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Lengrand & Miquel (2008). Greco-Roman Fω, orthogonality and symmetric candidates. Annals of Pure and Put on Logic 153:3-20.

We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is fundamentally the traditional one of Fω, whereas provability
of types is Hellenic. The proof-term calculus accounting for the Graeco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We testify that the hale calculus is powerfully normalising. For the
layer of type constructors, we utilize Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (authoritative) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We examine that orthogonality does not catch the
fixpoint construction of symmetrical candidates.

We plant the consistency of Fω^C, and bear on the calculus to the
traditional system Fω, likewise when the latter is extended with axioms for
Greco-Roman logic.

Lengrand & Miquel (2008). Graeco-Roman Fω, orthogonality and symmetrical candidates. Annals of Pure and Put on Logic 153:3-20.

We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is fundamentally the traditional one of Fω, whereas provability
of types is classic. The proof-term calculus accounting for the Graeco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We show that the hale calculus is powerfully normalising. For the
layer of type constructors, we utilize Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (classic) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We try that orthogonality does not catch the
fixpoint construction of symmetrical candidates.

We found the consistency of Fω^C, and pertain the calculus to the
traditional system Fω, as well when the latter is extended with axioms for
classic logic.

I take your feedback… I am chatting with some co-workers about the perception of in the.NET Community of what the System.* and Microsoft.* namespaces mean.    So I had the wild idea of but expecting you!  

For this exercise, I’d care you to flirt with a newfangled "feature area" of the.NET Framework… Would you instinctively make any conclusions about that area grounded on if the namespace where System.* or Microsoft.*?  If that feature area were in the Silverlight subset of.NET, would that interchange your mind at all?

There are fundamentally three schools of thought among my co-workers  — which one is closer to your perception? 

1) They are the same or it truly doesn’t matter.    The root namespace between System.* and Microsoft.* have no meaning…  Microsoft seems to be arbitrary about when functionality gos in one or the other. 

2) Part of the Framework vs.  Addons. 

System.* argues stuff that is logically part of the framework.  It is 100% sustained, self-coloured-longsighted term design that will not call for to moil, good to look on, stable, probably will catch outstanding joyriding support.  Contrived to be very interoperable and could act anyplace.NET is.  This may embark as part of the redist or perhaps an out of band (such as ASP.NET MVC, ASP.NET AJAX, etc). 

Microsoft.* is the runing edge stuff or value-add.  It is typically very nerveless stuff that supplies on to the framework and raises it, but perchance a work in progress… over time you might require some of those concepts to enter the framework.    As an example, the outstanding work patterns and practices does a great deal falls under this bucket. 

Lengrand & Miquel (2008). Hellenic Fω, orthogonality and symmetrical candidates. Annals of Pure and Put on Logic 153:3-20.

We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is fundamentally the traditional one of Fω, whereas provability
of types is Graeco-Roman. The proof-term calculus accounting for the Greco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We bear witness that the hale calculus is powerfully normalising. For the
layer of type constructors, we apply Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (definitive) layer of terms,
we expend Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We try that orthogonality does not catch the
fixpoint construction of symmetrical candidates.

We plant the consistency of Fω^C, and have-to doe with the calculus to the
traditional system Fω, too when the latter is extended with axioms for
Hellenic logic.

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