lambda - What is the Prolog operator `^` ("caret")?

Question

What is the Prolog operator ^ ?

Looking at The Prolog Built-in Directive op gives a list of the built-in operators.

I see

• ** is exponentiation
• / is or

but what is ^ ?

Each of the three current answers are of value and I learned something:

• Roy for the book
• false for the examples
• I accepted the answer by CapelliC because it made clear that ^/2 has multiple meanings
  depending on context which instantly cleared up my confusion.

Answer 1

The operator (^)/2 serves several purposes:

setof/3, bagof/3

Here it is used to denote the existential variables (set) of a term. Like in setof(Ch, P^child_of(Ch,P), Chs) where P is declared as an existential variable.

As a non-standard side effect to this, many systems have defined it as predicate with the following definition:

_^Goal :- Goal

But then, others do not have such a definition. It is in any case a good idea to avoid to define a predicate (^)/2.

(^)/2 - power

This is an evaluable functor accessible via (is)/2 and arithmetic comparison like (=:=)/2 and (>)/2. Also library(clpfd) uses it with this meaning. In contrast to (**)/2 which always results in a float, 2^2 is an integer - thereby permitting arithmetics with bigints. Just try ?- X is 7^7^7. to see if your system supports them.

Finally, there are user defined uses for (^)/2 that do not collide with above uses like lambda expressions via library(lambda) (source).

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There are a few general remarks about its use. (^)/2 associates to the right which means that: (7^7^7) = (7^(7^7)). It has a very low priority which means that you have to use brackets for arguments with standard operators.