Family Day update

Task/Vector-products/JavaScript/vector-products-2.js

@@ -0,0 +1,140 @@
+(() => {
+    'use strict';
+
+    // dotProduct :: [a] -> [a] -> Either String a
+    const dotProduct = xs =>
+        // Dot product of two vectors of equal dimension.
+        ys => xs.length !== ys.length ? (
+            Left('Dot product not defined - vectors differ in dimension.')
+        ) : Right(sum(
+            zipWith(mul)(Array.from(xs))(Array.from(ys))
+        ));
+
+    // crossProduct :: Num a => (a, a, a) -> (a, a, a)
+    // Either String -> (a, a, a)
+    const crossProduct = xs =>
+        // Cross product of two 3D vectors.
+        ys => 3 !== xs.length || 3 !== ys.length ? (
+            Left('crossProduct is defined only for 3d vectors.')
+        ) : Right((() => {
+            const [x1, x2, x3] = Array.from(xs);
+            const [y1, y2, y3] = Array.from(ys);
+            return [
+                x2 * y3 - x3 * y2,
+                x3 * y1 - x1 * y3,
+                x1 * y2 - x2 * y1
+            ];
+        })());
+
+    // scalarTriple :: Num a => (a, a, a) -> (a, a, a) -> (a, a a) ->
+    // Either String -> a
+    const scalarTriple = q =>
+        // The scalar triple product.
+        r => s => bindLR(crossProduct(r)(s))(
+            dotProduct(q)
+        );
+
+    // vectorTriple :: Num a => (a, a, a) -> (a, a, a) -> (a, a a) ->
+    // Either String -> (a, a, a)
+    const vectorTriple = q =>
+        // The vector triple product.
+        r => s => bindLR(crossProduct(r)(s))(
+            crossProduct(q)
+        );
+
+    // main :: IO ()
+    const main = () => {
+        // TEST -------------------------------------------
+        const
+            a = [3, 4, 5],
+            b = [4, 3, 5],
+            c = [-5, -12, -13],
+            d = [3, 4, 5, 6];
+
+        console.log(unlines(
+            zipWith(k => f => k + show(
+                saturated(f)([a, b, c])
+            ))(['a . b', 'a x b', 'a . (b x c)', 'a x (b x c)'])(
+                [dotProduct, crossProduct, scalarTriple, vectorTriple]
+            )
+            .concat([
+                'a . d' + show(
+                    dotProduct(a)(d)
+                ),
+                'a . (b x d)' + show(
+                    scalarTriple(a)(b)(d)
+                )
+            ])
+        ));
+    };
+
+
+    // GENERIC FUNCTIONS ----------------------------------
+
+    // Left :: a -> Either a b
+    const Left = x => ({
+        type: 'Either',
+        Left: x
+    });
+
+    // Right :: b -> Either a b
+    const Right = x => ({
+        type: 'Either',
+        Right: x
+    });
+
+    // bindLR (>>=) :: Either a -> (a -> Either b) -> Either b
+    const bindLR = m => mf =>
+        undefined !== m.Left ? (
+            m
+        ) : mf(m.Right);
+
+    // either :: (a -> c) -> (b -> c) -> Either a b -> c
+    const either = fl => fr => e =>
+        'Either' === e.type ? (
+            undefined !== e.Left ? (
+                fl(e.Left)
+            ) : fr(e.Right)
+        ) : undefined;
+
+    // identity :: a -> a
+    const identity = x => x;
+
+    // mul (*) :: Num a => a -> a -> a
+    const mul = a => b => a * b;
+
+    // Curried function -> [Argument] -> a more saturated value
+    const saturated = f =>
+        // A curried function applied successively to
+        // a list of arguments up to, but not beyond,
+        // the point of saturation.
+        args => 0 < args.length ? (
+            args.slice(1).reduce(
+                (a, x) => 'function' !== typeof a ? (
+                    a
+                ) : a(x),
+                f(args[0])
+            )
+        ) : f;
+
+    // show :: Either String a -> String
+    const show = x =>
+        either(x => ' => ' + x)(
+            x => ' = ' + JSON.stringify(x)
+        )(x);
+
+    // sum :: [Num] -> Num
+    const sum = xs => xs.reduce((a, x) => a + x, 0);
+
+    // unlines :: [String] -> String
+    const unlines = xs => xs.join('\n');
+
+    // zipWith:: (a -> b -> c) -> [a] -> [b] -> [c]
+    const zipWith = f => xs => ys =>
+        xs.slice(
+            0, Math.min(xs.length, ys.length)
+        ).map((x, i) => f(x)(ys[i]));
+
+    // MAIN ---
+    return main();
+})();