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//! # Continuation Monad
//!
//! The Continuation monad represents computations with explicit control flow, allowing
//! control flow to be expressed and composed via explicit continuations. It provides a way to
//! manipulate control flow in a purely functional manner.
//!
//! ## Quick Start
//!
//! Control program flow with continuations:
//!
//! ```rust
//! use rustica::datatypes::cont::Cont;
//!
//! // Create a simple continuation that passes a value to its continuation
//! let cont_value = Cont::return_cont(42);
//!
//! // Transform the value with fmap
//! let doubled = cont_value.fmap(|x| x * 2);
//!
//! // Run the continuation with an identity function
//! let result = doubled.run(|x| x);
//! assert_eq!(result, 84);
//!
//! // Chain continuations with bind
//! let chained = Cont::return_cont(10)
//! .bind(|x| Cont::return_cont(x + 5))
//! .bind(|x| Cont::return_cont(x * 2));
//!
//! let final_result = chained.run(|x| x);
//! assert_eq!(final_result, 30); // ((10 + 5) * 2)
//!
//! // Use continuations for early exit patterns
//! let early_exit = Cont::new(|k| {
//! // Simulate some computation that might want to exit early
//! let value = 100;
//! if value > 50 {
//! k(value) // Continue normally
//! } else {
//! // By not calling `k`, we bypass the rest of the continuation chain.
//! 0
//! }
//! });
//!
//! let exit_result = early_exit.run(|x| x + 1);
//! assert_eq!(exit_result, 101);
//! ```
//!
//! ## Core Concepts
//!
//! - **Continuation-Passing Style**: Functions receive an explicit continuation that represents "what to do next"
//! - **Explicit Control Flow**: Allows implementing advanced control flow patterns like exceptions, backtracking, or coroutines
//! - **Composable Computations**: Continuations can be composed and transformed using monadic operations
//!
//! ## Functional Programming Context
//!
//! In functional programming, continuations provide a way to represent and manipulate control flow
//! as first-class values. The Continuation monad encapsulates this pattern, making it composable
//! with other functional abstractions.
//!
//! The Continuation monad is particularly powerful because it can be used to implement other monads,
//! making it sometimes called the "mother of all monads." In category theory terms, the Continuation
//! monad is related to the concept of a Yoneda embedding, which provides a representation of objects
//! in terms of their relationships with other objects.
//!
//! Similar structures in other languages include:
//!
//! - Haskell's `Cont` monad in Control.Monad.Cont
//! - Scala's `Cont` in cats library
//! - JavaScript's CPS transformations in libraries like fantasy-land
//! - Scheme and Racket's first-class continuations via `call/cc`
//!
//! ## Functional Programming Methods
//!
//! `Cont<R, A>` provides inherent methods that follow functional programming patterns:
//!
//! - **Functor-like**: `fmap` transforms values inside the continuation
//! - **Applicative-like**: `apply` applies functions wrapped in continuations to values in continuations
//! - **Monad-like**: `bind` sequences continuation operations
//!
//! **Note**: These are inherent methods, not trait implementations. `Cont` does not implement
//! the `Functor`, `Applicative`, or `Monad` traits, but provides equivalent functionality
//! through its own methods optimized for continuation-passing style.
//!
//! ## Use Cases
//!
//! The Continuation monad is useful for:
//!
//! - **Custom Control Flow**: Implementing non-standard control flow patterns
//! - **Exception Handling**: Creating custom error handling mechanisms
//! - **Asynchronous Programming**: Representing callbacks and asynchronous operations
//! - **Backtracking Algorithms**: Implementing algorithms that need to explore multiple paths
//! - **Coroutines**: Building cooperative multitasking systems
//!
//! ## Functional Programming Laws
//!
//! The inherent methods of `Cont<R, A>` satisfy the functional programming laws:
//!
//! ### Functor Laws
//! - Identity: `fmap id == id`
//! - Composition: `fmap (f . g) == fmap f . fmap g`
//!
//! ### Applicative Laws
//! - Identity: `pure id <*> v = v`
//! - Homomorphism: `pure f <*> pure x = pure (f x)`
//! - Interchange: `u <*> pure y = pure ($ y) <*> u`
//! - Composition: `pure (.) <*> u <*> v <*> w = u <*> (v <*> w)`
//!
//! ### Monad Laws
//! - Left Identity: `return a >>= f = f a`
//! - Right Identity: `m >>= return = m`
//! - Associativity: `(m >>= f) >>= g = m >>= (\x -> f x >>= g)`
//!
//! See individual method documentation (e.g., `fmap`, `apply`, `bind`) for specific examples demonstrating these laws.
//!
//! ## Examples
//!
//! ### Basic Usage
//!
//! ```rust
//! use rustica::datatypes::cont::Cont;
//!
//! // Create a simple continuation
//! let cont = Cont::return_cont(42);
//!
//! // Run the continuation with a handler
//! let result = cont.clone().run(|x| x * 2);
//! assert_eq!(result, 84);
//!
//! // Chain continuations
//! let cont2 = cont.bind(|x| Cont::return_cont(x + 1));
//! let result2 = cont2.run(|x| x * 2);
//! assert_eq!(result2, 86);
//! ```
//!
//! ### Control Flow Example
//!
//! ```rust
//! use std::sync::Arc;
//! use rustica::datatypes::cont::Cont;
//!
//! // A function that uses continuations to implement early return
//! fn safe_divide(a: i32, b: i32) -> Cont<i32, i32> {
//! if b == 0 {
//! // Early return with a default value
//! Cont::new(|_| -1)
//! } else {
//! // Continue with the division
//! Cont::return_cont(a / b)
//! }
//! }
//!
//! // Run with different inputs
//! let result1 = safe_divide(10, 2).run(|x| x);
//! let result2 = safe_divide(10, 0).run(|x| x);
//!
//! assert_eq!(result1, 5);
//! assert_eq!(result2, -1);
//! ```
use cratecont_tContT;
use ;
use Arc;
use crateId;
/// Type alias for a continuation function
pub type ContFn<R, A> = ;
/// Type alias for a function wrapped in Arc with Send + Sync bounds, commonly used in continuation operations
pub type ContFn2<A, B> = ;
/// The `Cont` monad represents computations in continuation-passing style.
///
/// It captures a computation that takes a continuation (a function) and
/// returns a value of type `R`.
///
/// # Type Parameters
///
/// * `R` - The type of the final result
/// * `A` - The type of the intermediate value
///
/// # Examples
///
/// ```
/// use rustica::datatypes::cont::Cont;
///
/// // Create two continuations
/// let cont1 = Cont::return_cont(5);
/// let cont2 = Cont::return_cont(-1);
///
/// // Run the continuations with an identity continuation
/// let result1 = cont1.run(|x| x);
/// let result2 = cont2.run(|x| x);
///
/// assert_eq!(result1, 5);
/// assert_eq!(result2, -1);
/// ```
/// Allows conversion from a `ContT<R, Id<R>, A>` to a `Cont<R, A>`.
///
/// This implementation enables seamless conversion from the transformer type to the base type,
/// following the same pattern as `Reader` and `ReaderT`. Typically, this is only valid when the
/// base monad is `Id`.
///
/// # Examples
///
/// ```rust
/// use rustica::datatypes::cont::Cont;
/// use rustica::transformers::cont_t::ContT;
/// use rustica::datatypes::id::Id;
///
/// // Create a ContT that applies the continuation to the value 42
/// let cont_t: ContT<i32, Id<i32>, i32> = ContT::new(|k| k(42));
///
/// // Convert to Cont
/// let cont: Cont<i32, i32> = Cont::from(cont_t);
/// let result = cont.run(|x| x + 1);
/// assert_eq!(result, 43);
/// ```