Enum lambda_calculus::term::Term

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

Var(usize)Abs(Box<Term>)App(Box<Term>, Box<Term>)

Methods

impl Term

fn app(self, argument: Term) -> Term

Applies self to another term without substitution or reduction.

Example

use lambda_calculus::term::Term::*;
use lambda_calculus::arithmetic::{zero, succ};

assert_eq!(succ().app(zero()), App(Box::new(succ()), Box::new(zero())));

fn unvar(self) -> Result<usize, Error>

Consumes a lambda variable and returns its De Bruijn index.

Example

use lambda_calculus::term::Term::*;

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

fn unvar_ref(&self) -> Result<&usize, Error>

Returns a reference to a variable's index.

Example

use lambda_calculus::term::Term::*;

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

fn unabs(self) -> Result<Term, Error>

Consumes an abstraction and returns its underlying term.

Example

use lambda_calculus::term::Term::*;
use lambda_calculus::term::abs;

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

fn unabs_ref(&self) -> Result<&Term, Error>

Returns a reference to an abstraction's underlying term.

Example

use lambda_calculus::term::Term::*;
use lambda_calculus::term::abs;

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

fn unabs_ref_mut(&mut self) -> Result<&mut Term, Error>

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

Example

use lambda_calculus::term::Term::*;
use lambda_calculus::term::abs;

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

fn unapp(self) -> Result<(Term, Term), Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).unapp(), Ok((Var(0), Var(1))));

fn unapp_ref(&self) -> Result<(&Term, &Term), Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).unapp_ref(), Ok((&Var(0), &Var(1))));

fn unapp_ref_mut(&mut self) -> Result<(&mut Term, &mut Term), Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).unapp_ref_mut(), Ok((&mut Var(0), &mut Var(1))));

fn lhs(self) -> Result<Term, Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).lhs(), Ok(Var(0)));

fn lhs_ref(&self) -> Result<&Term, Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).lhs_ref(), Ok(&Var(0)));

fn lhs_ref_mut(&mut self) -> Result<&mut Term, Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).lhs_ref_mut(), Ok(&mut Var(0)));

fn rhs(self) -> Result<Term, Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).rhs(), Ok(Var(1)));

fn rhs_ref(&self) -> Result<&Term, Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).rhs_ref(), Ok(&Var(1)));

fn rhs_ref_mut(&mut self) -> Result<&mut Term, Error>

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

Example

use lambda_calculus::term::Term::*;

assert_eq!(Var(0).app(Var(1)).rhs_ref_mut(), Ok(&mut Var(1)));

fn apply(self, rhs: Term) -> Result<Term, Error>

Applies self to another term with substitution and variable update, consuming them in the process.

Example

use lambda_calculus::parser::parse;

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

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

fn eval(self) -> Result<Term, Error>

Reduces an Application by substitution and variable update.

Example

use lambda_calculus::term::{app, abs};
use lambda_calculus::term::Term::Var;
use lambda_calculus::arithmetic::zero;
use lambda_calculus::combinators::i;

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

impl Term

fn beta_once(&mut self)

Performs a single normal-order β-reduction on self.

Example

use lambda_calculus::arithmetic::succ;

// SUCC := λ λ λ 2 (3 2 1), ONE := λ λ 2 1
let mut succ_one = succ().app(1.into());
succ_one.beta_once();

assert_eq!(&*format!("{}", succ_one), "λλ2((λλ21)21)");

fn beta_full(&mut self)

Performs full normal-order β-reduction on self.

Example

use lambda_calculus::arithmetic::pred;

let mut pred_one = pred().app(1.into());
pred_one.beta_full();

assert_eq!(pred_one, 0.into());

impl Term

fn value(&self) -> Result<usize, Error>

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

Example

use lambda_calculus::arithmetic::one;

assert_eq!(one().value(), Ok(1));

fn is_cnum(&self) -> bool

Checks whether self is a Church-encoded number.

Example

use lambda_calculus::arithmetic::one;

assert!(one().is_cnum());

impl Term

fn is_pair(&self) -> bool

Checks whether self is a Church-encoded pair.

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let pair01 = pair().app(zero()).app(one());

assert!(pair01.is_pair());

fn unpair(self) -> Result<(Term, Term), Error>

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

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.unpair(), Ok((zero(), one())));

fn unpair_ref(&self) -> Result<(&Term, &Term), Error>

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

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.unpair_ref(), Ok((&zero(), &one())));

fn unpair_ref_mut(&mut self) -> Result<(&mut Term, &mut Term), Error>

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

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let mut pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.unpair_ref_mut(), Ok((&mut zero(), &mut one())));

fn fst(self) -> Result<Term, Error>

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

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.fst(), Ok(zero()));

fn fst_ref(&self) -> Result<&Term, Error>

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

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.fst_ref(), Ok(&zero()));

fn fst_ref_mut(&mut self) -> Result<&mut Term, Error>

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::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let mut pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.fst_ref_mut(), Ok(&mut zero()));

fn snd(self) -> Result<Term, Error>

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

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.snd(), Ok(one()));

fn snd_ref(&self) -> Result<&Term, Error>

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

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.snd_ref(), Ok(&one()));

fn snd_ref_mut(&mut self) -> Result<&mut Term, Error>

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

Example

use lambda_calculus::pair::pair;
use lambda_calculus::arithmetic::{zero, one};

let mut pair01 = pair().app(zero()).app(one());

assert_eq!(pair01.snd_ref_mut(), Ok(&mut one()));

impl Term

fn is_empty(&self) -> bool

Checks whether self is a Church-encoded empty list, i.e. nil().

Example

use lambda_calculus::list::nil;

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

fn is_list(&self) -> bool

Checks whether self is a Church-encoded list.

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert!(list_110.is_list());

fn uncons(self) -> Result<(Term, Term), Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.uncons(), Ok((one(), Term::from(vec![one(), zero()]))));

fn uncons_ref(&self) -> Result<(&Term, &Term), Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.uncons_ref(), Ok((&one(), &Term::from(vec![one(), zero()]))));

fn uncons_ref_mut(&mut self) -> Result<(&mut Term, &mut Term), Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let mut list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.uncons_ref_mut(),
           Ok((&mut one(), &mut Term::from(vec![one(), zero()]))));

fn head(self) -> Result<Term, Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.head(), Ok(one()));

fn head_ref(&self) -> Result<&Term, Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.head_ref(), Ok(&one()));

fn head_ref_mut(&mut self) -> Result<&mut Term, Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let mut list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.head_ref_mut(), Ok(&mut one()));

fn tail(self) -> Result<Term, Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.tail(), Ok(Term::from(vec![one(), zero()])));

fn tail_ref(&self) -> Result<&Term, Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.tail_ref(), Ok(&Term::from(vec![one(), zero()])));

fn tail_ref_mut(&mut self) -> Result<&mut Term, Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let mut list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.tail_ref_mut(), Ok(&mut Term::from(vec![one(), zero()])));

fn len(&self) -> Result<usize, Error>

Returns the length of a Church-encoded list

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.len(), Ok(3));

fn push(self, term: Term) -> Term

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.push(zero()), Term::from(vec![zero(), one(), one(), zero()]));

fn pop(&mut self) -> Result<Term, Error>

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

Example

use lambda_calculus::term::Term;
use lambda_calculus::arithmetic::{zero, one};

let mut list_110 = Term::from(vec![one(), one(), zero()]);

assert_eq!(list_110.pop(), Ok(one()));
assert_eq!(list_110, Term::from(vec![one(), zero()]));

Trait Implementations

impl Debug for Term

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

impl PartialEq for Term

fn eq(&self, __arg_0: &Term) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, __arg_0: &Term) -> bool

This method tests for !=.

impl Clone for Term

fn clone(&self) -> Term

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Display for Term

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl From<usize> for Term

fn from(n: usize) -> Self

Performs the conversion.

impl From<(Term, Term)> for Term

fn from((t1, t2): (Term, Term)) -> Self

Performs the conversion.

impl From<Vec<Term>> for Term

fn from(terms: Vec<Term>) -> Self

Performs the conversion.

impl Iterator for Term

type Item = Term

The type of the elements being iterated over.

fn next(&mut self) -> Option<Term>

Advances the iterator and returns the next value.

fn size_hint(&self) -> (usize, Option<usize>)

Returns the bounds on the remaining length of the iterator.

fn count(self) -> usize

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

fn last(self) -> Option<Self::Item>

Consumes the iterator, returning the last element.

fn nth(&mut self, n: usize) -> Option<Self::Item>

Returns the nth element of the iterator.

fn chain<U>(self, other: U) -> Chain<Self, U::IntoIter> where
    U: IntoIterator<Item = Self::Item>, 

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

fn zip<U>(self, other: U) -> Zip<Self, U::IntoIter> where
    U: IntoIterator, 

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

fn map<B, F>(self, f: F) -> Map<Self, F> where
    F: FnMut(Self::Item) -> B, 

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

fn filter<P>(self, predicate: P) -> Filter<Self, P> where
    P: FnMut(&Self::Item) -> bool, 

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

fn filter_map<B, F>(self, f: F) -> FilterMap<Self, F> where
    F: FnMut(Self::Item) -> Option<B>, 

Creates an iterator that both filters and maps.

fn enumerate(self) -> Enumerate<Self>

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

fn peekable(self) -> Peekable<Self>

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

fn skip_while<P>(self, predicate: P) -> SkipWhile<Self, P> where
    P: FnMut(&Self::Item) -> bool, 

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

fn take_while<P>(self, predicate: P) -> TakeWhile<Self, P> where
    P: FnMut(&Self::Item) -> bool, 

Creates an iterator that yields elements based on a predicate.

fn skip(self, n: usize) -> Skip<Self>

Creates an iterator that skips the first n elements.

fn take(self, n: usize) -> Take<Self>

Creates an iterator that yields its first n elements.

fn scan<St, B, F>(self, initial_state: St, f: F) -> Scan<Self, St, F> where
    F: FnMut(&mut St, Self::Item) -> Option<B>, 

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

fn flat_map<U, F>(self, f: F) -> FlatMap<Self, U, F> where
    F: FnMut(Self::Item) -> U,
    U: IntoIterator, 

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

fn fuse(self) -> Fuse<Self>

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

fn inspect<F>(self, f: F) -> Inspect<Self, F> where
    F: FnMut(&Self::Item) -> (), 

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

fn by_ref(&mut self) -> &mut Self

Borrows an iterator, rather than consuming it.

fn collect<B>(self) -> B where
    B: FromIterator<Self::Item>, 

Transforms an iterator into a collection.

fn partition<B, F>(self, f: F) -> (B, B) where
    B: Default + Extend<Self::Item>,
    F: FnMut(&Self::Item) -> bool, 

Consumes an iterator, creating two collections from it.

fn fold<B, F>(self, init: B, f: F) -> B where
    F: FnMut(B, Self::Item) -> B, 

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

fn all<F>(&mut self, f: F) -> bool where
    F: FnMut(Self::Item) -> bool, 

Tests if every element of the iterator matches a predicate.

fn any<F>(&mut self, f: F) -> bool where
    F: FnMut(Self::Item) -> bool, 

Tests if any element of the iterator matches a predicate.

fn find<P>(&mut self, predicate: P) -> Option<Self::Item> where
    P: FnMut(&Self::Item) -> bool, 

Searches for an element of an iterator that satisfies a predicate.

fn position<P>(&mut self, predicate: P) -> Option<usize> where
    P: FnMut(Self::Item) -> bool, 

Searches for an element in an iterator, returning its index.

fn rposition<P>(&mut self, predicate: P) -> Option<usize> where
    P: FnMut(Self::Item) -> bool,
    Self: ExactSizeIterator + DoubleEndedIterator, 

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

fn max(self) -> Option<Self::Item> where
    Self::Item: Ord, 

Returns the maximum element of an iterator.

fn min(self) -> Option<Self::Item> where
    Self::Item: Ord, 

Returns the minimum element of an iterator.

fn max_by_key<B, F>(self, f: F) -> Option<Self::Item> where
    B: Ord,
    F: FnMut(&Self::Item) -> B, 

Returns the element that gives the maximum value from the specified function.

fn max_by<F>(self, compare: F) -> Option<Self::Item> where
    F: FnMut(&Self::Item, &Self::Item) -> Ordering, 

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

fn min_by_key<B, F>(self, f: F) -> Option<Self::Item> where
    B: Ord,
    F: FnMut(&Self::Item) -> B, 

Returns the element that gives the minimum value from the specified function.

fn min_by<F>(self, compare: F) -> Option<Self::Item> where
    F: FnMut(&Self::Item, &Self::Item) -> Ordering, 

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

fn rev(self) -> Rev<Self> where
    Self: DoubleEndedIterator, 

Reverses an iterator's direction.

fn unzip<A, B, FromA, FromB>(self) -> (FromA, FromB) where
    FromA: Default + Extend<A>,
    FromB: Default + Extend<B>,
    Self: Iterator<Item = (A, B)>, 

Converts an iterator of pairs into a pair of containers.

fn cloned<'a, T>(self) -> Cloned<Self> where
    Self: Iterator<Item = &'a T>,
    T: 'a + Clone, 

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

fn cycle(self) -> Cycle<Self> where
    Self: Clone, 

Repeats an iterator endlessly.

fn sum<S>(self) -> S where
    S: Sum<Self::Item>, 

Sums the elements of an iterator.

fn product<P>(self) -> P where
    P: Product<Self::Item>, 

Iterates over the entire iterator, multiplying all the elements

fn cmp<I>(self, other: I) -> Ordering where
    I: IntoIterator<Item = Self::Item>,
    Self::Item: Ord, 

Lexicographically compares the elements of this Iterator with those of another.

fn partial_cmp<I>(self, other: I) -> Option<Ordering> where
    I: IntoIterator,
    Self::Item: PartialOrd<I::Item>, 

Lexicographically compares the elements of this Iterator with those of another.

fn eq<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialEq<I::Item>, 

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

fn ne<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialEq<I::Item>, 

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

fn lt<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialOrd<I::Item>, 

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

fn le<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialOrd<I::Item>, 

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

fn gt<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialOrd<I::Item>, 

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

fn ge<I>(self, other: I) -> bool where
    I: IntoIterator,
    Self::Item: PartialOrd<I::Item>, 

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

impl Index<usize> for Term

type Output = Term

The returned type after indexing

fn index(&self, i: usize) -> &Self::Output

The method for the indexing (container[index]) operation