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main.rs
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518 lines (382 loc) · 8.78 KB
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#![recursion_limit = "1024"] // necessary to generate solutions past N = 6
use std::marker::PhantomData;
////////// List //////////
struct Nil;
struct Cons<X, Xs>(PhantomData<(X, Xs)>);
////////// First //////////
trait First {
type Output;
}
impl First for Nil {
type Output = Nil;
}
impl<X, Xs> First for Cons<X, Xs> {
type Output = X;
}
////////// ListConcat //////////
trait ListConcat {
type Output;
}
impl<L2> ListConcat for (Nil, L2) {
type Output = L2;
}
impl<X, Xs, L2> ListConcat for (Cons<X, Xs>, L2)
where
(Xs, L2): ListConcat,
{
type Output = Cons<X, <(Xs, L2) as ListConcat>::Output>;
}
////////// ListConcatAll //////////
trait ListConcatAll {
type Output;
}
impl ListConcatAll for Nil {
type Output = Nil;
}
impl<L, Ls> ListConcatAll for Cons<L, Ls>
where
Ls: ListConcatAll,
(L, <Ls as ListConcatAll>::Output): ListConcat,
{
type Output = <(L, <Ls as ListConcatAll>::Output) as ListConcat>::Output;
}
////////// Bool //////////
struct False;
struct True;
trait Bool {}
impl Bool for False {}
impl Bool for True {}
////////// AnyTrue //////////
trait AnyTrue {
type Output: Bool;
}
impl AnyTrue for Nil {
type Output = False;
}
impl<L> AnyTrue for Cons<True, L> {
type Output = True;
}
impl<L> AnyTrue for Cons<False, L>
where
L: AnyTrue,
{
type Output = <L as AnyTrue>::Output;
}
////////// Not //////////
trait Not {
type Output: Bool;
}
impl Not for False {
type Output = True;
}
impl Not for True {
type Output = False;
}
////////// Or //////////
trait Or {
type Output: Bool;
}
impl Or for (True, True) {
type Output = True;
}
impl Or for (True, False) {
type Output = True;
}
impl Or for (False, True) {
type Output = True;
}
impl Or for (False, False) {
type Output = False;
}
////////// Nats //////////
struct Z;
struct S<N: Nat>(PhantomData<N>);
type N0 = Z;
type N1 = S<N0>;
type N2 = S<N1>;
type N3 = S<N2>;
type N4 = S<N3>;
type N5 = S<N4>;
type N6 = S<N5>;
trait Nat {}
impl Nat for Z {}
impl<N: Nat> Nat for S<N> {}
////////// PeanoEqual //////////
trait PeanoEqual {
type Output: Bool;
}
impl PeanoEqual for (Z, Z) {
type Output = True;
}
impl<N> PeanoEqual for (Z, S<N>)
where
N: Nat,
{
type Output = False;
}
impl<N> PeanoEqual for (S<N>, Z)
where
N: Nat,
{
type Output = False;
}
impl<N1, N2> PeanoEqual for (S<N1>, S<N2>)
where
N1: Nat,
N2: Nat,
(N1, N2): PeanoEqual,
{
type Output = <(N1, N2) as PeanoEqual>::Output;
}
////////// PeanoLT //////////
trait PeanoLT {
type Output: Bool;
}
impl PeanoLT for (Z, Z) {
type Output = False;
}
impl<N: Nat> PeanoLT for (S<N>, Z) {
type Output = False;
}
impl<N: Nat> PeanoLT for (Z, S<N>) {
type Output = True;
}
impl<N1, N2> PeanoLT for (S<N1>, S<N2>)
where
N1: Nat,
N2: Nat,
(N1, N2): PeanoLT,
{
type Output = <(N1, N2) as PeanoLT>::Output;
}
////////// PeanoAbsDiff //////////
trait PeanoAbsDiff {
type Output: Nat;
}
impl PeanoAbsDiff for (Z, Z) {
type Output = Z;
}
impl<N: Nat> PeanoAbsDiff for (Z, S<N>) {
type Output = S<N>;
}
impl<N: Nat> PeanoAbsDiff for (S<N>, Z) {
type Output = S<N>;
}
impl<N1, N2> PeanoAbsDiff for (S<N1>, S<N2>)
where
N1: Nat,
N2: Nat,
(N1, N2): PeanoAbsDiff,
{
type Output = <(N1, N2) as PeanoAbsDiff>::Output;
}
////////// Range //////////
trait Range {
type Output;
}
impl Range for Z {
type Output = Nil;
}
impl<N> Range for S<N>
where
N: Nat + Range,
{
type Output = Cons<N, <N as Range>::Output>;
}
////////// Higher order functions //////////
trait Apply<A> {
type Output;
}
struct Conj1<L>(PhantomData<L>);
impl<X, L> Apply<X> for Conj1<L> {
type Output = Cons<X, L>;
}
////////// Map //////////
trait Map {
type Output;
}
impl<F> Map for (F, Nil) {
type Output = Nil;
}
impl<F, X, Xs> Map for (F, Cons<X, Xs>)
where
F: Apply<X>,
(F, Xs): Map,
{
type Output = Cons<<F as Apply<X>>::Output, <(F, Xs) as Map>::Output>;
}
////////// MapCat //////////
trait MapCat {
type Output;
}
impl<F, L> MapCat for (F, L)
where
(F, L): Map,
<(F, L) as Map>::Output: ListConcatAll,
{
type Output = <<(F, L) as Map>::Output as ListConcatAll>::Output;
}
////////// AppendIf //////////
trait AppendIf {
type Output;
}
impl<X, Ys> AppendIf for (True, X, Ys) {
type Output = Cons<X, Ys>;
}
impl<X, Ys> AppendIf for (False, X, Ys) {
type Output = Ys;
}
////////// Filter //////////
trait Filter {
type Output;
}
impl<F> Filter for (F, Nil) {
type Output = Nil;
}
impl<F, X, Xs, FilterOutput> Filter for (F, Cons<X, Xs>)
where
F: Apply<X>,
(F, Xs): Filter<Output = FilterOutput>,
(<F as Apply<X>>::Output, X, FilterOutput): AppendIf,
{
type Output = <(<F as Apply<X>>::Output, X, <(F, Xs) as Filter>::Output) as AppendIf>::Output;
}
////////// Queen //////////
struct Queen<X, Y>(PhantomData<(X, Y)>);
struct Queen1<X>(PhantomData<X>);
impl<X: Nat, Y> Apply<Y> for Queen1<X> {
type Output = Queen<X, Y>;
}
////////// QueensInRow //////////
trait QueensInRow {
type Output;
}
impl<N, X> QueensInRow for (N, X)
where
N: Range,
(Queen1<X>, <N as Range>::Output): Map,
{
type Output = <(Queen1<X>, <N as Range>::Output) as Map>::Output;
}
////////// Threatens //////////
trait Threatens {
type Output: Bool;
}
impl<Ax, Ay, Bx, By> Threatens for (Queen<Ax, Ay>, Queen<Bx, By>)
where
(Ax, Bx): PeanoEqual,
(Ay, By): PeanoEqual,
(Ax, Bx): PeanoAbsDiff,
(Ay, By): PeanoAbsDiff,
(<(Ax, Bx) as PeanoEqual>::Output, <(Ay, By) as PeanoEqual >::Output): Or,
(<(Ax, Bx) as PeanoAbsDiff>::Output, <(Ay, By) as PeanoAbsDiff>::Output): PeanoEqual,
(<(<(Ax, Bx) as PeanoEqual>::Output, <(Ay, By) as PeanoEqual >::Output) as Or>::Output, <(<(Ax, Bx) as PeanoAbsDiff>::Output, <(Ay, By) as PeanoAbsDiff>::Output) as PeanoEqual>::Output): Or,
{
type Output = <
(
<(
<(Ax, Bx) as PeanoEqual>::Output,
<(Ay, By) as PeanoEqual>::Output,
) as Or>::Output,
<(
<(Ax, Bx) as PeanoAbsDiff>::Output,
<(Ay, By) as PeanoAbsDiff>::Output,
) as PeanoEqual>::Output,
) as Or>::Output;
}
struct Threatens1<A>(PhantomData<A>);
impl<Qa, Qb> Apply<Qb> for Threatens1<Qa>
where
(Qa, Qb): Threatens,
{
type Output = <(Qa, Qb) as Threatens>::Output;
}
////////// Safe //////////
trait Safe {
type Output: Bool;
}
impl<C, Q> Safe for (C, Q)
where
( Threatens1<Q>, C): Map,
<( Threatens1<Q>, C) as Map>::Output: AnyTrue,
<<(Threatens1<Q>, C) as Map>::Output as AnyTrue>::Output: Not,
{
type Output = <<<(Threatens1<Q>, C) as Map>::Output as AnyTrue>::Output as Not>::Output;
}
struct Safe1<C>(PhantomData<C>);
impl<C, Q> Apply<Q> for Safe1<C>
where
(C, Q): Safe,
{
type Output = <(C, Q) as Safe>::Output;
}
////////// AddQueen //////////
trait AddQueen {
type Output;
}
impl<N, X, C> AddQueen for (N, X, C)
where
(N, X): QueensInRow,
(Safe1<C>, <(N, X) as QueensInRow>::Output): Filter,
(Conj1<C>, <(Safe1<C>, <(N, X) as QueensInRow>::Output) as Filter>::Output): Map,
{
type Output = <(Conj1<C>, <(Safe1<C>, <(N, X) as QueensInRow>::Output) as Filter>::Output) as Map>::Output;
}
struct AddQueen2<N, X>(PhantomData<(N, X)>);
impl<N, X, C> Apply<C> for AddQueen2<N, X>
where
(N, X, C): AddQueen,
{
type Output = <(N, X, C) as AddQueen>::Output;
}
trait AddQueenToAll {
type Output;
}
impl<N, X, Cs> AddQueenToAll for (N, X, Cs)
where
(AddQueen2<N, X>, Cs): MapCat,
{
type Output = <(AddQueen2<N, X>, Cs) as MapCat>::Output;
}
////////// AddQueensIf //////////
trait AddQueensIf {
type Output;
}
impl<N, X, Cs> AddQueensIf for (False, N, X, Cs) {
type Output = Cs;
}
impl<N, X, Cs, AddQueenToAllOutput> AddQueensIf for (True, N, X, Cs)
where
X: Nat,
(N, X, Cs): AddQueenToAll<Output = AddQueenToAllOutput>,
(N, S<X>, AddQueenToAllOutput): AddQueens,
{
type Output = <(N, S<X>, <(N, X, Cs) as AddQueenToAll>::Output) as AddQueens>::Output;
}
trait AddQueens {
type Output;
}
impl<N, X, Cs, PeanoLTOutput> AddQueens for (N, X, Cs)
where
(X, N): PeanoLT<Output = PeanoLTOutput>,
(PeanoLTOutput, N, X, Cs): AddQueensIf,
{
type Output = <(<(X, N) as PeanoLT>::Output, N, X, Cs) as AddQueensIf>::Output;
}
////////// Solution //////////
trait Solution {
type Output;
}
impl<N, AddQueensIfOutput> Solution for N
where
N: Nat,
(Z, N): PeanoLT,
(<(Z, N) as PeanoLT>::Output, N, Z, Cons<Nil, Nil>): AddQueensIf<Output = AddQueensIfOutput>,
AddQueensIfOutput: First,
{
type Output = <<(N, Z, Cons<Nil, Nil>) as AddQueens>::Output as First>::Output;
}
////////// Reify //////////
fn main() {
println!("{}", std::any::type_name::< <N6 as Solution>::Output >().replace("ttti_rs::", ""));
}