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2.6 Predefined Predicates and Functions

The following predicates are predefined (/n denotes arity n):

true/0

The predicate denoting true.

formula true;
> true.

false/0

The predicate denoting false.

formula false;
> false.

Set/1

The predicate that returns true if and only if its argument is a set.

formula Set({});
> true.

Tuple/1

The predicate that returns true if its argument is a tuple.

formula Tuple(tuple(2, 3));
> true.

Nat/1

The predicate that returns true if its argument is a natural number.

formula Nat(1);
> true.

=/2

The equality of values.

formula =(2, +(1, 1));
> true.

in/2

The inclusion of an element (the first argument) in a set (the second argument).

formula in(1, join(1, {}));
> true.

<=/2

The predicate on natural numbers that returns true if and only if its first argument is not larger than the second one.

formula <=(1, 2);
> true.

Likewise the following functions are predefined:

length/1

The number of elements in a tuple.

term length(tuple(2, 3));
> 2.

{}/0

The empty set.

term {};
> {}.

join/2

The function that returns the set that results from joining an element (the first argument) to a set (the second argument).

term join (2, join(1, {}));
> {1, 2}.

nat/2

The interval of natural numbers from a lower bound (the first argument) up to and including an upper bound (the second argument).

term nat(1, 10);
> 1..10.
term set(x in nat(1, 10): true, x);
> {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

+/2

Addition on natural numbers.

term +(7, 8);
> 15.

*/2

Multiplication on natural numbers.

term *(2, 3);
> 6.

-/2

Subtraction of a natural number (the second argument) from another natural number (the first argument); the second argument must not be larger than the first one.

term -(7, 8);
> ERROR: no such difference.