr_accessor :cdr)
>  (def initialize(car,cdr)
>     (@car = car)
>     (@cdr = cdr)
>   end)
> end)
> 
> 
> Let's wrap this object into a functional abstraction layer:
> 
> (def cons(car,cdr)
>  (Cons . new(car,cdr))
> end)
> 
> (def car(x)
>  (x . car)
> end)
> 
> (def cdr(x)
>  (x . cdr)
> end)
> 
> (def null(x)
>  (x . nil?)
> end)
> 
> irb(main):040:0> (cons 1,2)
> #<Cons:0x7fdfb53eb808 @cdr=2, @car=1>
> irb(main):042:0> (car (cons 1,2))
> 1
> irb(main):043:0> (cdr (cons 1,2))
> 2
> irb(main):044:0> (null (cons 1,2))
> false
> irb(main):045:0> (null (car (cons 1,nil)))
> false
> irb(main):046:0> (null (cdr (cons 1,nil)))
> true
> 
> 
> 
> Then you can build a list over these cons cells:
> 
> (def list(*args)
>   (i = (args . length))
>   (r = nil)
>   (loop {
>      (if (i == 0)
>         (break)
>       else
>         (i = (i - 1))
>         (r = (cons (args [ i ]),r))
>      end)
>   })
>  r
> end) 
> 
> irb(main):127:0> (list 1,2,3)
> #<Cons:0x7fdfb53b81d8 @cdr=#<Cons:0x7fdfb53b8200
> @cdr=#<Cons:0x7fdfb53b8228 @cdr=nil, @car=3>, @car=2>, @car=1>
> 
> 
> Let's print them pretty:
> 
> (def printelements(cons)
>   (if (Cons === cons)
>       (if (Cons === (car cons))
>          (printlist (car cons))
>         else
>          (print (car cons))
>       end)
>       (if (Cons === (cdr cons))
>          (print " ")
>          (printelements (cdr cons))
>        elsif (not (null (cdr cons)))
>          (print " . ")
>          (print (cdr cons))
>       end)
>   else
>      (print cons)
>   end)
> end)
> 
> (def printlist(cons)
>  (print "(")
>  (printelements cons)
>  (print ")")
>  cons
> end)
> 
> (def terpri()
>   (print "\n")
> end)
> 
> 
> irb(main):263:0> (begin
>                    (terpri)
>                    (printlist (list 1,2,3))
>                    (terpri)
>                  end)
> 
> (1 2 3)
> nil
> 
> You can also add some higher level abstractions:
> 
> (def first(list)
>   (car list)
> end)
> 
> (def rest(list)
>   (cdr list)
> end)
> 
> (def endp(list)
>   (if (Cons === list)
>       nil
>    elsif (null list)
>       true
>    else
>       (error ("Expected a list instead of the atom " + (list . to_s)))
>    end)
> end)
> 
> 
> 
> Once you've got this list abstraction, you can build functions such
> as reverse:
> 
> (def revappend(list,tail)
>  (if (null list)
>      tail
>   else
>      (revappend (cdr list),(cons (car list),tail))
>   end)
> end)
> 
> (def reverse(list)
>  (revappend list,nil)
> end)
> 
> 
> 
> irb(main):267:0> (begin
>                    (printlist (reverse (list 1,2,3)))
>                    (terpri)
>                  end)
> (3 2 1)
> nil
> 
> 
> 
> Now we also need the function abstraction.  In ruby functions have to
> be in modules, and always qualified by the module name.  This is not
> pretty, so we will allow any method to be treated as a function, but 
> we will ignore it's recipient object, always passing self.
> 
> # For methods, the first function argument is the recipient of the
> # message:
> 
> (def method(designator,arity=(-1)) 
>    # Important: the given arity must include the recipient object,
> but not the recipient class:     # (method :==,2) .call(42,42)   vs.
> 42.==(42)    (if (arity == -1)
>       # This is the default, bugged behavior: 
>       (Proc . new {| x , *args | (x . send(designator , *args))})
>     elsif (arity == 0)
>       (raise (Exception.exception("An instance method must have an
> arity>=1, not 0.")))     else
>       (arity = (arity - 1))
>       (args = (((arity == 0)? "" : " , ") + (((1 .. arity) . map { |
> i | ("a" + i.to_s) }) . join(" , "))))       (eval("(Proc . new { |
> x" + args + " | " +             "( x . send( :" + (designator . to_s)
> + args + " ))})"))     end)
>  end)
> 
> 
> # for functions, the recipient of the message is always 'self', all
> # arguments are passed as arguments.
> 
> (def function(designator,arity=(-1)) 
>   # Important: the given arity must include the recipient object, but
> not the recipient class:    # (function "SOME_MODULE.someFunction",1)
> .call(42)   vs. SOME_MODULE.someFunction(42)   # (function
> :someFunction             ,2) .call(42)   vs. self.someFunction(42)
> or someFunction(42)   (if (String === designator)      mod , met =
> (designator . split("."))      (if (arity == -1)
>         # This is the default, bugged behavior:
>         (Proc . new {| *args | ((eval mod) . send((met . to_sym) ,
> *args))})       else
>         (args = (((1 .. arity) . map { | i | ("a" + i.to_s) }) .
> join(" , ")))         (sep = " ")
>         (if (0 < arity)
>            (sep = " , ")
>          end)
>         (eval("(Proc . new { | " + args + " | " +
>               "( " + mod  + " . send( :" + met + sep + args + "
> ))})"))       end)
>    else
>      (if (arity == -1)
>         # This is the default, bugged behavior:
>         (Proc . new {| x , *args | (x . send(designator , *args))})
>       elsif (arity == 0)
>         (eval("(Proc . new {" +
>               "(" + (designator . to_s) + " )})"))
>       else
>         (args = (((1 .. arity) . map { | i | ("a" + i.to_s) }) .
> join(" , ")))         (eval("(Proc . new { | " + args + " | " +
>               "(" + (designator . to_s) + " " + args + " )})"))
>       end)
>    end)
> end)
> 
> 
> (def funcall(fun,*args)
>   (fun . call(*args))
> end)
> 
> 
> 
> irb(main):370:0> (funcall (method :+,2),3,4)
> (funcall (method :+,2),3,4)
> 7
> 
> irb(main):478:0> (begin 
>                    (terpri)
>                    (printlist (funcall (function :reverse,1),(list
> 1,2,3)))                    (terpri)
>                  end)
> 
> (3 2 1)
> nil


You have certainly proved that everything is 10 times as hard
as it should be when you use Commune Lisp!

Ruby:

[1,2,3].reverse
    ==>[3, 2, 1]

[1,2,3].send :reverse
    ==>[3, 2, 1]



> 
> 
> 
> Now that you have first class functions, you can start to implement
> higher level functions:
> 
> (def mapcar (fun,list)
>  (if (endp list)
>     nil
>   else
>    (cons (funcall fun,(first list)),(mapcar fun,(rest list)))
>   end)
> end)
> 
> 
> irb(main):271:0> (begin
>                    (printlist (mapcar (lambda {|x| (x + 1)}),(list
> 1,2,3)))                    (terpri)
>                  end)
> 
> (2 3 4)
> nil
> 


Ruby:

[1,2,3].map{|x| x + 1}
    ==>[2, 3, 4]


or:

augment = proc{|x| x + 1}
    ==>#<Proc:0x0282c2cc@(irb):11>
[1,2,3].map &augment
    ==>[2, 3, 4]

> 
> 
> So at least, now you can find the smallest element of a list:
> 
> This function implements an accumulator pattern: we pass the partial
> result along with the parameters.  We process the list item by item
> and when its finished we return the result we've accumulated so far:
> 
> (def smallestElement(list,minimum)
>  (if (endp list)
>      minimum
>   elsif (minimum < (first list))
>      (smallestElement (rest list),minimum)
>   else
>      (smallestElement (rest list),(first list))
>   end)
> end)
> 
> (def smallest(list)
>  (smallestElement (rest list),(first list))
> end)
> 
> 
> 
> irb(main):422:0> 
> (begin 
>    (terpri)
>    (printlist (mapcar (function :smallest,1),(list (list 1),
>                                                    (list 1,1,1,1),
>                                                    (list 1,2,3,4),
>                                                    (list 4,3,2,1),
>                                                    (list
> 1,2,3,4,3,2,1),
> (list 4,3,2,1,2,3,4))))    (terpri)
> end)
> 
> (1 1 1 1 1 1)
> nil


Ruby:

[[1],[1,1,1,1],[1,2,3,4],[4,3,2,1],[1,2,3,4,3,2,1],[4,3,2,1,2,3,4]].
map{|a| a.min}
    ==>[1, 1, 1, 1, 1, 1]



Yes, COBOL Lisp is an ancient, cumbersome, and clunky language.
Ruby is to it as a transistor is to a vacuum tube.