protocol

# `setp`

Set protocol.

Author: Paulo Moura
Version: 1:6:0
Date: 2019-05-23
Compilation flags:
`static`
Dependencies:
(none)
Remarks:
(none)
Inherited public predicates:
(none)

- Public predicates

  - `as_set/2`

  - `as_list/2`

  - `delete/3`

  - `disjoint/2`

  - `equal/2`

  - `empty/1`

  - `insert/3`

  - `insert_all/3`

  - `intersect/2`

  - `intersection/3`

  - `intersection/4`

  - `size/2`

  - `member/2`

  - `memberchk/2`

  - `powerset/2`

  - `product/3`

  - `select/3`

  - `selectchk/3`

  - `subset/2`

  - `subtract/3`

  - `symdiff/3`

  - `union/3`

  - `union/4`

- Protected predicates

- Private predicates

- Operators

## Public predicates

### `as_set/2`

Returns a set with all unique elements from the given list.

Compilation flags:
`static`
Template:
`as_set(List,Set)`
Mode and number of proofs:
`as_set(@list,-set)` - `one`

### `as_list/2`

Returns a list with all elements of the given set.

Compilation flags:
`static`
Template:
`as_list(Set,List)`
Mode and number of proofs:
`as_list(@set,-list)` - `one`

### `delete/3`

Deletes an element from a set returning the set of remaining elements.

Compilation flags:
`static`
Template:
`delete(Set,Element,Remaining)`
Mode and number of proofs:
`delete(+set,@term,?set)` - `one`

### `disjoint/2`

True if the two sets have no element in common.

Compilation flags:
`static`
Template:
`disjoint(Set1,Set2)`
Mode and number of proofs:
`disjoint(+set,+set)` - `zero_or_one`

### `equal/2`

True if the two sets are equal.

Compilation flags:
`static`
Template:
`equal(Set1,Set2)`
Mode and number of proofs:
`equal(+set,+set)` - `zero_or_one`

### `empty/1`

True if the set is empty.

Compilation flags:
`static`
Template:
`empty(Set)`
Mode and number of proofs:
`empty(+set)` - `zero_or_one`

### `insert/3`

Inserts an element in a set, returning the resulting set.

Compilation flags:
`static`
Template:
`insert(In,Element,Out)`
Mode and number of proofs:
`insert(+set,+term,?set)` - `one`

### `insert_all/3`

Inserts a list of elements in a set, returning the resulting set.

Compilation flags:
`static`
Template:
`insert_all(List,In,Out)`
Mode and number of proofs:
`insert_all(+list,+set,?set)` - `one`

### `intersect/2`

True if the two sets have at least one element in common.

Compilation flags:
`static`
Template:
`intersect(Set1,Set2)`
Mode and number of proofs:
`intersect(+set,+set)` - `zero_or_one`

### `intersection/3`

Returns the intersection of `Set1` and `Set2`.

Compilation flags:
`static`
Template:
`intersection(Set1,Set2,Intersection)`
Mode and number of proofs:
`intersection(+set,+set,?set)` - `zero_or_one`

### `intersection/4`

True if `Intersection` is the intersection of `Set1` and `Set2` and `Difference` is the difference between `Set2` and `Set1`.

Compilation flags:
`static`
Template:
`intersection(Set1,Set2,Intersection,Difference)`
Mode and number of proofs:
`intersection(+set,+set,?set,?set)` - `zero_or_one`

### `size/2`

Number of set elements.

Compilation flags:
`static`
Template:
`size(Set,Size)`
Mode and number of proofs:
`size(+set,?integer)` - `zero_or_one`

### `member/2`

`Element` is a member of set `Set`.

Compilation flags:
`static`
Template:
`member(Element,Set)`
Mode and number of proofs:
`member(+term,+set)` - `zero_or_one`
`member(-term,+set)` - `zero_or_more`

### `memberchk/2`

Checks if a term is a member of a set.

Compilation flags:
`static`
Template:
`memberchk(Element,Set)`
Mode and number of proofs:
`memberchk(+term,+set)` - `zero_or_one`

### `powerset/2`

Returns the power set of a set, represented as a list of sets.

Compilation flags:
`static`
Template:
`powerset(Set,Powerset)`
Mode and number of proofs:
`powerset(+set,-list)` - `one`

### `product/3`

Returns the cartesian product of two sets.

Compilation flags:
`static`
Template:
`product(Set1,Set2,Product)`
Mode and number of proofs:
`product(+set,+set,-set)` - `one`

### `select/3`

Selects an element from a set, returning the set of remaining elements.

Compilation flags:
`static`
Template:
`select(Element,Set,Remaining)`
Mode and number of proofs:
`select(?term,+set,?set)` - `zero_or_more`

### `selectchk/3`

Checks that an element can be selected from a set, returning the set of remaining elements.

Compilation flags:
`static`
Template:
`selectchk(Element,Set,Remaining)`
Mode and number of proofs:
`selectchk(?term,+set,?set)` - `zero_or_one`

### `subset/2`

True if `Subset` is a subset of `Set`.

Compilation flags:
`static`
Template:
`subset(Subset,Set)`
Mode and number of proofs:
`subset(+set,+set)` - `zero_or_one`

### `subtract/3`

True when `Difference` contains all and only the elements of `Set1` which are not also in `Set2`.

Compilation flags:
`static`
Template:
`subtract(Set1,Set2,Difference)`
Mode and number of proofs:
`subtract(+set,+set,?set)` - `zero_or_one`

### `symdiff/3`

True if `Difference` is the symmetric difference of `Set1` and `Set2`, containing all elements that are not in the sets intersection.

Compilation flags:
`static`
Template:
`symdiff(Set1,Set2,Difference)`
Mode and number of proofs:
`symdiff(+set,+set,?set)` - `zero_or_one`

### `union/3`

True if `Union` is the union of `Set1` and `Set2`.

Compilation flags:
`static`
Template:
`union(Set1,Set2,Union)`
Mode and number of proofs:
`union(+set,+set,?set)` - `zero_or_one`

### `union/4`

True if `Union` is the union of `Set1` and `Set2` and `Difference` is the difference between `Set2` and `Set1`.

Compilation flags:
`static`
Template:
`union(Set1,Set2,Union,Difference)`
Mode and number of proofs:
`union(+set,+set,?set,?set)` - `zero_or_one`

## Protected predicates

(none)

## Private predicates

(none)

## Operators

(none)

See also

set, set(Type)