Boolean

equal

bool equal(interval<T> a, interval<T> b)

[source]

Details

Returns true if intervals $a$ and $b$ are equal.

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$=: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{B}$

For $a, b\neq \emptyset$:

$\underline{a} = \underline{b} \land \bar{a} = \bar{b}$.

Otherwise:

$a = \emptyset$	$b = \emptyset$	$a = b$
$0$	$1$	$0$
$1$	$0$	$0$
$1$	$1$	$1$

---

subset

bool subset(interval<T> a, interval<T> b)

[source]

Details

Returns true if $a$ is a subset of $b$.

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$\subseteq: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{B}$

For $a, b\neq \emptyset$:

$\underline{b} \leq \underline{a} \land \bar{a} \leq \bar{b}$.

Otherwise:

$a = \emptyset$	$b = \emptyset$	$a \subseteq b$
$0$	$1$	$0$
$1$	$0$	$1$
$1$	$1$	$1$

---

interior

bool interior(interval<T> a, interval<T> b)

[source]

Details

Returns true if $a$ is in the interior of $b$.

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$\mathrm{interior}: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{B}$

For $a, b\neq \emptyset$:

$\underline{b} < \underline{a} \land \bar{a} < \bar{b}$.

Otherwise:

$a = \emptyset$	$b = \emptyset$	$a \subset b$
$0$	$1$	$0$
$1$	$0$	$1$
$1$	$1$	$1$

---

disjoint

bool disjoint(interval<T> a, interval<T> b)

[source]

Details

Returns true if intervals $a$ and $b$ are disjoint.

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$\mathrm{disjoint}: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{B}$

For $a, b\neq \emptyset$:

$\bar{a} < \underline{b} \lor \bar{b} < \underline{a}$.

Otherwise:

$a = \emptyset$	$b = \emptyset$	$a \cap b = \emptyset$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$1$

---

less

bool less(interval<T> a, interval<T> b)

[source]

Details

Returns true if $a \leq b$.

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$\leq: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{B}$

For $a, b\neq \emptyset$:

$\underline{a} \leq \underline{b} \land \bar{a} \leq \bar{b}$.

Otherwise:

$a = \emptyset$	$b = \emptyset$	$a \leq b$
$0$	$1$	$0$
$1$	$0$	$0$
$1$	$1$	$1$

---

precedes

bool precedes(interval<T> a, interval<T> b)

[source]

Details

Returns true if $a$ precedes $b$.

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$\preceq: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{B}$

For $a, b\neq \emptyset$:

$\bar{a} \leq \underline{b}$.

Otherwise:

$a = \emptyset$	$b = \emptyset$	$a \preceq b$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$1$

---

empty

bool empty(interval<T> x)

[source]

Details

Returns true if interval $x$ is empty.

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$\mathrm{isEmpty}: \mathbb{IR} \rightarrow \mathbb{B}$

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entire

bool entire(interval<T> x)

[source]

Details

Returns true if interval $x$ is entire (covers all values).

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$\mathrm{isEntire}: \mathbb{IR} \rightarrow \mathbb{B}$

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just_zero

bool just_zero(interval<T> x)

[source]

Details

Returns true if interval $x$ is exactly zero.

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$\mathrm{justZero}: \mathbb{IR} \rightarrow \mathbb{B}$

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contains

bool contains(interval<T> x, T y)

[source]

Details

Returns true if interval $x$ contains value $y$.

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$\mathrm{contains}: \mathbb{IR}\times\mathbb{R} \rightarrow \mathbb{B}$

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bounded

bool bounded(interval<T> x)

[source]

Details

Returns true if interval $x$ is bounded.

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$\mathrm{bounded}: \mathbb{IR} \rightarrow \mathbb{B}$

---

isfinite

bool isfinite(interval<T> x)

[source]

Details

Returns true if interval $x$ is finite.

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$\mathrm{isfinite}: \mathbb{IR} \rightarrow \mathbb{B}$

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strict_less_or_both_inf

bool strict_less_or_both_inf(T x, T y)

[source]

Details

Returns true if $x < y$ or both are infinite.

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$\mathrm{strictLessOrBothInf}: \mathbb{R}\times\mathbb{R} \rightarrow \mathbb{B}$

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strict_less

bool strict_less(interval<T> a, interval<T> b)

[source]

Details

Returns true if $a \lt b$.

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$\lt: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{B}$

For $a, b\neq \emptyset$:

$\underline{a} < \underline{b} \land \bar{a} < \bar{b}$.

Otherwise:

$a = \emptyset$	$b = \emptyset$	$a < b$
$0$	$1$	$0$
$1$	$0$	$0$
$1$	$1$	$1$

---

strict_precedes

bool strict_precedes(interval<T> a, interval<T> b)

[source]

Details

Returns true if $a$ strictly precedes $b$.

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$\prec: \mathbb{IR}\times\mathbb{IR} \rightarrow \mathbb{B}$

For $a, b\neq \emptyset$:

$\bar{a} < \underline{b}$.

Otherwise:

$a = \emptyset$	$b = \emptyset$	$a \prec b$
$0$	$1$	$1$
$1$	$0$	$1$
$1$	$1$	$1$

---

isinf

bool isinf(interval<T> x)

[source]

Details

Returns true if interval $x$ is infinite.

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$\mathrm{isinf}: \mathbb{IR} \rightarrow \mathbb{B}$

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isnai

bool isnai(interval<T> x)

[source]

Details

Returns true if interval $x$ is Not an Interval (NAI).

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$\mathrm{isnai}: \mathbb{IR} \rightarrow \mathbb{B}$

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is_member

bool is_member(T x, interval<T> y)

[source]

Details

Returns true if $x \in y$.

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$\in: \mathbb{R}\times\mathbb{IR} \rightarrow \mathbb{B}$

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is_singleton

bool is_singleton(interval<T> x)

[source]

Details

Returns true if interval $x$ is a singleton.

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$\mathrm{isSingleton}: \mathbb{IR} \rightarrow \mathbb{B}$

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is_common_interval

bool is_common_interval(interval<T> x)

[source]

Details

Returns true if interval $x$ is a common interval.

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$\mathrm{isCommonInterval}: \mathbb{IR} \rightarrow \mathbb{B}$

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isnormal

bool isnormal(interval<T> x)

[source]

Details

Returns true if interval $x$ is normal.

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$\mathrm{isnormal}: \mathbb{IR} \rightarrow \mathbb{B}$

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is_atomic

bool is_atomic(interval<T> x)

[source]

Details

Returns true if interval $x$ is atomic.

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$\mathrm{isAtomic}: \mathbb{IR} \rightarrow \mathbb{B}$

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isnan

bool isnan(interval<T> x)

[source]

Details

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$\mathrm{isnan}: \mathbb{IR} \rightarrow \mathbb{B}$

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