object

natural

Natural numbers data type predicates.

Availability:

logtalk_load(types(loader))

Author: Paulo Moura

Version: 2:3:0

Date: 2026-05-13

Compilation flags:

static, context_switching_calls

Extends:

public integer

Uses:

list

numberlist

Remarks:

(none)

Inherited public predicates:

 (<)/2  (=:=)/2  (=<)/2  (=\=)/2  =~= / 2  (>)/2  (>=)/2  approximately_equal/2  approximately_equal/3  between/3  check/1  depth/2  essentially_equal/3  ground/1  new/1  numbervars/1  numbervars/3  occurs/2  plus/3  power_sequence/4  sequence/3  sequence/4  singletons/2  subsumes/2  subterm/2  succ/2  tolerance_equal/4  valid/1  variables/2  variant/2  varnumbers/2  varnumbers/3

Public predicates

factorial/2

Computes the factorial of a non-negative integer.

Compilation flags:

static

Template:

factorial(N,Factorial)

Mode and number of proofs:

factorial(+non_negative_integer,-non_negative_integer) - one

---

fibonacci/2

Computes the Fibonacci number of a non-negative integer.

Compilation flags:

static

Template:

fibonacci(N,Fibonacci)

Mode and number of proofs:

fibonacci(+non_negative_integer,-non_negative_integer) - one

---

lucas/2

Computes the Lucas number of a non-negative integer.

Compilation flags:

static

Template:

lucas(N,Lucas)

Mode and number of proofs:

lucas(+non_negative_integer,-non_negative_integer) - one

---

falling_factorial/3

Computes the falling factorial. N must be greater than or equal to K (fails otherwise).

Compilation flags:

static

Template:

falling_factorial(N,K,FallingFactorial)

Mode and number of proofs:

falling_factorial(+non_negative_integer,+non_negative_integer,-non_negative_integer) - zero_or_one

---

rising_factorial/3

Computes the rising factorial.

Compilation flags:

static

Template:

rising_factorial(N,K,RisingFactorial)

Mode and number of proofs:

rising_factorial(+non_negative_integer,+non_negative_integer,-non_negative_integer) - one

---

catalan/2

Computes the Catalan number of a non-negative integer.

Compilation flags:

static

Template:

catalan(N,Catalan)

Mode and number of proofs:

catalan(+non_negative_integer,-non_negative_integer) - one

---

subfactorial/2

Computes the subfactorial of a non-negative integer.

Compilation flags:

static

Template:

subfactorial(N,Subfactorial)

Mode and number of proofs:

subfactorial(+non_negative_integer,-non_negative_integer) - one

---

bell/2

Computes the Bell number of a non-negative integer.

Compilation flags:

static

Template:

bell(N,Bell)

Mode and number of proofs:

bell(+non_negative_integer,-non_negative_integer) - one

---

stirling_first/3

Computes the unsigned Stirling number of the first kind. N must be greater than or equal to K (fails otherwise).

Compilation flags:

static

Template:

stirling_first(N,K,Stirling)

Mode and number of proofs:

stirling_first(+non_negative_integer,+non_negative_integer,-non_negative_integer) - zero_or_one

---

stirling_second/3

Computes the Stirling number of the second kind. N must be greater than or equal to K (fails otherwise).

Compilation flags:

static

Template:

stirling_second(N,K,Stirling)

Mode and number of proofs:

stirling_second(+non_negative_integer,+non_negative_integer,-non_negative_integer) - zero_or_one

---

partition_number/2

Computes the partition number of a non-negative integer.

Compilation flags:

static

Template:

partition_number(N,PartitionNumber)

Mode and number of proofs:

partition_number(+non_negative_integer,-non_negative_integer) - one

---

binomial/3

Computes the binomial coefficient. N must be greater than or equal to K (fails otherwise).

Compilation flags:

static

Template:

binomial(N,K,Binomial)

Mode and number of proofs:

binomial(+non_negative_integer,+non_negative_integer,-non_negative_integer) - zero_or_one

---

multinomial/2

Computes the multinomial coefficient for a list of non-negative integers.

Compilation flags:

static

Template:

multinomial(Integers,Multinomial)

Mode and number of proofs:

multinomial(+list(non_negative_integer),-non_negative_integer) - one

---

Protected predicates

(no local declarations; see entity ancestors if any)

Private predicates

(no local declarations; see entity ancestors if any)

Operators

(none)