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From: Sebastian Fischer <sebf_at_informatik.uni-kiel.de>

Date: Thu, 16 Dec 2010 13:34:15 +0900

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 `?`.

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

inv a ? a = failure

for all expressions `a`.

Such inversion would allow to restrict nondeterministic computations not

only using predicates but also by defining another nondeterministic

operation and subtracting its results.

Can you image concrete examples where this would be useful?

Has this idea been studied before?

Sebastian

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

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Received on Thu Dec 16 2010 - 09:22:23 CET

Date: Thu, 16 Dec 2010 13:34:15 +0900

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 `?`.

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

inv a ? a = failure

for all expressions `a`.

Such inversion would allow to restrict nondeterministic computations not

only using predicates but also by defining another nondeterministic

operation and subtracting its results.

Can you image concrete examples where this would be useful?

Has this idea been studied before?

Sebastian

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

_______________________________________________

curry mailing list

curry_at_lists.RWTH-Aachen.DE

http://MailMan.RWTH-Aachen.DE/mailman/listinfo/curry

Received on Thu Dec 16 2010 - 09:22:23 CET

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