...more precisely: Four commonly known "big operations" ... ... But these are not "all ...in the sense of "all 'big' operations". 1. Sigma summation and integral ... your objection to the term "quantifier"). Like the english term "quantity",... integration, so what binary operation should it correspond to? :-) Derivative is ... x ( x 0 ) How can lambda abstraction be applied to a ...

...more precisely: Four commonly known "big operations" ... ... But these are not "all quantifiers...in the sense of "all 'big' operations". 1. Sigma summation and integral are... your objection to the term "quantifier"). In case of [Riemann] intergral the... integration, so what binary operation should it correspond to? :-) Derivative is ... x ( x 0 ) How can lambda abstraction be applied to a ...

... the sense of "all 'big' operations". 1. Sigma summation and integral ...integration, so what binary operation should it correspond to? :-) difference obviously...there must be a binary operation that lambda is iterative form...with categorial usage the existential quantifier is over X) to make...functoring terms (yes terms!) to corresponding categorial constructions there are existential...

.... But these are not "all quantifiers" in the sense of "all 'big' operations". 1. Sigma summation and integral are...of integration, so what binary operation should it correspond to? :-) 2. Pi-... Lattice supremum is iterative form binary meet. 5. Lattice infinum is ... there must be a binary operation that lambda is iterative form ... you can think of the lambda is only doing the "treat ...

..., there must be a binary operation that lambda is iterative form as...and the graph of f2. Then \lambda x . e is indeed {e1 ->... (finite) sums, products, and lattice operations. These are all non-trivial folds...If I'm inventive enough, I can of course find some binary operation everywhere. For example, every natural... won't get with this operation. And dealing with the infinite ...

...> Observation: all quantuifiers correspond to some binary algebraic operation. I would say...Lambda and limit are not quantifiers, but they are binding constructs. Consider: ... integral are iterative forms of binary plus. 2. Pi-capital product is... Lattice supremum is iterative form binary meet. 5. Lattice infinum is ... there must be a binary operation that lambda is iterative form ...

...corresond to the following associative noncommutative operation: (x,y) -> y which is ...how you want to generalize your binary operation for infinite sequences. So ...look up into a definition that uses quantifiers (that is other big ... case they reduce to lattice operations), but instead as elements of a... four examples (sum, product, lattice operations) doesn't mean it has ...

...: Limit seems to corresond to the following associative noncommutative operation: (x,y) -> y which is informally "take the second element". .... I suggest you look it up.) Well, if I wonder about big operators expressed in terms of binary operations, probably the last thing to do is to look up into a definition that uses quantifiers (that is other big operators)...

... am, Tegiri Nenashi <TegiriNena...@gmail.com> wrote: Limit is also quantifier, but I have trouble finding an associate binary operation! (My mistake was focusing on monothonic sequences only). ... sorry. Limit seems to corresond to the following associative noncommutative operation: (x,y) -> y which is informally "take the second element...

...> Hmm, limit is also quantifier (or "big operation" as you call it -- I... didn't quite follow your objection to the term "quantifier"). Limit is also quantifier, but I have trouble finding an associate binary operation! (My mistake was focusing on monothonic sequences...seems to corresond to the following associative noncommutative operation: (x,y) -> y which is informally "take ...