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)
initial commit
+7
Cargo.lock
+7
Cargo.lock
+6
Cargo.toml
+6
Cargo.toml
+96
flake.lock
+96
flake.lock
···
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{
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"nodes": {
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"flake-utils": {
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"inputs": {
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"systems": "systems"
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},
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"locked": {
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"lastModified": 1731533236,
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"narHash": "sha256-l0KFg5HjrsfsO/JpG+r7fRrqm12kzFHyUHqHCVpMMbI=",
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"owner": "numtide",
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"repo": "flake-utils",
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"rev": "11707dc2f618dd54ca8739b309ec4fc024de578b",
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"type": "github"
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},
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"original": {
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"owner": "numtide",
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"repo": "flake-utils",
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"type": "github"
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}
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},
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"nixpkgs": {
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"locked": {
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"lastModified": 1756617294,
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"narHash": "sha256-aGnd4AHIYCWQKChAkHPpX+YYCt7pA6y2LFFA/s8q0wQ=",
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"owner": "nixos",
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"repo": "nixpkgs",
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"rev": "b4c2c57c31e68544982226d07e4719a2d86302a8",
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"type": "github"
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},
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"original": {
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"owner": "nixos",
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"ref": "nixos-25.05",
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"repo": "nixpkgs",
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"type": "github"
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}
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},
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"nixpkgs_2": {
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"locked": {
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"lastModified": 1744536153,
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"narHash": "sha256-awS2zRgF4uTwrOKwwiJcByDzDOdo3Q1rPZbiHQg/N38=",
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"owner": "NixOS",
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"repo": "nixpkgs",
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"rev": "18dd725c29603f582cf1900e0d25f9f1063dbf11",
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"type": "github"
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},
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"original": {
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"owner": "NixOS",
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"ref": "nixpkgs-unstable",
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"repo": "nixpkgs",
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"type": "github"
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}
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},
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"root": {
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"inputs": {
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"flake-utils": "flake-utils",
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"nixpkgs": "nixpkgs",
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"rust-overlay": "rust-overlay"
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}
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},
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"rust-overlay": {
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"inputs": {
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"nixpkgs": "nixpkgs_2"
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},
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"locked": {
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"lastModified": 1756694554,
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"narHash": "sha256-z/Iy4qvcMqzhA2IAAg71Sw4BrMwbBHvCS90ZoPLsnIk=",
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"owner": "oxalica",
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"repo": "rust-overlay",
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"rev": "b29e5365120f344fe7161f14fc9e272fcc41ee56",
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"type": "github"
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},
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"original": {
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"owner": "oxalica",
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"repo": "rust-overlay",
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"type": "github"
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}
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},
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"systems": {
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"locked": {
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"lastModified": 1681028828,
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"narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=",
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"owner": "nix-systems",
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"repo": "default",
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"rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e",
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"type": "github"
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},
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"original": {
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"owner": "nix-systems",
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"repo": "default",
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"type": "github"
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}
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}
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},
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"root": "root",
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"version": 7
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}
+29
flake.nix
+29
flake.nix
···
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{
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description = "rspeano";
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inputs = {
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nixpkgs.url = "github:nixos/nixpkgs/nixos-25.05";
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rust-overlay.url = "github:oxalica/rust-overlay";
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flake-utils.url = "github:numtide/flake-utils";
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};
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outputs = { self, nixpkgs, rust-overlay, flake-utils, ... }:
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flake-utils.lib.eachDefaultSystem (system:
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let
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overlays = [ (import rust-overlay) ];
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pkgs = import nixpkgs {
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inherit system overlays;
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};
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# Change version here if needed
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rsTools = pkgs.rust-bin.stable."1.89.0".default;
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in {
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devShells.default = pkgs.mkShell {
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packages = [
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rsTools
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pkgs.bash ];
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};
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});
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}
+115
src/lib.rs
+115
src/lib.rs
···
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pub trait Nat {}
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pub struct Succ<T>(T);
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// Inductively define naturals
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pub type _0 = Succ<()>;
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impl Nat for _0 {}
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impl<T: Nat> Nat for Succ<T> {}
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pub mod prelude {
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pub type _1 = Succ<_0>;
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pub type _2 = Succ<_1>;
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pub type _3 = Succ<_2>;
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pub type _4 = Succ<_3>;
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pub type _5 = Succ<_4>;
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pub type _6 = Succ<_5>;
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pub type _7 = Succ<_6>;
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pub type _8 = Succ<_7>;
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pub use super::{
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Nat,
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Succ,
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_0,
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eq::Eq,
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eq::ProofEq,
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add::Add,
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mul::Times,
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exp::Exp
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};
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}
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pub mod eq {
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use super::prelude::*;
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pub trait Eq<A: Nat, B: Nat> {
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fn check() -> () {}
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}
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pub struct ProofEq<A: Nat, B: Nat>(A, B);
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impl<A: Nat, B: Nat> ProofEq<A, B> {}
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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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pub mod add {
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use super::prelude::*;
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pub trait Add<RHS: Nat> {
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type Result: Nat;
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}
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// Base case
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// N + 0 = N
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impl<T: Nat> Add<_0> for T {
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type Result = T;
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}
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// Induction
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// A + S(B) = S(A + B)
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impl<A: Nat, B: Nat> Add<Succ<B>> for A
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where
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A: Add<B>
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{
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type Result = Succ<<A as Add<B>>::Result>;
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}
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}
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pub mod mul {
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use super::prelude::*;
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pub trait Times<RHS: Nat> {
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type Result: Nat;
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}
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// Base case
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// N * 0 = 0
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impl<T: Nat> Times<_0> for T {
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type Result = _0;
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}
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// Induction
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// A * S(B) = A * B + A
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impl<A: Nat, B: Nat> Times<Succ<B>> for A
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where
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A: Times<B>,
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<A as Times<B>>::Result: Add<A>
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{
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type Result = <<A as Times<B>>::Result as Add<A>>::Result;
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}
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}
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pub mod exp {
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use super::prelude::*;
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pub trait Exp<Pow: Nat> {
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type Result: Nat;
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}
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// Base case
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// N ^ 0 = 1
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impl<T: Nat> Exp<_0> for T {
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type Result = _1;
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}
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// Induction
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// A ^ S(B) = A ^ B * A
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impl<A: Nat, B: Nat> Exp<Succ<B>> for A
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where
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A: Exp<B>,
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<A as Exp<B>>::Result: Times<A>
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{
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type Result =
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<<A as Exp<B>>::Result as Times<A>>::Result;
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}
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}
+65
src/main.rs
+65
src/main.rs
···
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use rspeano::prelude::*;
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fn five_plus_five_is_ten() {
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type Claimed10 = <_5 as Add<_5>>::Result;
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type Verified10 =
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Succ< // 1
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Succ< // 2
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Succ< // 3
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Succ< // 4
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Succ< // 5
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Succ< // 6
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Succ< // 7
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Succ< // 8
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Succ< // 9
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Succ< // 10
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_0
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>>>>>>>>>>;
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ProofEq::<Claimed10, Verified10>::check();
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}
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fn four_times_two_is_eight() {
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type Claimed8 = <_4 as Times<_2>>::Result;
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type Verified8 =
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Succ< // 1
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Succ< // 2
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Succ< // 3
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Succ< // 4
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Succ< // 5
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Succ< // 6
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Succ< // 7
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Succ< // 8
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_0
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>>>>>>>>;
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ProofEq::<Claimed8, Verified8>::check();
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}
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fn two_squared_is_four() {
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type Claimed4 = <_2 as Exp<_2>>::Result;
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type Verified4 =
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Succ<
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Succ<
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Succ<
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Succ<
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_0
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>>>>;
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ProofEq::<Claimed4, Verified4>::check();
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}
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fn main() {
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two_squared_is_four();
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four_times_two_is_eight();
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// fails:
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// type M0 = <_8 as Times<_1>>::Result;
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// ProofEq::<M0, _0>::check();
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five_plus_five_is_ten()
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}