ecsolticia.codeberg.page
Compile-time construction of Peano axioms-based natural numbers and addition, multiplication, and exponentiation defined through them within Rust. (Mirrored from Codeberg)
impl leq
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src/lib.rs
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src/lib.rs
···
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Nat,
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Succ,
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_0,
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+
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eq::Eq,
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eq::ProofEq,
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+
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+
leq::Leq,
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leq::ProofLeq,
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+
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add::Add,
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mul::Times,
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exp::Exp
···
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// Define equality of naturals
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impl<T: Nat> Eq<T, T> for ProofEq<T, T> {}
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+
}
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+
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pub mod leq {
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use super::prelude::*;
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pub trait Leq<A: Nat, B: Nat> {
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fn check() -> () {}
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}
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pub struct ProofLeq<A: Nat, B: Nat>(A, B);
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// Base case
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// 0 <= N for every N
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impl<A: Nat> Leq<_0, A> for ProofLeq<_0, A> {}
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+
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// Induction
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// A <= B means S(A) <= S(B)
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impl<A: Nat, B: Nat> Leq<Succ<A>, Succ<B>> for
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ProofLeq<Succ<A>, Succ<B>>
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where
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ProofLeq<A, B>: Leq<A, B>
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{}
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}
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pub mod add {