Martin Baker <ax87...@martinb.com> writes:
| Waldek,
|
| I have put your translation of the propositional logic code in here:
|
|
https://raw.github.com/martinbaker/fricas/master/src/algebra/boolean.spad.pamphlet
|
| In case you would like to include with FriCAS I have added some
documentation.
| It would be better if this were written, or at least checked, by the original
| author.
|
| There is a bug in the functions 'dual' and 'simplify' that is not in
| OpenAxiom:
|
| (8) -> dual(pq)
| Function: ?=? : (%,%) -> Boolean is missing from domain:
| PropositionalFormula(Symbol)
| Internal Error
| The function = with signature (Boolean)$$ is missing from domain
| PropositionalFormula(Symbol)
|
| '=' is declared in BasicType but it doesn't seem to be defined in
| PropositionalFormula. I can't see where this is defined in OpenAxiom.
Some notes:
-- See OpenAxiom's definition of BasicType.
Any domain is free to override =$BasicType, but most domains would
have regular enough representation that the default definition is
right and avoid endless boilerplate.
Another reason why someone would like to override the default is to
avoid the default search, but then the comparison must be doing
something so trivial that it is worth the trouble and enable domain
inlining -- see domain Byte for example.
-- In OpenAxiom, BooleanLogic is the category of domains implementing
"Boolean logic" (therefore are lattices, hence satisfy Logic.)
However, not all domains that are lattices are BooleanLogic instances.
Hence, in OpenAxiom BooleanLogic and Logic are not redundant.
Furthermore, BooleanLogic allows for shortcircuiting -- the
OpenAxiom compiler only implement half of it at the moment, but the
completion is planned (there are only 24 hours in a day.) This
allows parameterization over the boolean logic domain without
having to rewrite a program -- example of another boolean logic
domain is the trivalent logic implemented by KleeneTrivalentLogic.
(Due to a design bug afflicting all AXIOM flavours, care needs to
be exercised when using KleeneTrivalentLogic, but that should be
fixed when we have a unified parser.)
-- Gaby
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