[Inquiry] Re: Theme One Program -- Commentary Note -- Graft

[Jon Awbrey]

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TOP.  Commentary Note -- Graft

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Graft.

Graft is function from pairs of ideas to ideas.
It operates on the assumption that it is given
a pair of Cog-type structures as its arguments.
If both ideas are nil, then their graft is nil.
If either one of them is nil, then their graft
is equal to the other one.  If it happens that
both ideas are significant, then we may depict
the input arguments in the manner that follows:

 o-------------o   o-------------o
 |   o-----o   |   |   o-----o   |
 o-->| a 1 |---o   o-->| b 2 |---o
     o-----o           o-----o
     ^                 ^
that |            this |
     @                 @

Tracing through the function definition, as it applies to this case,
should be enough to convince the reader that the functional outcome
will be an idea-form structure that has the following configuration:

 o-------------------------------o
 |   o-----o           o-----o   |
 o-->| a 1 |---------->| b 2 |---o
     o-----o           o-----o
                       ^
                 graft |
                       @

To see the general case, it helps to view things in the following way:

Step 1.  that, this <> nil

 o-------------------------------o   o-------------------------------o
 |   o-----o           o-----o   |   |   o-----o           o-----o   |
 o-->| a   |--> ··· -->| c   |---o   o-->| x   |--> ··· -->| z   |---o
     o-----o           o-----o           o-----o           o-----o
                       ^                                   ^
                  that |                              this |
                       @                                   @

Step 2.  here := that^.by

 o-------------------------------o   o-------------------------------o
 |   o-----o           o-----o   |   |   o-----o           o-----o   |
 o-->| a   |--> ··· -->| c   |---o   o-->| x   |--> ··· -->| z   |---o
     o-----o           o-----o           o-----o           o-----o
     ^                 ^                                   ^
here |            that |                              this |
     @                 @                                   @

Step 3.  that^.by := this^.by

                                     o-------------------------------o
     o-----o           o-----o       |   o-----o           o-----o   |
     | a   |--> ··· -->| c   |-------o-->| x   |--> ··· -->| z   |---o
     o-----o           o-----o           o-----o           o-----o
     ^                 ^                                   ^
here |            that |                              this |
     @                 @                                   @

Step 4.  this^.by := here

 o-------------------------------------------------------------------o
 |   o-----o           o-----o           o-----o           o-----o   |
 o-->| a   |--> ··· -->| c   |---------->| x   |--> ··· -->| z   |---o
     o-----o           o-----o           o-----o           o-----o
     ^                 ^                                   ^
here |            that |                              this |
     @                 @                                   @

Step 5.  graft := this

 o-------------------------------------------------------------------o
 |   o-----o           o-----o           o-----o           o-----o   |
 o-->| a   |--> ··· -->| c   |---------->| x   |--> ··· -->| z   |---o
     o-----o           o-----o           o-----o           o-----o
                                                           ^
                                                     graft |
                                                           @

function graft (that, this: idea): idea;
var here: idea;
begin
 here := nil;
 if this = nil then here := that
  else
   begin
    if that <> nil then
     begin
      here := that^.by;
      that^.by := this^.by;
      this^.by := here
     end;
    here := this
   end;
 graft := here
end;

(5324)(7664)

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