Enum lambda_calculus::term::Term [] [src]

pub enum Term {
    Var(usize),
    Abs(Box<Term>),
    App(Box<Term>, Box<Term>),
}

A lambda term that is either a variable with a De Bruijn index, an abstraction over a term or an applicaction of one term to another.

Variants

a variable

an abstraction

an application

Methods

impl Term
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Applies self to another term without substitution or reduction.

Example

use lambda_calculus::term::*;

assert_eq!(Var(1).app(Var(2)), App(Box::new(Var(1)), Box::new(Var(2))));

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Consumes a lambda variable and returns its De Bruijn index.

Example

use lambda_calculus::term::*;

assert_eq!(Var(1).unvar(), Ok(1));

Errors

The function will return an error if self is not a Variable.

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Returns a reference to a variable's index.

Example

use lambda_calculus::term::*;

assert_eq!(Var(1).unvar_ref(), Ok(&1));

Errors

The function will return an error if self is not a Variable.

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Returns a mutable reference to a variable's index.

Example

use lambda_calculus::term::*;

assert_eq!(Var(1).unvar_mut(), Ok(&mut 1));

Errors

The function will return an error if self is not a Variable.

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Consumes an abstraction and returns its underlying term.

Example

use lambda_calculus::term::*;

assert_eq!(abs(Var(1)).unabs(), Ok(Var(1)));

Errors

The function will return an error if self is not an Abstraction.

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Returns a reference to an abstraction's underlying term.

Example

use lambda_calculus::term::*;

assert_eq!(abs(Var(1)).unabs_ref(), Ok(&Var(1)));

Errors

The function will return an error if self is not an Abstraction.

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Returns a mutable reference to an abstraction's underlying term.

Example

use lambda_calculus::term::*;

assert_eq!(abs(Var(1)).unabs_mut(), Ok(&mut Var(1)));

Errors

The function will return an error if self is not an Abstraction.

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Consumes an application and returns a pair containing its underlying terms.

Example

use lambda_calculus::term::*;

assert_eq!(app(Var(1), Var(2)).unapp(), Ok((Var(1), Var(2))));

Errors

The function will return an error if self is not an Application.

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Returns a pair containing references to an application's underlying terms.

Example

use lambda_calculus::term::*;

assert_eq!(app(Var(1), Var(2)).unapp_ref(), Ok((&Var(1), &Var(2))));

Errors

The function will return an error if self is not an Application.

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Returns a pair containing mutable references to an application's underlying terms.

Example

use lambda_calculus::term::*;

assert_eq!(app(Var(1), Var(2)).unapp_mut(), Ok((&mut Var(1), &mut Var(2))));

Errors

The function will return an error if self is not an Application.

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Returns the left-hand side term of an application. Consumes self.

Example

use lambda_calculus::term::*;

assert_eq!(Var(1).app(Var(2)).lhs(), Ok(Var(1)));

Errors

The function will return an error if self is not an Application.

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Returns a reference to the left-hand side term of an application.

Example

use lambda_calculus::term::*;

assert_eq!(app(Var(1), Var(2)).lhs_ref(), Ok(&Var(1)));

Errors

The function will return an error if self is not an Application.

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Returns a mutable reference to the left-hand side term of an application.

Example

use lambda_calculus::term::*;

assert_eq!(app(Var(1), Var(2)).lhs_mut(), Ok(&mut Var(1)));

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Returns the right-hand side term of an application. Consumes self.

Example

use lambda_calculus::term::*;

assert_eq!(app(Var(1), Var(2)).rhs(), Ok(Var(2)));

Errors

The function will return an error if self is not an Application.

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Returns a reference to the right-hand side term of an application.

Example

use lambda_calculus::term::*;

assert_eq!(app(Var(1), Var(2)).rhs_ref(), Ok(&Var(2)));

Errors

The function will return an error if self is not an Application.

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Returns a mutable reference to the right-hand side term of an application.

Example

use lambda_calculus::term::*;

assert_eq!(app(Var(1), Var(2)).rhs_mut(), Ok(&mut Var(2)));

Errors

The function will return an error if self is not an Application.

impl Term
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Applies self to another Term and performs substitution, consuming self in the process.

Example

use lambda_calculus::parser::*;

let lhs    = parse(&"λλ42(λ13)", DeBruijn).unwrap();
let rhs    = parse(&"λ51", DeBruijn).unwrap();
let result = parse(&"λ3(λ61)(λ1(λ71))", DeBruijn).unwrap();

assert_eq!(lhs.apply(&rhs), Ok(result));

Errors

The function will return an error if self is not an Abstraction.

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Reduces an Application by substitution and variable update.

Example

use lambda_calculus::*;
use lambda_calculus::combinators::i;

assert_eq!(app(i(), Var(1)).eval(), Ok(Var(1)));

Errors

The function will return an error if self is not an Application or if its left hand side term is not an Abstraction.

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Performs β-reduction on a Term with the specified evaluation Order, an optional limit on number of reductions (0 means no limit) and optional display of reduction steps; it returns the number of performed reductions.

Example

use lambda_calculus::*;

let expression = parse(&"(λa.λb.λc.b (a b c)) (λa.λb.b)", Classic);
let reduced    = parse(&"λa.λb.a b", Classic);

assert!(expression.is_ok());
assert!(reduced.is_ok());

let mut expression = expression.unwrap();
expression.beta(NOR, 0, false);

assert_eq!(expression, reduced.unwrap());

impl Term
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Returns the value of self if it's a Church-encoded number.

Example

use lambda_calculus::*;

assert_eq!(Term::from(1).value(), Ok(1));

Errors

The function will return an error if self is not a Church number.

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Checks whether self is a Church-encoded number.

Example

use lambda_calculus::*;

assert!(Term::from(1).is_cnum());
assert!(!Var(1).is_cnum());
assert!(!Term::from(true).is_cnum(), false);

impl Term
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Checks whether self is a Church-encoded pair.

Example

use lambda_calculus::*;

assert!(Term::from((1.into(), 2.into())).is_pair());

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Splits a Church-encoded pair into a pair of terms, consuming self.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from((1.into(), 2.into())).unpair(),
    Ok((1.into(), 2.into()))
);

Errors

The function will return an error if self is not a Church pair.

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Splits a Church-encoded pair into a pair of references to its underlying terms.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from((1.into(), 2.into())).unpair_ref(),
    Ok((&1.into(), &2.into()))
);

Errors

The function will return an error if self is not a Church pair.

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Splits a Church-encoded pair into a pair of mutable references to its underlying terms.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from((1.into(), 2.into())).unpair_mut(),
    Ok((&mut 1.into(), &mut 2.into()))
);

Errors

The function will return an error if self is not a Church pair.

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Returns the first term from a Church-encoded pair, consuming self.

Example

use lambda_calculus::*;

assert_eq!(Term::from((1.into(), 2.into())).fst(), Ok(1.into()));

Errors

The function will return an error if self is not a Church pair.

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Returns a reference to the first term of a Church-encoded pair.

Example

use lambda_calculus::*;

assert_eq!(Term::from((1.into(), 2.into())).fst_ref(), Ok(&1.into()));

Errors

The function will return an error if self is not a Church pair.

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Returns a mutable reference to the first term of a Church-encoded pair. Returns a reference to the first term of a Church-encoded pair.

Example

use lambda_calculus::*;

assert_eq!(Term::from((1.into(), 2.into())).fst_mut(), Ok(&mut 1.into()));

Errors

The function will return an error if self is not a Church pair.

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Returns the second term from a Church-encoded pair, consuming self.

Example

use lambda_calculus::*;

assert_eq!(Term::from((1.into(), 2.into())).snd(), Ok(2.into()));

Errors

The function will return an error if self is not a Church pair.

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Returns a reference to the second term of a Church-encoded pair.

Example

use lambda_calculus::*;

assert_eq!(Term::from((1.into(), 2.into())).snd_ref(), Ok(&2.into()));

Errors

The function will return an error if self is not a Church pair.

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Returns a mutable reference to the second term of a Church-encoded pair.

Example

use lambda_calculus::*;

assert_eq!(Term::from((1.into(), 2.into())).snd_mut(), Ok(&mut 2.into()));

Errors

The function will return an error if self is not a Church pair.

impl Term
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Checks whether self is a empty Church list, i.e. nil().

Example

use lambda_calculus::church::lists::nil;

assert!(nil().is_empty());

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Checks whether self is a Church list.

Example

use lambda_calculus::*;

assert!(Term::from(vec![1.into(), 2.into(), 3.into()]).is_list());

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Splits a Church list into a pair containing its first term and a list of all the other terms, consuming self.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).uncons(),
    Ok((1.into(), vec![2.into(), 3.into()].into()))
);

Errors

The function will return an error if self is not a Church list.

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Splits a Church list into a pair containing references to its first term and a to list of all the other terms.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).uncons_ref(),
    Ok((&1.into(), &vec![2.into(), 3.into()].into()))
);

Errors

The function will return an error if self is not a Church list.

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Splits a Church list into a pair containing mutable references to its first term and a to list of all the other terms.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).uncons_mut(),
    Ok((&mut 1.into(), &mut vec![2.into(), 3.into()].into()))
);

Errors

The function will return an error if self is not a Church list.

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Returns the first term from a Church list, consuming self.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).head(),
    Ok(1.into())
);

Errors

The function will return an error if self is not a Church list.

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Returns a reference to the first term of a Church list.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).head_ref(),
    Ok(&1.into())
);

Errors

The function will return an error if self is not a Church list.

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Returns a mutable reference to the first term of a Church list.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).head_mut(),
    Ok(&mut 1.into())
);

Errors

The function will return an error if self is not a Church list.

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Returns a list of all the terms of a Church list but the first one, consuming self.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).tail(),
    Ok(vec![2.into(), 3.into()].into())
);

Errors

The function will return an error if self is not a Church list.

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Returns a reference to a list of all the terms of a Church list but the first one.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).tail_ref(),
    Ok(&vec![2.into(), 3.into()].into())
);

Errors

The function will return an error if self is not a Church list.

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Returns a mutable reference to a list of all the terms of a Church list but the first one.

Example

use lambda_calculus::*;

assert_eq!(
    Term::from(vec![1.into(), 2.into(), 3.into()]).tail_mut(),
    Ok(&mut vec![2.into(), 3.into()].into())
);

Errors

The function will return an error if self is not a Church list.

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Returns the length of a Church list

Example

use lambda_calculus::*;

assert_eq!(Term::from(vec![1.into(), 2.into(), 3.into()]).len(), Ok(3));

Errors

The function will return an error if self is not a Church list.

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Adds a term to the beginning of a Church list and returns the new list. Consumes self and the argument.

Example

use lambda_calculus::*;

let list_from_vec = Term::from(vec![1.into(), 2.into(), 3.into()]);
let list_pushed = Term::from(vec![])
                  .push(3.into())
                  .and_then(|t| t.push(2.into()))
                  .and_then(|t| t.push(1.into()))
                  .unwrap();

assert_eq!(list_from_vec, list_pushed);

Errors

The function will return an error if self is not a Church list or a nil().

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Removes the first element from a Church list and returns it.

Example

use lambda_calculus::*;

let mut list = Term::from(vec![1.into(), 2.into(), 3.into()]);

assert_eq!(list.pop(), Ok(1.into()));
assert_eq!(list, vec![2.into(), 3.into()].into());
assert_eq!(list.pop(), Ok(2.into()));
assert_eq!(list, vec![3.into()].into());
assert_eq!(list.pop(), Ok(3.into()));
assert_eq!(list, vec![].into());

assert!(list.is_empty())

Errors

The function will return an error if self is not a Church list.

Trait Implementations

impl PartialEq for Term
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This method tests for self and other values to be equal, and is used by ==. Read more

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This method tests for !=.

impl Clone for Term
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Returns a copy of the value. Read more

1.0.0
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Performs copy-assignment from source. Read more

impl Hash for Term
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Feeds this value into the given [Hasher]. Read more

1.3.0
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Feeds a slice of this type into the given [Hasher]. Read more

impl Eq for Term
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impl Display for Term
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Formats the value using the given formatter. Read more

impl Debug for Term
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Formats the value using the given formatter.

impl From<usize> for Term
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Performs the conversion.

impl From<bool> for Term
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Performs the conversion.

impl From<(Term, Term)> for Term
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Performs the conversion.

impl From<Vec<Term>> for Term
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Performs the conversion.

impl Iterator for Term
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The type of the elements being iterated over.

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Advances the iterator and returns the next value. Read more

1.0.0
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Returns the bounds on the remaining length of the iterator. Read more

1.0.0
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Consumes the iterator, counting the number of iterations and returning it. Read more

1.0.0
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Consumes the iterator, returning the last element. Read more

1.0.0
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Returns the nth element of the iterator. Read more

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🔬 This is a nightly-only experimental API. (iterator_step_by)

unstable replacement of Range::step_by

Creates an iterator starting at the same point, but stepping by the given amount at each iteration. Read more

1.0.0
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Takes two iterators and creates a new iterator over both in sequence. Read more

1.0.0
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'Zips up' two iterators into a single iterator of pairs. Read more

1.0.0
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Takes a closure and creates an iterator which calls that closure on each element. Read more

1.22.0
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Calls a closure on each element of an iterator. Read more

1.0.0
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Creates an iterator which uses a closure to determine if an element should be yielded. Read more

1.0.0
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Creates an iterator that both filters and maps. Read more

1.0.0
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Creates an iterator which gives the current iteration count as well as the next value. Read more

1.0.0
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Creates an iterator which can use peek to look at the next element of the iterator without consuming it. Read more

1.0.0
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Creates an iterator that [skip]s elements based on a predicate. Read more

1.0.0
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Creates an iterator that yields elements based on a predicate. Read more

1.0.0
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Creates an iterator that skips the first n elements. Read more

1.0.0
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Creates an iterator that yields its first n elements. Read more

1.0.0
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An iterator adaptor similar to [fold] that holds internal state and produces a new iterator. Read more

1.0.0
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Creates an iterator that works like map, but flattens nested structure. Read more

1.0.0
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Creates an iterator which ends after the first [None]. Read more

1.0.0
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Do something with each element of an iterator, passing the value on. Read more

1.0.0
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Borrows an iterator, rather than consuming it. Read more

1.0.0
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Transforms an iterator into a collection. Read more

1.0.0
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Consumes an iterator, creating two collections from it. Read more

1.0.0
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An iterator adaptor that applies a function, producing a single, final value. Read more

1.0.0
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Tests if every element of the iterator matches a predicate. Read more

1.0.0
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Tests if any element of the iterator matches a predicate. Read more

1.0.0
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Searches for an element of an iterator that satisfies a predicate. Read more

1.0.0
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Searches for an element in an iterator, returning its index. Read more

1.0.0
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Searches for an element in an iterator from the right, returning its index. Read more

1.0.0
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Returns the maximum element of an iterator. Read more

1.0.0
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Returns the minimum element of an iterator. Read more

1.6.0
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Returns the element that gives the maximum value from the specified function. Read more

1.15.0
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Returns the element that gives the maximum value with respect to the specified comparison function. Read more

1.6.0
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Returns the element that gives the minimum value from the specified function. Read more

1.15.0
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Returns the element that gives the minimum value with respect to the specified comparison function. Read more

1.0.0
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Reverses an iterator's direction. Read more

1.0.0
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Converts an iterator of pairs into a pair of containers. Read more

1.0.0
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Creates an iterator which [clone]s all of its elements. Read more

1.0.0
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Repeats an iterator endlessly. Read more

1.11.0
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Sums the elements of an iterator. Read more

1.11.0
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Iterates over the entire iterator, multiplying all the elements Read more

1.5.0
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Lexicographically compares the elements of this Iterator with those of another. Read more

1.5.0
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Lexicographically compares the elements of this Iterator with those of another. Read more

1.5.0
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Determines if the elements of this Iterator are equal to those of another. Read more

1.5.0
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Determines if the elements of this Iterator are unequal to those of another. Read more

1.5.0
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Determines if the elements of this Iterator are lexicographically less than those of another. Read more

1.5.0
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Determines if the elements of this Iterator are lexicographically less or equal to those of another. Read more

1.5.0
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Determines if the elements of this Iterator are lexicographically greater than those of another. Read more

1.5.0
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Determines if the elements of this Iterator are lexicographically greater than or equal to those of another. Read more

impl Index<usize> for Term
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The returned type after indexing.

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Performs the indexing (container[index]) operation.

impl From<Option<Term>> for Term
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Performs the conversion.