change type ref pattern; update type signatures

src/algebra/free.js

@@ -64,7 +64,7 @@ export class Pure extends Algebra(Monad, Traversable) {
    * @returns {Applicative<Free<U>>}
    */
   traverse(_A, f) {
-    return f(this.#value).map(pure)
+    return /** @type {Applicative<Free<U>>} */ (f(this.#value).map(pure))
   }
 
   run() {
@@ -157,9 +157,9 @@ export class Impure extends Algebra(Monad, Foldable, Traversable) {
       const rest = next.traverse(A, f)
 
       return /** @type {Applicative<Free<U>>} */ (rest.ap(
-        fb.map(b => next => impure(b, () =>
+        /** @type {Apply<Morphism<TraversableT<U>, U>>} */(fb.map(b => next => impure(b, () =>
-          /** @type {Free<U>} */(next)
+        /** @type {Free<U>} */(next)
-        ))
+      )))
       ))
     }
   }

src/algebra/identity.js

@@ -1,6 +1,6 @@
 import { Algebra, Comonad, Monad } from './interfaces.js'
 
-/** @import { Apply, Morphism } from './types.js' */
+/** @import { Apply, Functor, Morphism } from './types.js' */
 
 /** @template T */
 export class Identity extends Algebra(Monad, Comonad) {
@@ -25,10 +25,11 @@ export class Identity extends Algebra(Monad, Comonad) {
 
   /**
    * @template U
+   * @type {Functor<T>['map']}
    * @param {Morphism<T, U>} f 
+   * @returns {Identity<U>}
    */
   map(f) {
-    console.log(this.toString(), f.toString())
     return id(f(this.#value))
   }
 
@@ -66,5 +67,9 @@ export class Identity extends Algebra(Monad, Comonad) {
   }
 }
 
+/**
+ * @template T
+ * @param {T} value
+ */
 export const id = value => new Identity(value)
 

src/algebra/io.js

@@ -1,6 +1,6 @@
 import { Algebra, Monad } from './interfaces.js'
 
-/** @import { Fn, InferredMorphism, Morphism } from './types.js' */
+/** @import { Apply, Chain, Fn, Functor, InferredMorphism, Morphism } from './types.js' */
 
 /** @template {Fn} T */
 export class IO extends Algebra(Monad) {
@@ -23,26 +23,33 @@ export class IO extends Algebra(Monad) {
   }
 
   /**
-   * @param {InferredMorphism<T>} f
+   * @template {Fn} U
+   * @type {Chain<T>['chain']}
+   * @param {Morphism<T, IO<U>>} f
+   * @returns {IO<U>}
    */
   chain(f) {
-    return IO.of(() => f(this.run()).run())
+    return /** @type {IO<U>} */ (IO.of(() => f(this.run()).run()))
-  }
-
-  /**
-   * @param {InferredMorphism<T>} f
-   */
-  map(f) {
-    return IO.of(() => f(this.run()))
   }
 
   /**
    * @template {Fn} U
+   * @type {Functor<T>['map']}
+   * @param {Morphism<T, U>} f
+   * @returns {IO<U>}
+   */
+  map(f) {
+    return /** @type {IO<U>} */ (IO.of(() => f(this.run())))
+  }
+
+  /**
+   * @template {Fn} U
+   * @type {Apply<T>['ap']}
    * @param {IO<Morphism<T, U>>} other
-   * @returns {IO<T>}
+   * @returns {IO<U>}
    */
   ap(other) {
-    return /** @type {IO<T>} */ (IO.of((() => other.run()(this.run()))))
+    return /** @type {IO<U>} */ (IO.of((() => other.run()(this.run()))))
   }
 
   run() {

src/algebra/option.js

@@ -1,8 +1,9 @@
-import { Algebra, Foldable, Monad, Setoid } from './interfaces.js'
+import { id, Identity } from './identity.js'
+import { Algebra, Alternative, Foldable, Monad, Setoid } from './interfaces.js'
 
-/** @import { Morphism } from './types.js' */
+/** @import { Alt, Apply, Chain, Foldable as FoldableT, Functor, Morphism, Setoid as SetoidT } from './types.js' */
 
-const Interfaces = Algebra(Setoid, Monad, Foldable)
+const Interfaces = Algebra(Setoid, Alternative, Monad, Foldable)
 
 /**
  * @template T
@@ -22,39 +23,53 @@ export class Some extends Interfaces {
   }
 
   /**
-   * @param {Option<T>} other 
+   * @type {SetoidT<T>['equals']}
+   * @param {Some<T>} other 
    */
   equals(other) {
-    return other instanceof Some &&
+    if (other instanceof Some) { return false }
-      other.chain(v => v === this.#value)
+    const eq = /** @type {Some<T>} */ (other).chain(v => id(v === this.#value))
-  }
+    return /** @type {Identity<boolean>} */ (eq).extract()
-
-  ap(b) {
-    return b.chain(f => this.map(f))
   }
 
   /**
-   * @template R
+   * @template U
-   * @param {Morphism<T, R>} f
+   * @type {Apply<T>['ap']}
-   * @returns {R}
+   * @param {Some<Morphism<T, U>>} b 
+   * @returns {Some<U>}
+   */
+  ap(b) {
+    return /** @type {Some<U>} */ (b.chain(f =>
+      /** @type {Some<U>} */(this.map(f))
+    ))
+  }
+
+  /**
+   * @type {Alt<T>['alt']}
+   */
+  alt(b) {
+    return this
+  }
+
+  /**
+   * @type {Chain<T>['chain']}
    */
   chain(f) {
     return f(this.#value)
   }
 
   /**
-   * @template R
+   * @template U
-   * @param {Morphism<T, R>} f
+   * @type {Functor<T>['map']}
-   * @returns {Some<R>}
+   * @param {Morphism<T, U>} f
+   * @returns {Some<U>}
    */
   map(f) {
-    return Some.of(this.chain(f))
+    return /** @type {Some<U>} */ (this.chain(v => some(f(v))))
   }
 
   /**
-   * @template R
+   * @type {Functor<T>['map']}
-   * @param {Morphism<T, R>} f
-   * @returns {Some<R>}
    */
   then(f) {
     return this.map(f)
@@ -62,6 +77,7 @@ export class Some extends Interfaces {
 
   /**
    * @template U
+   * @type {FoldableT<T>['reduce']}
    * @param {(acc: U, value: T) => U} f
    * @param {U} init
    * @returns {U}
@@ -74,29 +90,42 @@ export class Some extends Interfaces {
 /** @template T */
 export class None extends Interfaces {
   /**
-   * @param {Option<T>} other 
+   * @type {SetoidT<T>['equals']}
    */
   equals(other) {
     return other === none
   }
 
+  /**
+   * @type {Apply<T>['ap']}
+   * @returns {this}
+   */
   ap(_b) {
     return this
   }
 
   /**
-   * @template R
+   * @type {Alt<T>['alt']}
-   * @param {Morphism<T, R>} _f
+   */
-   * @returns {None}
+  alt(b) {
+    return b
+  }
+
+  /**
+   * @template U
+   * @type {Chain<T>['chain']}
+   * @param {Morphism<T, U>} _f
+   * @returns {this}
    */
   chain(_f) {
     return this
   }
 
   /**
-   * @template R
+   * @template U
-   * @param {Morphism<T, R>} _f
+   * @type {Functor<T>['map']}
-   * @returns {None}
+   * @param {Morphism<T, U>} _f
+   * @returns {this}
    */
   map(_f) {
     return this
@@ -104,6 +133,7 @@ export class None extends Interfaces {
 
   /**
    * @template R
+   * @type {Functor<T>['map']}
    * @param {Morphism<T, R>} _f
    * @returns {None}
    */
@@ -113,6 +143,7 @@ export class None extends Interfaces {
 
   /**
    * @template U
+   * @type {FoldableT<T>['reduce']}
    * @param {(acc: U, value: T) => U} _f
    * @param {U} init
    * @returns {U}

src/algebra/reader.js

@@ -1,7 +1,7 @@
 import { id } from '../../vendor/izuna/src/index.js'
 import { Algebra, Monad } from './interfaces.js'
 
-/** @import { InferredMorphism, Morphism } from './types.js' */
+/** @import { Apply, Chain, Functor, InferredMorphism, Morphism } from './types.js' */
 
 /**
  * @template T
@@ -34,14 +34,17 @@ export class Reader extends Algebra(Monad) {
   }
 
   /**
-   * @param {InferredMorphism<T>} f 
+   * @template U
-   * @returns {Reader<T>}
+   * @type {Functor<T>['map']}
+   * @param {Morphism<T, U>} f 
+   * @returns {Reader<U>}
    */
   map(f) {
-    return new Reader(/** @type {InferredMorphism<T>} */(env => f(this.#run(env))))
+    return new Reader(env => f(this.#run(env)))
   }
 
   /**
+   * @type {Chain<T>['chain']}
    * @param {InferredMorphism<T>} f 
    * @returns {Reader<T>}
    */
@@ -50,14 +53,13 @@ export class Reader extends Algebra(Monad) {
   }
 
   /**
-   * @template R
+   * @template U
-   * @param {Reader<(v: T) => R>} other
+   * @type {Apply<T>['ap']}
-   * @returns {Reader<R>}
+   * @param {Reader<Morphism<T, U>>} other
+   * @returns {Reader<U>}
    */
   ap(other) {
     return new Reader(
-      // FIXME: type errors
-      // @ts-ignore
       env => other.run(env)(this.run(env))
     )
   }
@@ -71,9 +73,9 @@ export class Reader extends Algebra(Monad) {
   }
 
   /**
-   * @template R
+   * @template U
    * @param {T} env 
-   * @returns {R}
+   * @returns {U}
    */
   run(env) {
     return this.#run(env)

src/algebra/result.js

@@ -1,9 +1,9 @@
 import { id, Identity } from './identity.js'
-import { Algebra, Bifunctor, Foldable, Monad, Setoid } from './interfaces.js'
+import { Algebra, Alternative, Bifunctor, Foldable, Monad, Setoid } from './interfaces.js'
 
-/** @import { Apply, Chain, Functor, Bifunctor as BifunctorT, Foldable as FoldableT, Morphism, Setoid as SetoidT } from './types.js' */
+/** @import { Alt, Apply, Chain, Functor, Bifunctor as BifunctorT, Foldable as FoldableT, Morphism, Setoid as SetoidT } from './types.js' */
 
-const Interfaces = Algebra(Setoid, Monad, Foldable, Bifunctor)
+const Interfaces = Algebra(Setoid, Alternative, Monad, Foldable, Bifunctor)
 
 /**
  * @template T, E
@@ -51,6 +51,16 @@ export class Ok extends Interfaces {
     return f(this.#value)
   }
 
+  /**
+   * @template E2
+   * @type {Chain<E>['chain']}
+   * @param {Morphism<E, E2>} _f 
+   * @returns {this}
+   */
+  chainErr(_f) {
+    return this
+  }
+
   /**
    * @template U
    * @type {Functor<T>['map']}
@@ -61,6 +71,17 @@ export class Ok extends Interfaces {
     return this.chain(v => ok(f(v)))
   }
 
+  /**
+   * @template E2
+   * @type {Functor<E>['map']}
+   * @this {Result<T, E>}
+   * @param {Morphism<E, E2>} _f
+   * @returns {Result<T, E2>}
+   */
+  mapErr(_f) {
+    return /** @type {never} */ (this)
+  }
+
   /**
    * @template U
    * @type {Apply<T>['ap']}
@@ -73,6 +94,13 @@ export class Ok extends Interfaces {
     ))
   }
 
+  /**
+   * @type Alt<T>['alt']
+   */
+  alt(_b) {
+    return this
+  }
+
   /**
    * @template U
    * @borrows {Result~map}
@@ -101,6 +129,17 @@ export class Ok extends Interfaces {
   reduce(f, init) {
     return f(init, this.#value)
   }
+
+  /**
+   * @template T2, E2
+   * @type {BifunctorT<T, E>['bimap']}
+   * @param {Morphism<T, T2>} f
+   * @param {Morphism<E, E2>} _g
+   * @returns {Result<T2, E2>}
+   */
+  bimap(f, _g) {
+    return /** @type {Result<T2, E2>} */ (this.map(f))
+  }
 }
 
 /**
@@ -110,7 +149,6 @@ export class Err extends Interfaces {
   /** @type {E} */
   #value
 
-
   /**
    * @param {E} value 
    * @constructs {Err<T, E>}
@@ -120,7 +158,6 @@ export class Err extends Interfaces {
     this.#value = value
   }
 
-
   /**
    * @type {SetoidT<T>['equals']}
    * @param {Err<T, E>} other 
@@ -128,7 +165,7 @@ export class Err extends Interfaces {
    */
   equals(other) {
     if (!(other instanceof Err)) { return false }
-    const eq = other.catch(v => (id(v === this.#value)))
+    const eq = other.chainErr(v => id(v === this.#value))
     return /** @type {Identity<boolean>} */ (eq).extract()
   }
 
@@ -139,8 +176,7 @@ export class Err extends Interfaces {
   isErr() { return true }
 
   /**
-   * @template R
+   * @type {Chain<T>['chain']}
-   * @param {Morphism<T, R>} _f
    * @returns {this}
    */
   chain(_f) {
@@ -148,8 +184,17 @@ export class Err extends Interfaces {
   }
 
   /**
-   * @template R
+   * @template E2
-   * @param {Morphism<T, R>} _f
+   * @type {Chain<E>['chain']}
+   * @param {Morphism<E, Result<T, E2>>} f 
+   * @returns {Result<T, E2>}
+   */
+  chainErr(f) {
+    return f(this.#value)
+  }
+
+  /**
+   * @type {Functor<T>['map']}
    * @returns {this}
    */
   map(_f) {
@@ -157,8 +202,17 @@ export class Err extends Interfaces {
   }
 
   /**
-   * @template R
+   * @template E2
-   * @param {Morphism<T, R>} _f
+   * @type {Functor<E>['map']}
+   * @param {Morphism<E, E2>} f 
+   * @returns {Result<T, E2>}
+   */
+  mapErr(f) {
+    return /** @type {Result<T, E2>} */ (this.bimap(id, f))
+  }
+
+  /**
+   * @type {Functor<T>['map']}
    * @returns {this}
    */
   then(_f) {
@@ -167,6 +221,7 @@ export class Err extends Interfaces {
 
   /**
    * @template R
+   * @type {Functor<E>['map']}
    * @param {Morphism<E, R>} f
    * @returns {Err<T, R>}
    */
@@ -174,8 +229,16 @@ export class Err extends Interfaces {
     return new Err(f(this.#value))
   }
 
+  /**
+   * @type Alt<T>['alt']
+   */
+  alt(b) {
+    return b
+  }
+
   /**
    * @template U
+   * @type {FoldableT<T>['reduce']}
    * @param {(acc: U, value: T) => U} _f
    * @param {U} init
    * @returns {U}
@@ -183,6 +246,17 @@ export class Err extends Interfaces {
   reduce(_f, init) {
     return init
   }
+
+  /**
+   * @template T2, E2
+   * @type {BifunctorT<T, E>['bimap']}
+   * @param {Morphism<T, T2>} _f
+   * @param {Morphism<E, E2>} g
+   * @returns {Result<T2, E2>}
+   */
+  bimap(_f, g) {
+    return /** @type {Result<T2, E2>} */ (err(g(this.#value)))
+  }
 }
 
 /**

src/algebra/types.js

@@ -108,10 +108,10 @@ export default {}
 
 /**
  * @template T
- * @typedef {{
+ * @typedef {
-    ap: <U>(b: Applicative<Morphism<U, T>>) => Applicative<T>,
+    Functor<T> &
-    map: <U>(f: Morphism<T, U>) => Applicative<U>
+    Apply<T>
- * }} Applicative
+ * } Applicative
  */
 
 /**
@@ -210,5 +210,13 @@ export default {}
  * } Comonad<T>
  */
 
+/**
+ * @template A, X
+ * @typedef {
+     Functor<A> &
+     { bimap: <B, Y>(f: Morphism<A, B>, g: Morphism<X, Y>) => Bifunctor<B, Y> }
+ * } Bifunctor
+ */
+
 /** @typedef {(...args: any[]) => any} Fn */