On 30/03/13 12:01, Ralf Hemmecke wrote:
Unless you specify what solver you intend to write, it's probably an
unsolvable task to write a general solver that works for all types of
algebras.
Ralf
Agreed, but I was thinking more about doing it on a per-domain basis and
building up gradually.
So we start with a very simple algebra that we want to create a equation
solver for, for example we might want to create an algebra domain based
on this category:
MyAlgebra() : Category with
myOp1 : ($,$) -> $
myOp2 : ($) -> $
Then create an expression holder that is specific to that algebra:
MyAlgebraExpression() : Exports == Implementation where
Implementation == add
Rep := Union(_
literalTerm : MyAlgebra, _
variableTerm : Symbol, _
myOp1Term : Record(left: $, right: $), _
myOp2Term : $_
)
bind : (Symbol,MyAlgebra,$) -> $
canonicalForm : $ -> $
decomposeMyOp1 : $ -> ($,$)
decomposeMyOp2 : $ -> ($)
Then create an equation solver that is also specific to that algebra:
MyAlgebraEquation() : Exports == Implementation where
Implementation == add
Rep := Record(left: MyAlgebraExpression, right: MyAlgebraExpression)
solveFor : (Symbol,$) -> MyAlgebraExpression
This would require 3 domains for every algebra that we wanted to be able
to solve but why not have some separate common rule interpreter code. So
MyAlgebraEquation domain would consist mostly of a set of substitution
rules for that particular algebra?
Martin
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