from The American Heritage® Dictionary of the English Language, 4th Edition
- n. One that performs an operation or a function.
- n. Grammar See function word.
from Wiktionary, Creative Commons Attribution/Share-Alike License
- n. a function word
- n. a function object
- n. a structure-preserving mapping between categories: if F is a functor from category C to category D, then F maps objects of C to objects of D and morphisms of C to morphisms of D such that any morphism f:X→Y of C is mapped to a morphism F(f): F(X) → F(Y) of D, such that if then , and such that identity morphisms (and only identity morphisms) are mapped to identity morphisms. Note: the functor just described is covariant.
In the regimented environment of LeÅniewski's logical languages this always takes place in the following way: a combining expression, which we may call a functor, precedes a left parenthesis of some kind, which is then followed by a sequence of one or more argument expressions, followed by a right parenthesis symmetric to the other one, which terminates the complex.
Strict memoization (really hyper-strict) is centered on a family of trie functors, defined as a functor
"functor" we need to be clear whether we're talking about one of these objects (ie a functor in the underlying category), or about a functor over this category.
I am pretty sure that violates one of the applicative functor laws. (f pure x = pure ($x) f).
So quantum mechanics and general relativity at least within this “partial functor” are equivalent, and might ultimately prove to be two aspects of an identical system.
Since quotations are functor expressions without internal structure, (BQ2) is explained: there's no possibility for quantifying into a quotation on this view.
For example, “is” has s/nn as its categorial index; it says that” is “is a two-placed functor of two nominal arguments which forms a sentence.
Moreover, in GEM the generalized Product principle (P. 16Ï) is also derivable as a theorem, with ˜Ï™ as weak as the requirement of mutual overlap, and we can introduce a corresponding functor as follows:
Coarse-graining might be represented as a functor, or something like that, establishing some kind of equivalence which lets you have a weaker notion of isomorphism.
With Protothetic launched, LeÅniewski could now look back on his system of foundations and see that it consisted of a hierarchy of three systems, developed in reverse order: Protothetic, introducing connectives, quantifiers and higher functions; Ontology, introducing the new category of names, with the new primitive ˜is™, and Mereology, based on a primitive mereological functor such as