Cartesian product of two or more lists: Difference between revisions

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@@ Line 1,114: / Line 1,114: @@
-Even more economically, we can define the cartesian product in terms of an applicative operator:
+Abstracting a little more, we can define the cartesian product quite economically in terms of a general applicative operator:
 <lang Javascript>(() => {
-    // CARTESIAN PRODUCT OF TWO LISTS -----------------------------------------
+    // CARTESIAN PRODUCT OF TWO LISTS ---------------------
     // cartesianProduct :: [a] -> [b] -> [(a, b)]
-    const cartesianProduct = (xs, ys) =>
+    const cartesianProduct = xs =>
-        ap(xs.map(x => y => [x, y]), ys);
+        ap(xs.map(Tuple));
-    // GENERIC FUNCTIONS ------------------------------------------------------
+    // GENERIC FUNCTIONS ----------------------------------
     // e.g. [(*2),(/2), sqrt] <*> [1,2,3]
@@ Line 1,134: / Line 1,134: @@
     // ap (<*>) :: [(a -> b)] -> [a] -> [b]
-    const ap = (fs, xs) => //
+    const ap = fs => xs =>
+        // The sequential application of each of a list
-        fs.reduce((a, f) => a.concat(
-            xs.reduce((a, x) => a.concat([f(x)]), [])
+        // of functions to each of a list of values.
-        ), []);
+        fs.flatMap(
+            f => xs.map(f)
+        );
+    // Tuple (,) :: a -> b -> (a, b)
-    // TEST -------------------------------------------------------------------
+    const Tuple = a => b => [a, b];
+    // TEST -----------------------------------------------
     return [
-            cartesianProduct([1, 2], [3, 4]),
+            cartesianProduct([1, 2])([3, 4]),
-            cartesianProduct([3, 4], [1, 2]),
+            cartesianProduct([3, 4])([1, 2]),
-            cartesianProduct([1, 2], []),
+            cartesianProduct([1, 2])([]),
-            cartesianProduct([], [1, 2]),
+            cartesianProduct([])([1, 2]),
         ]
         .map(JSON.stringify)