Enum Term

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

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§

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Var(usize)

a variable

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Abs(Box<Term>)

an abstraction

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App(Box<(Term, Term)>)

an application

Implementations§

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impl Term

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pub fn unvar(self) -> Result<usize, TermError>

Returns a variable’s De Bruijn index, consuming it in the process.

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not a Variable.

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

Returns a reference to a variable’s De Bruijn index.

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not a Variable.

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pub fn unvar_mut(&mut self) -> Result<&mut usize, TermError>

Returns a mutable reference to a variable’s De Bruijn index.

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not a Variable.

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pub fn unabs(self) -> Result<Term, TermError>

Returns an abstraction’s underlying term, consuming it in the process.

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Abstraction.

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

Returns a reference to an abstraction’s underlying term.

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Abstraction.

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pub fn unabs_mut(&mut self) -> Result<&mut Term, TermError>

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

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Abstraction.

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pub fn unapp(self) -> Result<(Term, Term), TermError>

Returns a pair containing an application’s underlying terms, consuming it in the process.

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Application.

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

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

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Application.

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pub fn unapp_mut(&mut self) -> Result<(&mut Term, &mut Term), TermError>

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

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Application.

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pub fn lhs(self) -> Result<Term, TermError>

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

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Application.

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

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

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Application.

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pub fn lhs_mut(&mut self) -> Result<&mut Term, TermError>

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

§Example
use lambda_calculus::*;

assert_eq!(app(Var(1), Var(2)).lhs_mut(), Ok(&mut Var(1)));
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pub fn rhs(self) -> Result<Term, TermError>

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

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Application.

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

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

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Application.

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pub fn rhs_mut(&mut self) -> Result<&mut Term, TermError>

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

§Example
use lambda_calculus::*;

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

Returns a TermError if self is not an Application.

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pub fn is_supercombinator(&self) -> bool

Returns true if self is a supercombinator.

§Example
use lambda_calculus::*;

let term1 = abs(app(Var(1), abs(Var(1)))); // λ 1 (λ 1)
let term2 = app(abs(Var(2)), abs(Var(1))); // (λ 2) (λ 1)

assert_eq!(term1.is_supercombinator(), true);
assert_eq!(term2.is_supercombinator(), false);
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pub fn max_depth(&self) -> u32

Returns the maximum depth of lambda abstractions in the given Term.

§Example
use lambda_calculus::*;

assert_eq!(abs(Var(1)).max_depth(), 1);
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pub fn is_isomorphic_to(&self, other: &Term) -> bool

Returns true if self is structurally isomorphic to other.

§Example
use lambda_calculus::*;

let term1 = abs(Var(1)); // λ 1
let term2 = abs(Var(2)); // λ 2
let term3 = abs(Var(1)); // λ 1

assert_eq!(term1.is_isomorphic_to(&term2), false);
assert_eq!(term1.is_isomorphic_to(&term3), true);
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pub fn has_free_variables(&self) -> bool

Returns true if self has any free vairables.

§Example
use lambda_calculus::*;

let with_freevar = abs(Var(2));     // λ 2
let without_freevar = abs(Var(1));  // λ 1

assert!(with_freevar.has_free_variables());
assert!(!without_freevar.has_free_variables());
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impl Term

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pub fn apply(&mut self, rhs: &Term) -> Result<(), TermError>

Applies a Term to self via substitution and variable update.

§Example
use lambda_calculus::*;

let mut term1  = parse(&"λλ42(λ13)", DeBruijn).unwrap();
let term2      = parse(&"λ51", DeBruijn).unwrap();
let result     = parse(&"λ3(λ61)(λ1(λ71))", DeBruijn).unwrap();

term1.apply(&term2);

assert_eq!(term1, result);
§Errors

Returns a TermError if self is not an Abstraction.

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pub fn reduce(&mut self, order: Order, limit: usize) -> usize

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

§Example
use lambda_calculus::*;

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

expression.reduce(NOR, 0);

assert_eq!(expression, reduced);

Trait Implementations§

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impl Clone for Term

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fn clone(&self) -> Term

Returns a copy of the value. Read more
1.0.0 · Source§

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

Performs copy-assignment from source. Read more
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impl Debug for Term

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

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

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

Formats the value using the given formatter. Read more
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impl From<(Term, Term)> for Term

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fn from((a, b): (Term, Term)) -> Term

Converts to this type from the input type.
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impl From<Option<Term>> for Term

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fn from(option: Option<Term>) -> Term

Converts to this type from the input type.
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impl From<Result<Term, Term>> for Term

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fn from(result: Result<Term, Term>) -> Term

Converts to this type from the input type.
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impl From<Vec<Term>> for Term

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fn from(vec: Vec<Term>) -> Term

Converts to this type from the input type.
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impl From<bool> for Term

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fn from(b: bool) -> Term

Converts to this type from the input type.
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impl Hash for Term

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fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher. Read more
1.3.0 · Source§

fn hash_slice<H>(data: &[Self], state: &mut H)
where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher. Read more
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impl PartialEq for Term

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

Tests for self and other values to be equal, and is used by ==.
1.0.0 · Source§

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl Eq for Term

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impl StructuralPartialEq for Term

Auto Trait Implementations§

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impl Freeze for Term

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impl RefUnwindSafe for Term

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impl Send for Term

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impl Sync for Term

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impl Unpin for Term

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impl UnwindSafe for Term

Blanket Implementations§

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.