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// Copyright (C) 2026 Industrial Algebra
// SPDX-License-Identifier: Apache-2.0
use crate::contravariant::PredicateF;
use crate::decide::Decide;
#[cfg(all(not(feature = "std"), feature = "alloc"))]
use alloc::boxed::Box;
/// Conclude: the contravariant analogue of Plus.
///
/// Adds a `conclude` operation (the identity for `choose`).
/// `conclude` takes a function `A -> Infallible`, witnessing that `A` is
/// uninhabited — so the resulting predicate is vacuously true.
///
/// Laws:
/// - Left identity: `choose(f, conclude(absurd), fa) ≈ contramap(from_right . f, fa)`
/// - Right identity: `choose(f, fa, conclude(absurd)) ≈ contramap(from_left . f, fa)`
pub trait Conclude: Decide {
fn conclude<A: 'static>(f: impl Fn(A) -> core::convert::Infallible + 'static) -> Self::Of<A>;
}
impl Conclude for PredicateF {
fn conclude<A: 'static>(
_f: impl Fn(A) -> core::convert::Infallible + 'static,
) -> Box<dyn Fn(A) -> bool> {
// Vacuously true: if `f` could produce Infallible, `A` is uninhabited,
// so this predicate will never actually be called with a real value.
// For inhabited types, the predicate is simply always true.
Box::new(|_| true)
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn predicate_conclude() {
// For any inhabited type, conclude gives a predicate that's always true
let p: Box<dyn Fn(i32) -> bool> = PredicateF::conclude(|_: i32| unreachable!());
// We can't actually call it with the intent of testing the Infallible path,
// but we can test that the predicate is true for any value
assert!(p(42));
assert!(p(-1));
}
}
#[cfg(test)]
mod law_tests {
use super::*;
use proptest::prelude::*;
proptest! {
// Left identity: choose(|a| Err(a), conclude(absurd), fa)(x) == fa(x)
#[test]
fn predicate_left_identity(x in any::<i32>()) {
let fa: Box<dyn Fn(i32) -> bool> = Box::new(|a| a > 0);
let expected = fa(x);
let fa2: Box<dyn Fn(i32) -> bool> = Box::new(|a| a > 0);
let result = PredicateF::choose(
|a: i32| -> Result<core::convert::Infallible, i32> { Err(a) },
PredicateF::conclude(|i: core::convert::Infallible| -> core::convert::Infallible { i }),
fa2,
);
prop_assert_eq!(result(x), expected);
}
// Right identity: choose(|a| Ok(a), fa, conclude(absurd))(x) == fa(x)
#[test]
fn predicate_right_identity(x in any::<i32>()) {
let fa: Box<dyn Fn(i32) -> bool> = Box::new(|a| a > 0);
let expected = fa(x);
let fa2: Box<dyn Fn(i32) -> bool> = Box::new(|a| a > 0);
let result = PredicateF::choose(
|a: i32| -> Result<i32, core::convert::Infallible> { Ok(a) },
fa2,
PredicateF::conclude(|i: core::convert::Infallible| -> core::convert::Infallible { i }),
);
prop_assert_eq!(result(x), expected);
}
}
}