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From: Sergio Antoy <antoy_at_cs.pdx.edu>

Date: Wed, 15 Dec 2010 22:11:27 -0800

On Thu, 16 Dec 2010, Sebastian Fischer wrote:

* > Hello,
*

* >
*

* > if we assume that
*

* >
*

* > - `a ? b` means the same as `b ? a` and
*

* > - `a ? (b ? c)` means the same as `(a ? b) ? c`
*

* >
*

* > we can regard Curry expressions as a commutative monoid: failure is the
*

* > unit of `?`.
*

All good up to here.

* > There is a universal way of making a commutative monoid into an abelian
*

* > group, that is, adding an inverse operation [1]. For Curry this would
*

* > mean
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* >
*

* > inv a ? a = failure
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* >
*

* > for all expressions `a`.
*

Suppose, by way of an example, that a is True. There is no

expression b such that b ? True is a failure.

* > Such inversion would allow to restrict nondeterministic computations not
*

* > only using predicates but also by defining another nondeterministic
*

* > operation and subtracting its results.
*

I'd like to see an example.

* > Can you image concrete examples where this would be useful?
*

* >
*

* > Has this idea been studied before?
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* >
*

* > Sebastian
*

* >
*

* > [1]: http://en.wikipedia.org/wiki/Grothendieck_group
*

Cheers,

Sergio

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Received on Do Dez 16 2010 - 09:22:23 CET

Date: Wed, 15 Dec 2010 22:11:27 -0800

On Thu, 16 Dec 2010, Sebastian Fischer wrote:

All good up to here.

Suppose, by way of an example, that a is True. There is no

expression b such that b ? True is a failure.

I'd like to see an example.

Cheers,

Sergio

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Received on Do Dez 16 2010 - 09:22:23 CET

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