diff --git a/sketching/september_2025/hkt/functor.dm b/sketching/september_2025/hkt/functor.dm
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+pub trait Functor[*T]
+    fn <U> map(ftu: fn (t: &*T) -> U) -> Self<U>
+end
+
+pub trait Functor[*L -> *R]
+    fn mapLeft(flr: fn (l: &*L) -> *R) -> Self<*L, *R>
+end
+
+pub enum Option<T>
+    Some(T),
+    None
+end
+
+pub enum Either<L, R>
+    Left(L),
+    Right(R)
+end
+
+pub inst Functor[*T] for Option<T>
+    impl fn <U> map(ftu: fn (t: T) -> U) -> Self<U>
+        if self is Some(t) then
+            Some(ftu(t))
+        else
+            None
+        end
+    end
+end
+
+pub inst Functor[*T] for Either<_, *T>
+    impl fn <U> map(ftu: fn (t: *T) -> U) -> Self<U>
+        if self is Right(t) then
+            Right(ftu(t))
+        else
+            self
+        end
+    end
+end
+
+pub inst Functor[*L -> *R] for Either<L, R>
+    impl fn mapLeft(flr: fn (l: *L) -> *R) -> Self<*L, *R>
+        if self is Left(l) then
+            Right(flr(l))
+        else
+            self
+        end
+    end
+end
+
+pub trait Monad[*T]
+    static fn lift(t: *T) -> Self<*T>
+    fn <U> flatMap(f: fn (t: *T) -> Self<U>) -> Self<U>
+end
+
+pub trait Default
+    static fn default() -> Self
+end
+
+pub trait Empty[*T] where *T has Default
+    static fn empty() -> Self<*T>
+end
+
+pub trait Semigroup[*T]
+    fn concat(other: &Self<*T>) -> Self<&*T>
+    cons fn consConcat(other: Self<*T>) -> Self<*T>
+end
+
+pub int Iterable<T>
+    fn iter() -> Iterator<T>
+    cons fn consIter() -> ConsIterator<T>
+end
+
+pub int Iterator<T>
+    fn next() -> Option<&T>
+    fn withIndex() -> Iterator<Option<(Int, &T)>>
+end
+
+pub int ConsIterator<T>
+    fn next() -> Option<T>
+    fn withIndex() -> Iterator<Option<(Int, T)>>
+end
+
+pub int List<T> : Iterable<T> req Monad, Functor, Semigroup, Empty
+    fn add(t: T) -> Void
+end
+
+pub inst Functor[*T] for List<*T> where *T has Default
+    impl fn <U> map(ftu: (t: *T) -> U) -> Self<U>
+        let mut result: Self<U> = Self::empty()
+        for t in self do
+            result += Self::lift(ftu(t))
+        end
+        result
+    end
+end
+
+pub class ArrayList<T> : List<T>
+
+    let init: fn () -> T // ?: sugar for Option<fn () -> T>
+    let capacity: USize
+    let mut ts: Array<T>
+    let count: USize = 0
+
+    pub ctor(startCapacity: USize = 10, init: fn () -> T = Default::default) where T has Default
+        := init
+        capacity = startCapacity  // ?= sugar for Some(expr)
+        ts = array(startCapacity, init)
+    end
+
+    pub ctor(init: fn () -> T, startCapacity: USize = 10)
+        := init
+        capacity = startCapacity
+        ts = array(startCapacity, init)
+    end
+
+    impl fn iter() -> Iterator<T>
+        todo()
+    end
+
+    impl fn add(t: T) -> Void
+        ts[count] = t
+        count++
+        if count == capacity then
+            resize()
+        end
+    end
+
+    fn resize() -> Void
+        let oldTs = mem::take(&ts, array(capacity * 2, init))
+        for (i, t) in oldTs.consIter().withIndex() do
+            ts[i] = t
+        end
+    end
+
+end
+
+pub inst Empty[*T] for ArrayList<*T>
+    where *T has Default
+    impl static fn empty() -> List<*T> = Self()
+end
+
+pub inst Semigroup[*T] for ArrayList<*T>
+    where *T has Default
+    impl fn concat(other: List<*T>) -> List<*T>
+        let result = Self()
+        for t in self do
+            result.add(t)
+        end
+        for t in other do
+            result.add(t)
+        end
+        result
+    end
+end
+
+pub inst Monad[*T] for ArrayList<*T>
+    where T has Default
+    impl static fn lift(t: *T) -> List<*T>
+        let result: List<*T> = Self()
+        result.add(t)
+        result
+    end
+
+    impl fn <U> flatMap(f: fn (t: *T) -> List<U>) -> List<U>
+        let result: List<U> = Self()
+        for t in self do
+            for u in f(t) do
+                result.add(u)
+            end
+        end
+        result
+    end
+end
+
+pub mod std::core
+
+    pub mod mem
+        pub native fn <T> take(target: &T, replacement: T) -> T
+    end
+
+    pub native fn <T> array(capacity: USize, init: fn () -> T) -> Array<T>
+
+    pub native fn <T> array(capacity: USize) -> Array<T> where T has Default
+
+    pub fn <T> list(...items: Array<T>) -> List<T> where T has Default
+        let result = ArrayList(items.capacity(), Default[T]::default)
+        for item in items.consIter() do
+            result.add(item)
+        end
+        result
+    end
+
+end
+
+// other file
+use std::collections::List
+use std::hkt::{Functor[List], Monad[List]}
+
+fn main()
+    let someNums: List<Int> = [1, 2, 3, 4, 5]
+    let plusOnes = someNums.map { it + 1 }
+    println plusOnes // 2, 3, 4, 5, 6
+    let twoOfEach = someNums.flatMap { [it, it] }
+    println twoOfEach // 1, 1, 2, 2, 3, 3, 4, 4, 5, 5
+end
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