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//! [Church pair](https://en.wikipedia.org/wiki/Church_encoding#Church_pairs) use term::*; use term::Term::*; use term::Error::*; use booleans::*; /// Produces a Church-encoded pair; applying it to two other terms puts them inside it. /// /// PAIR := λxyz.z x y = λ λ λ 1 3 2 /// /// # 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())); /// assert_eq!(pair01.snd_ref(), Ok(&one())); /// ``` pub fn pair() -> Term { abs(abs(abs( Var(1) .app(Var(3)) .app(Var(2)) ))) } /// Applied to a Church-encoded pair `(a, b)` it yields `a`. /// /// FIRST := λp.p TRUE = λ 1 TRUE /// /// # Example /// ``` /// use lambda_calculus::pair::{pair, first}; /// use lambda_calculus::arithmetic::{zero, one}; /// use lambda_calculus::reduction::beta_full; /// /// let pair_0_1 = pair().app(zero()).app(one()); /// /// assert_eq!(beta_full(first().app(pair_0_1)), zero()); /// ``` pub fn first() -> Term { abs(Var(1).app(tru())) } /// Applied to a Church-encoded pair `(a, b)` it yields `b`. /// /// SECOND := λp.p FALSE = λ 1 FALSE /// /// # Example /// ``` /// use lambda_calculus::pair::{pair, second}; /// use lambda_calculus::arithmetic::{zero, one}; /// use lambda_calculus::reduction::beta_full; /// /// let pair_0_1 = pair().app(zero()).app(one()); /// /// assert_eq!(beta_full(second().app(pair_0_1)), one()); /// ``` pub fn second() -> Term { abs(Var(1).app(fls())) } impl Term { /// 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()); /// ``` pub fn is_pair(&self) -> bool { self.fst_ref().is_ok() && self.snd_ref().is_ok() } /// 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()))); /// ``` pub fn unpair(self) -> Result<(Term, Term), Error> { if let Abs(_) = self { if let Ok((wrapped_a, b)) = self.unabs().and_then(|t| t.unapp()) { Ok((try!(wrapped_a.rhs()), b)) } else { Err(NotAPair) } } else { if let Ok((wrapped_a, b)) = self.unapp() { Ok((try!(wrapped_a.rhs()), b)) } else { Err(NotAPair) } } } /// 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()))); /// ``` pub fn unpair_ref(&self) -> Result<(&Term, &Term), Error> { if let Abs(_) = *self { if let Ok((wrapped_a, b)) = self.unabs_ref().and_then(|t| t.unapp_ref()) { Ok((try!(wrapped_a.rhs_ref()), b)) } else { Err(NotAPair) } } else { if let Ok((wrapped_a, b)) = self.unapp_ref() { Ok((try!(wrapped_a.rhs_ref()), b)) } else { Err(NotAPair) } } } /// 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()))); /// ``` pub fn unpair_ref_mut(&mut self) -> Result<(&mut Term, &mut Term), Error> { if let Abs(_) = *self { if let Ok((wrapped_a, b)) = self.unabs_ref_mut().and_then(|t| t.unapp_ref_mut()) { Ok((try!(wrapped_a.rhs_ref_mut()), b)) } else { Err(NotAPair) } } else { if let Ok((wrapped_a, b)) = self.unapp_ref_mut() { Ok((try!(wrapped_a.rhs_ref_mut()), b)) } else { Err(NotAPair) } } } /// 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())); /// ``` pub fn fst(self) -> Result<Term, Error> { Ok(try!(self.unpair()).0) } /// 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())); /// ``` pub fn fst_ref(&self) -> Result<&Term, Error> { Ok(try!(self.unpair_ref()).0) } /// 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())); /// ``` pub fn fst_ref_mut(&mut self) -> Result<&mut Term, Error> { Ok(try!(self.unpair_ref_mut()).0) } /// 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())); /// ``` pub fn snd(self) -> Result<Term, Error> { Ok(try!(self.unpair()).1) } /// 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())); /// ``` pub fn snd_ref(&self) -> Result<&Term, Error> { Ok(try!(self.unpair_ref()).1) } /// 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())); /// ``` pub fn snd_ref_mut(&mut self) -> Result<&mut Term, Error> { Ok(try!(self.unpair_ref_mut()).1) } } impl From<(Term, Term)> for Term { fn from((t1, t2): (Term, Term)) -> Self { abs( Var(1) .app(t1) .app(t2) ) } } #[cfg(test)] mod test { use super::*; use reduction::beta_full; #[test] fn pair_from_pair() { assert_eq!(Term::from((0.into(), 1.into())), beta_full(pair().app(0.into()).app(1.into()))); } #[test] fn pair_operations() { let pair_four_three = beta_full(pair().app(4.into()).app(3.into())); assert!(pair_four_three.is_pair()); assert_eq!(pair_four_three.fst_ref(), Ok(&4.into())); assert_eq!(pair_four_three.snd_ref(), Ok(&3.into())); let unpaired = pair_four_three.unpair(); assert_eq!(unpaired, Ok((4.into(), 3.into()))); } }