composition

.gitignore

@@ -1,14 +1,3 @@
 book
-
-
-# Added by cargo
-
-/target
-
-
-# Added by cargo
-#
-# already existing elements were commented out
-
-#/target
-/Cargo.lock
+target
+Cargo.lock

src/SUMMARY.md

@@ -11,5 +11,7 @@
 - [Chapter 2](./chapter_2.md)
   - [AnyStr](./exercises/anystr.md)
   - [Mode](./exercises/mode.md)
+- [Chapter 3](./chapter_3.md)
+  - [Composition](./exercises/composition.md)
 
 [Topics (Spoilers)](./topics.md)

src/chapter_3.md

@@ -0,0 +1 @@
+# Chapter 3

src/exercises/composition.md

@@ -0,0 +1,115 @@
+```rust
+# use std::ops::ControlFlow;
+
+trait Monad<'a>: 'a {
+    type W<A: 'a>: 'a;
+
+    fn map<A: 'a, B: 'a>(
+        wa: Self::W<A>,
+        f: impl FnOnce(A) -> B,
+    ) -> Self::W<B>;
+
+    fn pure<A: 'a>(
+        a: A,
+    ) -> Self::W<A>;
+
+    fn collect<A: 'a, B: 'a>(
+        wab: (Self::W<A>, Self::W<B>),
+    ) -> Self::W<(A, B)>;
+
+    fn bind<A: 'a, B: 'a>(
+        wa: Self::W<A>,
+        f: impl FnOnce(A) -> Self::W<B>,
+    ) -> Self::W<B>;
+
+    fn iterate<A: 'a>(
+        i: impl Iteration<'a, A = A, M = Self>,
+    ) -> Self::W<A>;
+}
+
+trait Iteration<'a>: 'a + Sized {
+    type A: 'a;
+
+    type M: ?Sized + Monad<'a>;
+
+    fn next(self) -> IWrap<'a, Self>;
+}
+
+type Wrap<'a, M, A> = <M as Monad<'a>>::W<A>;
+
+type IOutput<'a, I> = ControlFlow<<I as Iteration<'a>>::A, I>;
+
+type IWrap<'a, I> = Wrap<'a, <I as Iteration<'a>>::M, IOutput<'a, I>>;
+
+struct Composition<U, V>(U, V);
+
+impl<'a, U, V> Monad<'a> for Composition<U, V>
+where
+    U: Monad<'a>,
+    V: Monad<'a>,
+    // something missing here?
+# V: Local<'a>,
+{
+    type W<A: 'a> = U::W<V::W<A>>;
+
+    fn map<A: 'a, B: 'a>(
+        wa: Self::W<A>,
+        f: impl FnOnce(A) -> B,
+    ) -> Self::W<B> {
+        U::map(wa, |va| V::map(va, f))
+    }
+
+    fn pure<A: 'a>(
+        a: A,
+    ) -> Self::W<A> {
+        U::pure(V::pure(a))
+    }
+
+    fn collect<A: 'a, B: 'a>(
+        wab: (Self::W<A>, Self::W<B>),
+    ) -> Self::W<(A, B)> {
+        U::map(U::collect(wab), V::collect)
+    }
+
+    fn bind<A: 'a, B: 'a>(
+        wa: Self::W<A>,
+        f: impl FnOnce(A) -> Self::W<B>,
+    ) -> Self::W<B> {
+        // impossible
+# U::bind(wa, |va| U::map(V::wrap::<_, U>(V::map(va, f)), |vvb| V::bind(vvb, |vb| vb)))
+    }
+
+    fn iterate<A: 'a>(
+        i: impl Iteration<'a, A = A, M = Self>,
+    ) -> Self::W<A> {
+        // impossible
+# U::iterate(ComposedIteration(i))
+    }
+}
+
+# trait Local<'a>: Monad<'a> { fn wrap<A: 'a, M: Monad<'a>>(wa: Self::W<M::W<A>>) -> M::W<Self::W<A>>; }
+# struct CfInstance<E>(ControlFlow<(), E>);
+# use ControlFlow::{Continue, Break};
+# impl<'a, E: 'a> Monad<'a> for CfInstance<E> {
+# type W<A: 'a> = ControlFlow<A, E>;
+# fn map<A: 'a, B: 'a>(wa: Self::W<A>, f: impl FnOnce(A) -> B) -> Self::W<B> {
+# match wa { Continue(c) => Continue(c), Break(a) => Break(f(a)) }
+# }
+# fn pure<A: 'a>(a: A) -> Self::W<A> { Break(a) }
+# fn collect<A: 'a, B: 'a>(wab: (Self::W<A>, Self::W<B>)) -> Self::W<(A, B)> {
+# match wab { (Continue(e), _) => Continue(e), (_, Continue(e)) => Continue(e), (Break(a), Break(b)) => Break((a, b)) }
+# }
+# fn bind<A: 'a, B: 'a>(wa: Self::W<A>, f: impl FnOnce(A) -> Self::W<B>) -> Self::W<B> {
+# match wa { Continue(e) => Continue(e), Break(a) => f(a) }
+# }
+# fn iterate<A: 'a>(mut i: impl Iteration<'a, A = A, M = Self>) -> Self::W<A> {
+# loop { match i.next() { Continue(e) => break Continue(e), Break(Continue(next_i)) => i = next_i, Break(Break(a)) => break Break(a) } }
+# }
+# }
+# struct ComposedIteration<F>(F);
+# impl<'a, U: Monad<'a>, V: Local<'a>, F: Iteration<'a, M = Composition<U, V>>> Iteration<'a> for ComposedIteration<F> {
+# type A = Wrap<'a, V, F::A>;
+# type M = U;
+# fn next(self) -> IWrap<'a, Self> { U::map(self.0.next(), |vstate| { ControlFlow::Continue(Self(V::wrap::<_, CfInstance<_>>(vstate)?)) }) }
+# }
+```

src/topics.md

@@ -2,11 +2,11 @@
 
 Rows are ordered based on estimated difficulty.
 
-| lifetimes              | `trait`s           | `struct`s   |
+| lifetimes\[-adjacent\] | `trait`s           | `struct`s   |
 |------------------------|--------------------|-------------|
 | [explicit lifetimes]   | [`Fn`?]            |             |
 | [extracting lifetimes] | [exclusive traits] | [`RcChars`] |
-|                        | [`AnyStr`]         |             |
+| [composition]          | [`AnyStr`]         |             |
 |                        | [merging traits]   |             |
 
 
@@ -17,3 +17,4 @@ Rows are ordered based on estimated difficulty.
 [exclusive traits]: ./exercises/multiple_blanket.md
 [merging traits]: ./exercises/modes.md
 [`AnyStr`]: ./exercises/anystr.md
+[composition]: ./exercises/composition.md