oxilean-std 0.1.2

//! Auto-generated module
//!
//! 🤖 Generated with [SplitRS](https://github.com/cool-japan/splitrs)

use super::functions::*;

/// Futumorphism: anamorphism with look-ahead capability.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct Futumorphism {
    pub coalgebra_name: String,
}
#[allow(dead_code)]
impl Futumorphism {
    pub fn new(coalgebra_name: &str) -> Self {
        Self {
            coalgebra_name: coalgebra_name.to_string(),
        }
    }
    /// Interleave two lists (futumorphism example).
    pub fn interleave<A: Clone>(xs: &[A], ys: &[A]) -> Vec<A> {
        let mut result = Vec::new();
        for i in 0..xs.len().max(ys.len()) {
            if i < xs.len() {
                result.push(xs[i].clone());
            }
            if i < ys.len() {
                result.push(ys[i].clone());
            }
        }
        result
    }
}
/// Defunctionalized closure representation.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct DefunctClosure {
    pub tag: String,
    pub free_variables: Vec<(String, String)>,
    pub apply_case: String,
}
#[allow(dead_code)]
impl DefunctClosure {
    /// Create a defunctionalized closure.
    pub fn new(tag: &str, free_vars: Vec<(&str, &str)>, apply: &str) -> Self {
        Self {
            tag: tag.to_string(),
            free_variables: free_vars
                .iter()
                .map(|(n, t)| (n.to_string(), t.to_string()))
                .collect(),
            apply_case: apply.to_string(),
        }
    }
    /// Arity of the closure (number of captured variables).
    pub fn arity(&self) -> usize {
        self.free_variables.len()
    }
    /// Apply description.
    pub fn apply_description(&self) -> String {
        format!("apply({}) = {}", self.tag, self.apply_case)
    }
}
/// A zipper over a non-empty vector: models a focused list comonad.
///
/// The zipper is the canonical comonad for list-like structures:
/// extract = current element, extend = apply f to each focus position.
#[derive(Clone)]
pub struct Zipper<A> {
    pub left: Vec<A>,
    pub focus: A,
    pub right: Vec<A>,
}
impl<A: Clone> Zipper<A> {
    /// Create a zipper focused on index `i` of `data`.
    ///
    /// Returns `None` if `data` is empty or `i` is out of bounds.
    pub fn new(data: Vec<A>, i: usize) -> Option<Self> {
        if data.is_empty() || i >= data.len() {
            return None;
        }
        let mut v = data;
        let right = v.split_off(i + 1);
        let focus = v
            .pop()
            .expect("v is non-empty: i < data.len() and v is data[..=i]");
        Some(Self {
            left: v,
            focus,
            right,
        })
    }
    /// Extract the focused element (counit / extract).
    pub fn extract(&self) -> &A {
        &self.focus
    }
    /// Extend the zipper comonad: apply `f` at every position.
    ///
    /// This implements `extend f w` for the zipper comonad.
    pub fn extend<B: Clone>(&self, f: impl Fn(&Zipper<A>) -> B) -> Zipper<B> {
        let all: Vec<A> = self
            .left
            .iter()
            .cloned()
            .chain(std::iter::once(self.focus.clone()))
            .chain(self.right.iter().cloned())
            .collect();
        let focus_idx = self.left.len();
        let results: Vec<B> = (0..all.len())
            .map(|i| {
                let z = Zipper::new(all.clone(), i)
                    .expect("i < all.len(): iterating over 0..all.len()");
                f(&z)
            })
            .collect();
        Zipper::new(results, focus_idx).expect(
            "focus_idx < results.len(): focus_idx == left.len() < all.len() == results.len()",
        )
    }
    /// Move focus one step to the left.
    pub fn move_left(&self) -> Option<Zipper<A>> {
        if self.left.is_empty() {
            return None;
        }
        let mut new_left = self.left.clone();
        let new_focus = new_left
            .pop()
            .expect("new_left is non-empty: left is non-empty, checked by early return");
        let mut new_right = vec![self.focus.clone()];
        new_right.extend(self.right.iter().cloned());
        Some(Zipper {
            left: new_left,
            focus: new_focus,
            right: new_right,
        })
    }
    /// Move focus one step to the right.
    pub fn move_right(&self) -> Option<Zipper<A>> {
        if self.right.is_empty() {
            return None;
        }
        let mut new_right = self.right.clone();
        let new_focus = new_right.remove(0);
        let mut new_left = self.left.clone();
        new_left.push(self.focus.clone());
        Some(Zipper {
            left: new_left,
            focus: new_focus,
            right: new_right,
        })
    }
    /// Collect all elements in order.
    pub fn to_vec(&self) -> Vec<A> {
        self.left
            .iter()
            .cloned()
            .chain(std::iter::once(self.focus.clone()))
            .chain(self.right.iter().cloned())
            .collect()
    }
    /// Length of the full sequence.
    pub fn len(&self) -> usize {
        self.left.len() + 1 + self.right.len()
    }
    /// A zipper always has at least one element (the focus), so it is never empty.
    pub fn is_empty(&self) -> bool {
        false
    }
    /// Returns true if the zipper has only one element.
    pub fn is_singleton(&self) -> bool {
        self.left.is_empty() && self.right.is_empty()
    }
}
/// Apomorphism: anamorphism with early termination.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct Apomorphism {
    pub coalgebra_name: String,
}
#[allow(dead_code)]
impl Apomorphism {
    pub fn new(coalgebra_name: &str) -> Self {
        Self {
            coalgebra_name: coalgebra_name.to_string(),
        }
    }
    /// Insert into sorted list as apomorphism.
    pub fn insert_sorted(mut xs: Vec<i64>, x: i64) -> Vec<i64> {
        let pos = xs.partition_point(|&v| v <= x);
        xs.insert(pos, x);
        xs
    }
}
/// Church encoding utilities for natural numbers.
#[allow(dead_code)]
pub struct ChurchNumerals;
#[allow(dead_code)]
impl ChurchNumerals {
    /// Church numeral zero: Λf.Λx. x (conceptual).
    pub fn church_zero_desc() -> &'static str {
        "λf. λx. x"
    }
    /// Church numeral succ: Λn.Λf.Λx. f (n f x).
    pub fn church_succ_desc() -> &'static str {
        "λn. λf. λx. f (n f x)"
    }
    /// Convert Church numeral to actual u64 (simulation).
    pub fn church_to_u64(n: u64) -> u64 {
        n
    }
    /// Church addition: λm.λn.λf.λx. m f (n f x).
    pub fn church_add(m: u64, n: u64) -> u64 {
        m + n
    }
    /// Church multiplication: λm.λn.λf. m (n f).
    pub fn church_mul(m: u64, n: u64) -> u64 {
        m * n
    }
    /// Church exponentiation: λm.λn. n m.
    pub fn church_pow(m: u64, n: u64) -> u64 {
        m.pow(n as u32)
    }
}
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct TraversableData {
    pub container_type: String,
    pub traverse_type: String,
    pub is_foldable: bool,
    pub naturality_condition: String,
}
#[allow(dead_code)]
impl TraversableData {
    pub fn list_traversable() -> Self {
        TraversableData {
            container_type: "List".to_string(),
            traverse_type: "Applicative f => (a -> f b) -> [a] -> f [b]".to_string(),
            is_foldable: true,
            naturality_condition: "t . traverse g = traverse (t . g)".to_string(),
        }
    }
    pub fn map_traversable() -> Self {
        TraversableData {
            container_type: "Map k".to_string(),
            traverse_type: "Applicative f => (a -> f b) -> Map k a -> f (Map k b)".to_string(),
            is_foldable: true,
            naturality_condition: "t . traverse g = traverse (t . g)".to_string(),
        }
    }
    pub fn laws(&self) -> Vec<String> {
        vec![
            "Naturality: t . traverse f = traverse (t . f) for natural t".to_string(),
            "Identity: traverse Identity = Identity".to_string(),
            "Composition: traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f"
            .to_string(),
        ]
    }
    pub fn efficient_mapaccum(&self) -> String {
        format!(
            "mapAccumL/R for {}: O(n) traversal with accumulated state",
            self.container_type
        )
    }
}
/// A traversal focusing on zero or more As inside S.
pub struct Traversal<S, A> {
    /// Extract all focused values.
    to_list: Box<dyn Fn(&S) -> Vec<A>>,
    /// Reconstruct S from modified values (must have same length as to_list output).
    from_list: Box<dyn Fn(Vec<A>, &S) -> S>,
}
impl<S: 'static + Clone, A: 'static + Clone> Traversal<S, A> {
    /// Create a traversal from to_list and from_list.
    pub fn new(
        to_list: impl Fn(&S) -> Vec<A> + 'static,
        from_list: impl Fn(Vec<A>, &S) -> S + 'static,
    ) -> Self {
        Self {
            to_list: Box::new(to_list),
            from_list: Box::new(from_list),
        }
    }
    /// Collect all focused values.
    pub fn view(&self, s: &S) -> Vec<A> {
        (self.to_list)(s)
    }
    /// Modify all focused values.
    pub fn over(&self, f: impl Fn(A) -> A, s: S) -> S {
        let vals: Vec<A> = (self.to_list)(&s).into_iter().map(&f).collect();
        (self.from_list)(vals, &s)
    }
}
/// `RecursionSchemeEval` provides catamorphism and anamorphism over `RoseTree`.
pub struct RecursionSchemeEval;
impl RecursionSchemeEval {
    /// Catamorphism (fold) over a `RoseTree`.
    ///
    /// `alg(a, children_results)` computes the result at each node.
    pub fn cata<A, B>(tree: RoseTree<A>, alg: &dyn Fn(A, Vec<B>) -> B) -> B {
        match tree {
            RoseTree::Node(a, children) => {
                let results: Vec<B> = children.into_iter().map(|c| Self::cata(c, alg)).collect();
                alg(a, results)
            }
        }
    }
    /// Anamorphism (unfold) to produce a `RoseTree` from a seed.
    ///
    /// `coalg(seed)` returns `(label, child_seeds)`.
    pub fn ana<A, S: Clone>(seed: S, coalg: &dyn Fn(S) -> (A, Vec<S>)) -> RoseTree<A> {
        let (a, children) = coalg(seed);
        let subtrees = children.into_iter().map(|s| Self::ana(s, coalg)).collect();
        RoseTree::Node(a, subtrees)
    }
    /// Hylomorphism (unfold then fold) without materializing the intermediate tree.
    pub fn hylo<A, B, S: Clone>(
        seed: S,
        coalg: &dyn Fn(S) -> (A, Vec<S>),
        alg: &dyn Fn(A, Vec<B>) -> B,
    ) -> B {
        let (a, children) = coalg(seed);
        let results: Vec<B> = children
            .into_iter()
            .map(|s| Self::hylo(s, coalg, alg))
            .collect();
        alg(a, results)
    }
}
/// Paramorphism: catamorphism with access to original sub-trees.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct Paramorphism {
    pub algebra_name: String,
}
#[allow(dead_code)]
impl Paramorphism {
    pub fn new(algebra_name: &str) -> Self {
        Self {
            algebra_name: algebra_name.to_string(),
        }
    }
    /// Factorial as paramorphism over Nat: para(zero->1, succ(n,acc) -> (n+1)*acc).
    pub fn factorial_para(n: u64) -> u64 {
        (1..=n).product()
    }
    /// Tails as paramorphism over lists.
    pub fn tails_para<A: Clone>(xs: &[A]) -> Vec<Vec<A>> {
        (0..=xs.len()).map(|i| xs[i..].to_vec()).collect()
    }
}
/// Reader monad: Reader r a = r -> a.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ReaderMonad<R: Clone, A: Clone> {
    _phantom_r: std::marker::PhantomData<R>,
    _phantom_a: std::marker::PhantomData<A>,
    pub description: String,
}
#[allow(dead_code)]
impl<R: Clone, A: Clone> ReaderMonad<R, A> {
    pub fn new(desc: &str) -> Self {
        Self {
            _phantom_r: std::marker::PhantomData,
            _phantom_a: std::marker::PhantomData,
            description: desc.to_string(),
        }
    }
    pub fn ask_desc(&self) -> String {
        format!("ask :: Reader {}", std::any::type_name::<R>())
    }
    pub fn local_desc(&self) -> String {
        format!(
            "local :: ({0} -> {0}) -> Reader {0} _",
            std::any::type_name::<R>()
        )
    }
}
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ArrowData {
    pub arrow_name: String,
    pub arr_type: String,
    pub compose_type: String,
    pub first_type: String,
    pub is_arrowchoice: bool,
    pub is_arrowloop: bool,
}
#[allow(dead_code)]
impl ArrowData {
    pub fn function_arrow() -> Self {
        ArrowData {
            arrow_name: "->".to_string(),
            arr_type: "(b -> c) -> Arrow b c".to_string(),
            compose_type: "Arrow b c -> Arrow c d -> Arrow b d".to_string(),
            first_type: "Arrow b c -> Arrow (b, d) (c, d)".to_string(),
            is_arrowchoice: true,
            is_arrowloop: true,
        }
    }
    pub fn kleisli_arrow(monad: &str) -> Self {
        ArrowData {
            arrow_name: format!("Kleisli {}", monad),
            arr_type: format!("(b -> {} c) -> Kleisli {} b c", monad, monad),
            compose_type: format!(
                "Kleisli {} b c -> Kleisli {} c d -> Kleisli {} b d",
                monad, monad, monad
            ),
            first_type: format!("Kleisli {} b c -> Kleisli {} (b,d) (c,d)", monad, monad),
            is_arrowchoice: false,
            is_arrowloop: false,
        }
    }
    pub fn hughes_laws(&self) -> Vec<String> {
        vec![
            "arr id = id".to_string(),
            "arr (f . g) = arr f . arr g".to_string(),
            "first (arr f) = arr (f *** id)".to_string(),
            "first (f . g) = first f . first g".to_string(),
        ]
    }
    pub fn freyd_category_connection(&self) -> String {
        "Arrows generalize Freyd categories (Power-Thielecke): model effectful computations"
            .to_string()
    }
}
/// A type-erased type-level map (heterogeneous map keyed by strings).
pub struct HMap {
    entries: Vec<(String, Box<dyn std::any::Any>)>,
}
impl HMap {
    /// Create an empty HMap.
    pub fn new() -> Self {
        Self {
            entries: Vec::new(),
        }
    }
    /// Insert a key-value pair.
    pub fn insert<V: 'static>(&mut self, key: impl Into<String>, value: V) {
        self.entries.push((key.into(), Box::new(value)));
    }
    /// Look up a key and downcast.
    pub fn get<V: 'static>(&self, key: &str) -> Option<&V> {
        self.entries
            .iter()
            .find(|(k, _)| k == key)
            .and_then(|(_, v)| v.downcast_ref::<V>())
    }
    /// Number of entries.
    pub fn len(&self) -> usize {
        self.entries.len()
    }
    /// Returns true if empty.
    pub fn is_empty(&self) -> bool {
        self.entries.is_empty()
    }
}
/// A prism focusing on one variant of a sum type.
pub struct Prism<S, A> {
    preview: Box<dyn Fn(S) -> Option<A>>,
    review: Box<dyn Fn(A) -> S>,
}
impl<S: 'static, A: 'static> Prism<S, A> {
    /// Create a prism from preview and review functions.
    pub fn new(
        preview: impl Fn(S) -> Option<A> + 'static,
        review: impl Fn(A) -> S + 'static,
    ) -> Self {
        Self {
            preview: Box::new(preview),
            review: Box::new(review),
        }
    }
    /// Try to extract the focused value.
    pub fn preview(&self, s: S) -> Option<A> {
        (self.preview)(s)
    }
    /// Inject a value into the sum type.
    pub fn review(&self, a: A) -> S {
        (self.review)(a)
    }
}
/// A free monad over `ConsoleEffect` for console programs.
#[allow(dead_code)]
pub enum ConsoleProg<A> {
    /// Pure result.
    Done(A),
    /// Perform an effect and continue.
    Step(ConsoleEffect, Box<dyn FnOnce(String) -> ConsoleProg<A>>),
}
/// State monad: State s a = s -> (a, s).
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct StateMonad<S: Clone, A: Clone> {
    _phantom_s: std::marker::PhantomData<S>,
    _phantom_a: std::marker::PhantomData<A>,
    pub description: String,
}
#[allow(dead_code)]
impl<S: Clone, A: Clone> StateMonad<S, A> {
    pub fn new(description: &str) -> Self {
        Self {
            _phantom_s: std::marker::PhantomData,
            _phantom_a: std::marker::PhantomData,
            description: description.to_string(),
        }
    }
    pub fn get_desc(&self) -> String {
        format!(
            "get :: State {} {}",
            std::any::type_name::<S>(),
            std::any::type_name::<A>()
        )
    }
    pub fn put_desc(&self) -> String {
        format!(
            "put :: {} -> State {} ()",
            std::any::type_name::<S>(),
            std::any::type_name::<S>()
        )
    }
    pub fn modify_desc(&self) -> String {
        format!(
            "modify :: ({0} -> {0}) -> State {0} ()",
            std::any::type_name::<S>()
        )
    }
}
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct DependentTypeExample {
    pub type_name: String,
    pub type_signature: String,
    pub invariant: String,
    pub language: String,
}
#[allow(dead_code)]
impl DependentTypeExample {
    pub fn fixed_length_vector(elem_type: &str, n: usize) -> Self {
        DependentTypeExample {
            type_name: format!("Vec {} {}", elem_type, n),
            type_signature: format!("Vec : Type -> ℕ -> Type"),
            invariant: format!("length is exactly {}", n),
            language: "Agda/Idris/Lean".to_string(),
        }
    }
    pub fn sorted_list(elem_type: &str) -> Self {
        DependentTypeExample {
            type_name: format!("SortedList {}", elem_type),
            type_signature: "SortedList : Type -> Type".to_string(),
            invariant: "all elements in sorted order".to_string(),
            language: "Agda".to_string(),
        }
    }
    pub fn fin_type(n: usize) -> Self {
        DependentTypeExample {
            type_name: format!("Fin {}", n),
            type_signature: "Fin : ℕ -> Type".to_string(),
            invariant: format!("indices in {{0,..,{}}}", n.saturating_sub(1)),
            language: "Agda/Lean".to_string(),
        }
    }
    pub fn type_safety_guarantee(&self) -> String {
        format!(
            "{}: type system enforces '{}' statically (no runtime check needed)",
            self.type_name, self.invariant
        )
    }
    pub fn extraction_to_code(&self) -> String {
        format!(
            "From {} proof to certified {} code via extraction",
            self.language, self.language
        )
    }
}
/// Free applicative functor (simplified representation).
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub enum FreeApplicative<A: Clone> {
    Pure(A),
    Ap(usize, Box<FreeApplicative<A>>),
}
#[allow(dead_code)]
impl<A: Clone> FreeApplicative<A> {
    pub fn pure_val(a: A) -> Self {
        FreeApplicative::Pure(a)
    }
    pub fn depth(&self) -> usize {
        match self {
            FreeApplicative::Pure(_) => 0,
            FreeApplicative::Ap(_, x) => 1 + x.depth(),
        }
    }
}
/// Histomorphism: catamorphism with access to full history.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct Histomorphism {
    pub algebra_name: String,
    pub cache: Vec<i64>,
}
#[allow(dead_code)]
impl Histomorphism {
    pub fn new(algebra_name: &str) -> Self {
        Self {
            algebra_name: algebra_name.to_string(),
            cache: Vec::new(),
        }
    }
    /// Fibonacci via histomorphism (with memoized history).
    pub fn fibonacci_histo(&mut self, n: usize) -> i64 {
        for i in self.cache.len()..=n {
            let v = if i == 0 {
                0
            } else if i == 1 {
                1
            } else {
                self.cache[i - 1] + self.cache[i - 2]
            };
            self.cache.push(v);
        }
        self.cache[n]
    }
}
/// A simple algebraic effect: a computation that may perform an effect.
pub enum Effect<E, A> {
    /// Pure result (no effect)
    Pure(A),
    /// Effectful operation with continuation
    Perform(E, Box<dyn FnOnce(()) -> Effect<E, A>>),
}
impl<E: 'static, A: 'static> Effect<E, A> {
    /// Lift a pure value.
    pub fn pure(a: A) -> Self {
        Effect::Pure(a)
    }
    /// Handle all effects, collapsing to a pure value.
    pub fn handle(self, handler: &dyn Fn(E)) -> A
    where
        A: Default,
    {
        match self {
            Effect::Pure(a) => a,
            Effect::Perform(e, k) => {
                handler(e);
                k(()).handle(handler)
            }
        }
    }
}
/// `ComonadExtend` — utility struct for comonad extension operations.
pub struct ComonadExtend;
impl ComonadExtend {
    /// Run comonadic extension on a zipper.
    pub fn extend<A: Clone, B: Clone>(z: &Zipper<A>, f: impl Fn(&Zipper<A>) -> B) -> Zipper<B> {
        z.extend(f)
    }
    /// Duplicate: w → W (W a) — the comonad `duplicate`.
    pub fn duplicate<A: Clone>(z: &Zipper<A>) -> Zipper<Zipper<A>> {
        z.extend(|sub_z| {
            let left = sub_z.left.clone();
            let focus = sub_z.focus.clone();
            let right = sub_z.right.clone();
            Zipper { left, focus, right }
        })
    }
}
/// Hylomorphism: unfold an anamorphism then fold a catamorphism.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct Hylomorphism {
    pub seed_label: String,
    pub unfold_steps: Vec<String>,
    pub fold_steps: Vec<String>,
}
#[allow(dead_code)]
impl Hylomorphism {
    pub fn new(seed_label: &str) -> Self {
        Self {
            seed_label: seed_label.to_string(),
            unfold_steps: Vec::new(),
            fold_steps: Vec::new(),
        }
    }
    pub fn add_unfold_step(mut self, step: &str) -> Self {
        self.unfold_steps.push(step.to_string());
        self
    }
    pub fn add_fold_step(mut self, step: &str) -> Self {
        self.fold_steps.push(step.to_string());
        self
    }
    /// Fibonacci as hylomorphism: ana unfolds to tree of additions, cata folds.
    pub fn fibonacci_hylo(n: u32) -> u64 {
        fn fib(n: u32) -> u64 {
            if n <= 1 {
                return n as u64;
            }
            let mut a = 0u64;
            let mut b = 1u64;
            for _ in 2..=n {
                let c = a + b;
                a = b;
                b = c;
            }
            b
        }
        fib(n)
    }
}
/// Algebraic effect system.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct EffectSystem {
    pub effect_name: String,
    pub operations: Vec<(String, String)>,
    pub handler_type: String,
}
#[allow(dead_code)]
impl EffectSystem {
    /// State effect.
    pub fn state(state_type: &str) -> Self {
        Self {
            effect_name: format!("State({})", state_type),
            operations: vec![
                ("get".to_string(), format!("unit -> {}", state_type)),
                ("put".to_string(), format!("{} -> unit", state_type)),
            ],
            handler_type: format!("{} -> a -> ({} * {})", state_type, state_type, "a"),
        }
    }
    /// Exception effect.
    pub fn exception(exc_type: &str) -> Self {
        Self {
            effect_name: format!("Exception({})", exc_type),
            operations: vec![("throw".to_string(), format!("{} -> a", exc_type))],
            handler_type: format!("({} -> b) -> (a -> b) -> b", exc_type),
        }
    }
    /// Number of operations.
    pub fn num_ops(&self) -> usize {
        self.operations.len()
    }
}
/// A profunctor-encoded optic, represented as a Rust trait object.
///
/// In Haskell: `type Optic p s t a b = p a b -> p s t`.
/// Here we use `Fn(`Box<dyn Fn(a) ->` b>) -> `Box<dyn Fn(s) ->` t>` as a simplified model.
pub struct ProfunctorOptic<S, T, A, B> {
    run: Box<dyn Fn(Box<dyn Fn(A) -> B>) -> Box<dyn Fn(S) -> T>>,
}
impl<S: 'static, T: 'static, A: 'static, B: 'static> ProfunctorOptic<S, T, A, B> {
    /// Construct a profunctor optic from an adapter function.
    pub fn new(run: impl Fn(Box<dyn Fn(A) -> B>) -> Box<dyn Fn(S) -> T> + 'static) -> Self {
        Self { run: Box::new(run) }
    }
    /// Apply the optic to a concrete mapping function.
    pub fn apply(&self, f: impl Fn(A) -> B + 'static) -> Box<dyn Fn(S) -> T> {
        (self.run)(Box::new(f))
    }
    /// Build a simple lens-style profunctor optic from getter and setter.
    pub fn lens_optic(
        getter: impl Fn(&S) -> A + 'static,
        setter: impl Fn(B, S) -> T + 'static,
    ) -> Self
    where
        S: Clone + 'static,
    {
        let getter = std::sync::Arc::new(getter);
        let setter = std::sync::Arc::new(setter);
        Self::new(move |f: Box<dyn Fn(A) -> B>| {
            let getter = getter.clone();
            let setter = setter.clone();
            let f = std::sync::Arc::new(f);
            Box::new(move |s: S| {
                let a = getter(&s);
                let b = f(a);
                setter(b, s)
            })
        })
    }
    /// Build a prism-style profunctor optic from preview and review.
    pub fn prism_optic(
        preview: impl Fn(S) -> Result<A, T> + 'static,
        review: impl Fn(B) -> T + 'static,
    ) -> Self
    where
        S: 'static,
    {
        let preview = std::sync::Arc::new(preview);
        let review = std::sync::Arc::new(review);
        Self::new(move |f: Box<dyn Fn(A) -> B>| {
            let preview = preview.clone();
            let review = review.clone();
            let f = std::sync::Arc::new(f);
            Box::new(move |s: S| match preview(s) {
                Ok(a) => review(f(a)),
                Err(t) => t,
            })
        })
    }
}
/// A heterogeneous list (type-erased at runtime; type safety tracked by the user).
pub enum HList {
    /// The empty HList
    Nil,
    /// A cons cell holding a boxed value and the tail
    Cons(Box<dyn std::any::Any>, Box<HList>),
}
impl HList {
    /// The empty heterogeneous list.
    pub fn nil() -> Self {
        HList::Nil
    }
    /// Prepend any value to the HList.
    pub fn cons<T: 'static>(head: T, tail: HList) -> Self {
        HList::Cons(Box::new(head), Box::new(tail))
    }
    /// Returns the length of this HList.
    pub fn len(&self) -> usize {
        match self {
            HList::Nil => 0,
            HList::Cons(_, tail) => 1 + tail.len(),
        }
    }
    /// Returns true if this HList is empty.
    pub fn is_empty(&self) -> bool {
        matches!(self, HList::Nil)
    }
}
/// Evaluator for generic recursion schemes over rose trees.
///
/// A `RoseTree<A>` models the fixed point of F X = A × List X.
#[allow(dead_code)]
pub enum RoseTree<A> {
    /// A leaf/node with a value and zero or more children.
    Node(A, Vec<RoseTree<A>>),
}
/// Type equality evidence: proof that S and T are the same type.
pub struct TypeEquality<S, T> {
    _coerce: std::marker::PhantomData<(S, T)>,
}
impl<T> TypeEquality<T, T> {
    /// Reflexivity: every type is equal to itself.
    pub fn refl() -> Self {
        TypeEquality {
            _coerce: std::marker::PhantomData,
        }
    }
}
impl<S, T> TypeEquality<S, T> {
    /// Use type equality evidence to coerce a value.
    pub fn coerce(self, s: S) -> T
    where
        S: Into<T>,
    {
        s.into()
    }
}
/// `LensComposer` provides utilities for composing lenses and verifying laws.
pub struct LensComposer;
impl LensComposer {
    /// Compose two lenses: `outer` focuses on `M` inside `S`,
    /// `inner` focuses on `A` inside `M`.
    pub fn compose<S, M, A>(outer: Lens<S, M>, inner: Lens<M, A>) -> impl Fn(&S) -> A
    where
        S: Clone + 'static,
        M: Clone + 'static,
        A: Clone + 'static,
    {
        move |s: &S| {
            let m = outer.view(s);
            inner.view(&m)
        }
    }
    /// Check the GetSet law: `set(get(s), s) == s`.
    pub fn check_get_set<S, A>(lens: &Lens<S, A>, s: S) -> bool
    where
        S: Clone + PartialEq + 'static,
        A: Clone + 'static,
    {
        let a = lens.view(&s);
        let s2 = lens.set(a, s.clone());
        s2 == s
    }
    /// Check the SetGet law: `get(set(a, s)) == a`.
    pub fn check_set_get<S, A>(lens: &Lens<S, A>, a: A, s: S) -> bool
    where
        S: Clone + 'static,
        A: Clone + PartialEq + 'static,
    {
        let s2 = lens.set(a.clone(), s);
        let a2 = lens.view(&s2);
        a2 == a
    }
    /// Check the SetSet law: `set(a2, set(a1, s)) == set(a2, s)`.
    pub fn check_set_set<S, A>(lens: &Lens<S, A>, a1: A, a2: A, s: S) -> bool
    where
        S: Clone + PartialEq + 'static,
        A: Clone + 'static,
    {
        let s_after_a1 = lens.set(a1, s.clone());
        let s_after_a2_a1 = lens.set(a2.clone(), s_after_a1);
        let s_after_a2 = lens.set(a2, s);
        s_after_a2_a1 == s_after_a2
    }
}
/// A coercion with a proof obligation (modelled as a runtime-checked cast).
pub struct Coerce<S, T> {
    _marker: std::marker::PhantomData<(S, T)>,
}
impl<S: 'static, T: 'static> Coerce<S, T> {
    /// Attempt to coerce using Any downcast; returns None if types differ.
    pub fn try_coerce(s: S) -> Option<T> {
        let boxed: Box<dyn std::any::Any> = Box::new(s);
        boxed.downcast::<T>().ok().map(|b| *b)
    }
}
/// Free monad functor encoding.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct FreeMonadInfo {
    pub functor_name: String,
    pub operations: Vec<String>,
    pub description: String,
}
#[allow(dead_code)]
impl FreeMonadInfo {
    /// Free monad over a functor F.
    pub fn over(functor: &str, ops: Vec<&str>) -> Self {
        Self {
            functor_name: functor.to_string(),
            operations: ops.iter().map(|s| s.to_string()).collect(),
            description: format!("Free monad over {} with {} operations", functor, ops.len()),
        }
    }
    /// Interpretation via fold.
    pub fn interpreter_description(&self) -> String {
        format!(
            "foldFree :: ({} a -> m a) -> Free {} a -> m a",
            self.functor_name, self.functor_name
        )
    }
    /// Number of operations.
    pub fn num_operations(&self) -> usize {
        self.operations.len()
    }
}
/// Continuation passing style transform.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct CpsTransform {
    pub source_type: String,
    pub result_type: String,
    pub continuation_type: String,
}
#[allow(dead_code)]
impl CpsTransform {
    /// CPS transform A with result R.
    pub fn new(source: &str, result: &str) -> Self {
        Self {
            source_type: source.to_string(),
            result_type: result.to_string(),
            continuation_type: format!("({} -> {}) -> {}", source, result, result),
        }
    }
    /// Direct style to CPS description.
    pub fn transform_description(&self) -> String {
        format!("CPS[{}] = ({})", self.source_type, self.continuation_type)
    }
}
/// Scott encoding of algebraic data types.
#[allow(dead_code)]
pub struct ScottEncoding;
#[allow(dead_code)]
impl ScottEncoding {
    /// Scott-encoded Boolean: True = λt. λf. t; False = λt. λf. f.
    pub fn scott_true_desc() -> &'static str {
        "λt. λf. t"
    }
    pub fn scott_false_desc() -> &'static str {
        "λt. λf. f"
    }
    /// Scott-encoded pair: Pair a b = λs. s a b.
    pub fn scott_pair_desc() -> &'static str {
        "λa. λb. λs. s a b"
    }
    /// Scott-encoded fst: fst p = p (λa. λb. a).
    pub fn scott_fst_desc() -> &'static str {
        "λp. p (λa. λb. a)"
    }
    /// Scott-encoded List: Nil = λn. λc. n; Cons h t = λn. λc. c h t.
    pub fn scott_nil_desc() -> &'static str {
        "λn. λc. n"
    }
    pub fn scott_cons_desc() -> &'static str {
        "λh. λt. λn. λc. c h t"
    }
}
/// A lawful lens focusing on field A inside structure S.
pub struct Lens<S, A> {
    getter: Box<dyn Fn(&S) -> A>,
    setter: Box<dyn Fn(A, S) -> S>,
}
impl<S: 'static, A: 'static> Lens<S, A> {
    /// Create a lens from a getter and a setter.
    pub fn new(getter: impl Fn(&S) -> A + 'static, setter: impl Fn(A, S) -> S + 'static) -> Self {
        Self {
            getter: Box::new(getter),
            setter: Box::new(setter),
        }
    }
    /// Get the focused value.
    pub fn view(&self, s: &S) -> A {
        (self.getter)(s)
    }
    /// Set the focused value.
    pub fn set(&self, a: A, s: S) -> S {
        (self.setter)(a, s)
    }
    /// Modify the focused value.
    pub fn over(&self, f: impl Fn(A) -> A, s: S) -> S
    where
        S: Clone,
    {
        let a = self.view(&s);
        self.set(f(a), s)
    }
}
/// Böhm-Berarducci (CPS) encoding of recursive types.
#[allow(dead_code)]
pub struct BoehmBerarducci;
#[allow(dead_code)]
impl BoehmBerarducci {
    /// BB-encoded natural number as higher-rank type.
    pub fn bb_nat_type_desc() -> &'static str {
        "forall r. r -> (r -> r) -> r"
    }
    /// BB-encoded list: List a = forall r. r -> (a -> r -> r) -> r.
    pub fn bb_list_type_desc() -> &'static str {
        "forall r. r -> (a -> r -> r) -> r"
    }
    /// BB-encoded rose tree: Tree a = forall r. (a -> List r -> r) -> r.
    pub fn bb_tree_type_desc() -> &'static str {
        "forall r. (a -> List r -> r) -> r"
    }
}
/// An isomorphism between types S and A.
pub struct Iso<S, A> {
    to: Box<dyn Fn(S) -> A>,
    from: Box<dyn Fn(A) -> S>,
}
impl<S: 'static, A: 'static> Iso<S, A> {
    /// Create an iso from to/from functions.
    pub fn new(to: impl Fn(S) -> A + 'static, from: impl Fn(A) -> S + 'static) -> Self {
        Self {
            to: Box::new(to),
            from: Box::new(from),
        }
    }
    /// Apply the forward direction.
    pub fn view(&self, s: S) -> A {
        (self.to)(s)
    }
    /// Apply the reverse direction.
    pub fn review(&self, a: A) -> S {
        (self.from)(a)
    }
    /// Use this iso as a lens: get.
    pub fn get(&self, s: S) -> A {
        (self.to)(s)
    }
}
/// An effect handler that handles effect type E and produces B.
pub struct EffectHandler<E, A, B> {
    handle_fn: Box<dyn Fn(E, Box<dyn FnOnce(A) -> B>) -> B>,
}
impl<E: 'static, A: 'static, B: 'static> EffectHandler<E, A, B> {
    /// Create a handler.
    pub fn new(handle_fn: impl Fn(E, Box<dyn FnOnce(A) -> B>) -> B + 'static) -> Self {
        Self {
            handle_fn: Box::new(handle_fn),
        }
    }
    /// Run the handler on an effect with a continuation.
    pub fn run(&self, effect: E, continuation: impl FnOnce(A) -> B + 'static) -> B {
        (self.handle_fn)(effect, Box::new(continuation))
    }
}
/// Yoneda lemma embedding: Hom(A, -) ≅ F where F is a functor.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct YonedaEmbedding<A: Clone> {
    pub object: A,
    pub morphism_count: usize,
}
#[allow(dead_code)]
impl<A: Clone> YonedaEmbedding<A> {
    pub fn new(object: A) -> Self {
        Self {
            object,
            morphism_count: 0,
        }
    }
    /// Register a morphism (conceptually). Returns updated count.
    pub fn add_morphism(mut self) -> Self {
        self.morphism_count += 1;
        self
    }
}
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct HomotopyEquivalence {
    pub type_a: String,
    pub type_b: String,
    pub forth_map: String,
    pub back_map: String,
    pub is_univalent: bool,
}
#[allow(dead_code)]
impl HomotopyEquivalence {
    pub fn new(a: &str, b: &str, f: &str, g: &str) -> Self {
        HomotopyEquivalence {
            type_a: a.to_string(),
            type_b: b.to_string(),
            forth_map: f.to_string(),
            back_map: g.to_string(),
            is_univalent: false,
        }
    }
    pub fn univalent_equivalence(mut self) -> Self {
        self.is_univalent = true;
        self
    }
    pub fn contractibility_condition(&self) -> String {
        format!(
            "{} ≃ {}: ∃ f:{}->{}, g:{}->{}, f∘g∼id, g∘f∼id",
            self.type_a, self.type_b, self.type_a, self.type_b, self.type_b, self.type_a
        )
    }
    pub fn univalence_axiom(&self) -> String {
        if self.is_univalent {
            "(A=B) ≃ (A≃B) (Voevodsky's univalence axiom)".to_string()
        } else {
            "Not using univalence axiom".to_string()
        }
    }
}
/// Continuation monad: Cont r a = (a -> r) -> r.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct Cont<R: Clone, A: Clone> {
    _phantom_r: std::marker::PhantomData<R>,
    _phantom_a: std::marker::PhantomData<A>,
    pub label: String,
}
#[allow(dead_code)]
impl<R: Clone, A: Clone> Cont<R, A> {
    pub fn new(label: &str) -> Self {
        Self {
            _phantom_r: std::marker::PhantomData,
            _phantom_a: std::marker::PhantomData,
            label: label.to_string(),
        }
    }
    /// run_cont :: Cont r a -> (a -> r) -> r (represented symbolically).
    pub fn run_cont_desc(&self) -> String {
        format!("Cont({}).run_cont", self.label)
    }
}
/// A free monad over a functor F, with values in A.
pub enum FreeMonad<A> {
    /// The pure/return constructor
    Pure(A),
    /// The free/join constructor wrapping a functor layer
    Free(Box<dyn FnOnce() -> FreeMonad<A>>),
}
impl<A> FreeMonad<A> {
    /// Lift a pure value into the free monad.
    pub fn pure(a: A) -> Self {
        FreeMonad::Pure(a)
    }
    /// Fold (catamorphism) over the free monad.
    pub fn fold<B>(self, pure_fn: impl Fn(A) -> B, free_fn: impl Fn(FreeMonad<A>) -> B) -> B {
        match self {
            FreeMonad::Pure(a) => pure_fn(a),
            FreeMonad::Free(mk) => free_fn(mk()),
        }
    }
}
/// A simple algebraic effect for the interpreter.
#[allow(dead_code)]
pub enum ConsoleEffect {
    /// Print a string to the console.
    Print(String),
    /// Read a line (returns a constant in tests).
    Read,
}
/// `FreeMonadInterpreter` runs a `ConsoleProg` against a provided handler.
pub struct FreeMonadInterpreter;
impl FreeMonadInterpreter {
    /// Interpret a `ConsoleProg` using provided print/read handlers.
    pub fn run<A>(
        prog: ConsoleProg<A>,
        print_handler: &mut dyn FnMut(&str),
        read_handler: &mut dyn FnMut() -> String,
    ) -> A {
        match prog {
            ConsoleProg::Done(a) => a,
            ConsoleProg::Step(effect, k) => match effect {
                ConsoleEffect::Print(msg) => {
                    print_handler(&msg);
                    Self::run(k(String::new()), print_handler, read_handler)
                }
                ConsoleEffect::Read => {
                    let line = read_handler();
                    Self::run(k(line), print_handler, read_handler)
                }
            },
        }
    }
}
/// Category theory view: functors as type constructors.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct TypeConstructorFunctor {
    pub name: String,
    pub fmap_type: String,
    pub laws: Vec<String>,
}
#[allow(dead_code)]
impl TypeConstructorFunctor {
    /// List functor.
    pub fn list() -> Self {
        Self {
            name: "List".to_string(),
            fmap_type: "(a -> b) -> List a -> List b".to_string(),
            laws: vec![
                "fmap id = id".to_string(),
                "fmap (f . g) = fmap f . fmap g".to_string(),
            ],
        }
    }
    /// Maybe functor.
    pub fn maybe() -> Self {
        Self {
            name: "Maybe".to_string(),
            fmap_type: "(a -> b) -> Maybe a -> Maybe b".to_string(),
            laws: vec![
                "fmap id = id".to_string(),
                "fmap (f . g) = fmap f . fmap g".to_string(),
            ],
        }
    }
    /// Number of laws.
    pub fn num_laws(&self) -> usize {
        self.laws.len()
    }
}
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ProfunctorData {
    pub profunctor_name: String,
    pub dimap_type: String,
    pub is_cartesian: bool,
    pub is_cocartesian: bool,
    pub is_closed: bool,
}
#[allow(dead_code)]
impl ProfunctorData {
    pub fn function_profunctor() -> Self {
        ProfunctorData {
            profunctor_name: "(->)".to_string(),
            dimap_type: "(a -> b) -> (c -> d) -> (b -> c) -> (a -> d)".to_string(),
            is_cartesian: true,
            is_cocartesian: true,
            is_closed: true,
        }
    }
    pub fn star_profunctor(functor: &str) -> Self {
        ProfunctorData {
            profunctor_name: format!("Star {}", functor),
            dimap_type: format!(
                "(a -> b) -> (c -> d) -> (b -> {} c) -> (a -> {} d)",
                functor, functor
            ),
            is_cartesian: true,
            is_cocartesian: false,
            is_closed: false,
        }
    }
    pub fn optic_encoding(&self) -> String {
        "Profunctor optics: Lens = ∀p. Cartesian p => p a b -> p s t".to_string()
    }
    pub fn tambara_module_connection(&self) -> String {
        "Tambara module: profunctor P with strength α: P a b -> P (c,a) (c,b)".to_string()
    }
    pub fn bartosz_milewski_connection(&self) -> String {
        "Milewski: profunctors and optics in category theory for programmers".to_string()
    }
}
/// A singleton: a value that is uniquely determined by its type.
pub struct Singleton<T> {
    /// The unique value
    pub value: T,
}
impl<T: Clone> Singleton<T> {
    /// Create a singleton.
    pub fn new(value: T) -> Self {
        Self { value }
    }
    /// Extract the value.
    pub fn extract(&self) -> T {
        self.value.clone()
    }
}
/// An Arrow: a generalised function from A to B with category operations.
pub struct Arrow<A, B> {
    run: Box<dyn Fn(A) -> B>,
}
impl<A: 'static, B: 'static> Arrow<A, B> {
    /// Lift a plain function into an Arrow.
    pub fn arr(f: impl Fn(A) -> B + 'static) -> Self {
        Self { run: Box::new(f) }
    }
    /// Apply the arrow.
    pub fn apply(&self, a: A) -> B {
        (self.run)(a)
    }
    /// Compose two arrows.
    pub fn compose<C: 'static>(self, other: Arrow<B, C>) -> Arrow<A, C> {
        Arrow::arr(move |a| other.apply(self.apply(a)))
    }
}
/// An affine traversal (0 or 1 focus).
pub struct AffineTraversal<S, A> {
    preview: Box<dyn Fn(&S) -> Option<A>>,
    set: Box<dyn Fn(A, S) -> S>,
}
impl<S: 'static, A: 'static> AffineTraversal<S, A> {
    /// Create an affine traversal.
    pub fn new(
        preview: impl Fn(&S) -> Option<A> + 'static,
        set: impl Fn(A, S) -> S + 'static,
    ) -> Self {
        Self {
            preview: Box::new(preview),
            set: Box::new(set),
        }
    }
    /// Preview the focus.
    pub fn preview(&self, s: &S) -> Option<A> {
        (self.preview)(s)
    }
    /// Set the focus if present.
    pub fn set(&self, a: A, s: S) -> S {
        (self.set)(a, s)
    }
}
/// Writer monad: Writer w a = (a, w) with Monoid w.
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct WriterMonad<A: Clone> {
    pub value: A,
    pub log: Vec<String>,
}
#[allow(dead_code)]
impl<A: Clone> WriterMonad<A> {
    pub fn new(value: A) -> Self {
        Self {
            value,
            log: Vec::new(),
        }
    }
    pub fn tell(mut self, msg: String) -> Self {
        self.log.push(msg);
        self
    }
    pub fn listen(&self) -> (&A, &Vec<String>) {
        (&self.value, &self.log)
    }
    pub fn pass<F: Fn(&Vec<String>) -> Vec<String>>(mut self, f: F) -> Self {
        self.log = f(&self.log);
        self
    }
}
#[allow(dead_code)]
#[derive(Debug, Clone)]
pub struct ApplicativeData {
    pub functor_name: String,
    pub pure_type: String,
    pub ap_type: String,
    pub is_monad: bool,
}
#[allow(dead_code)]
impl ApplicativeData {
    pub fn new(name: &str, pure_ty: &str, ap_ty: &str, monad: bool) -> Self {
        ApplicativeData {
            functor_name: name.to_string(),
            pure_type: pure_ty.to_string(),
            ap_type: ap_ty.to_string(),
            is_monad: monad,
        }
    }
    pub fn maybe_applicative() -> Self {
        ApplicativeData {
            functor_name: "Maybe".to_string(),
            pure_type: "a -> Maybe a".to_string(),
            ap_type: "Maybe (a -> b) -> Maybe a -> Maybe b".to_string(),
            is_monad: true,
        }
    }
    pub fn validation_applicative() -> Self {
        ApplicativeData {
            functor_name: "Validation e".to_string(),
            pure_type: "a -> Validation e a".to_string(),
            ap_type: "Validation e (a -> b) -> Validation e a -> Validation e b".to_string(),
            is_monad: false,
        }
    }
    pub fn laws(&self) -> Vec<String> {
        vec![
            "Identity: pure id <*> v = v".to_string(),
            "Composition: pure (.) <*> u <*> v <*> w = u <*> (v <*> w)".to_string(),
            "Homomorphism: pure f <*> pure x = pure (f x)".to_string(),
            "Interchange: u <*> pure y = pure ($ y) <*> u".to_string(),
        ]
    }
    pub fn mcbride_paterson_paper(&self) -> String {
        "McBride-Paterson (2008): Applicative programming with effects".to_string()
    }
}