FOM: Correction to Comment of Bishop.

[Steve Stevenson]

Ayan:

Sorry ... the "that" has an ambiguous antecedent.
The thing that is missing in functional languages is a controlled way
to do constructive sets as Bishop proposed them...Category theory fits
from Rydeheard and Burstall's *Computational Category Theory*,
although I have not tried to use this work in any systematic way. 

Bishop's view appeals much more to me than the category approach. I
don't have a copy of Bishop handy, so I can't comment further, except
the idea of "witnesses" through functions for the logical operations
seems to be a good design idea. My interest is in numerical things, so
Bishop is a natural way to think of things.

best,
steve


@book{burstall,
  author =	 {Rod Burstall and David Rydeheard},
  title =	 {Computational Category Theory},
  publisher =	 {Prentice Hall},
  year =	 {1988}
}

Ayan Mahalanobis writes:
 > It had always seemed to me that Errett Bishop's view was a correct
 > one. Functional languages have reached a point from which we can get
 > highly efficient code. The thing that was missing constructive set
 > approach of Bishop...
 > 
 > I am not sure if I understood your last remark. If you have some
 > dissatisfaction with constructive set theory, which as a matter of fact I
 > do, then category theory is a good substitute, I think.
 > 
 > I will be interested to know some application of Bishop's mathematics as you
 > mentioned.
 > 
 > --Ayan
 > 
 >