the ARROW language

RE01 Rice Brian T. EM2
Mon, 14 Dec 1998 16:41:34 +0600

more stuff... hope you enjoy...

this is just an elaboration on the interface description that i was working
on last time, along with some semantic issues i've been dealing with.

for one, the grouping of arrows within panes or something will be used for a
geometrical metaphor, with parallel planes existing as domain and range, for
instanc, of a relation between them. this is exactly the idea in categories.
this relation should be decomposable into small parts, even to the point of
taking an individual 'parallelogram' whose sides are two arrows in the
mapping and whose other two sides are one existing arrow in the first pane
and a second arrow (perhaps only constructed by the mapping) in the second.
for further intuitive representation, we would draw this parallelogram in a
_third_ pane, a crosscutting pane.

well, there are many mappings that we would like to make to many groups of
arrows, perhaps infinitely many in some or all cases (maybe most will be
implicit).  the point is that we will only want to look at a few at a time,
like we would want to restrict the message response window via interfaces in
OOP to simplify analysis.  so, the interface should provide some sort of
factorization of interfaces between the groups in a user-controllable way.

another thing is that the combinator becomes undecidable when one of the
arrows is pointed to or in a group pointed to by the other argument arrow.
this means that this operator should be restricted to arrow-diagram
fragments, i.e. standard directed multigraphs, which in the example
interface would be the small panes in the viewing window.

more when i get the time.  a new set of semantical operators should be
coming soon, as soon as i can work out the logic.