lib/tests: add more tests for fold functions

Also the invocation of tests is documented.

lib/tests.nix

@@ -1,3 +1,6 @@
+# to run these tests:
+# nix-instantiate --eval --strict nixpkgs/lib/tests.nix
+# if the resulting list is empty, all tests passed
 let inherit (builtins) add; in
 with import ./default.nix;
 
@@ -45,10 +48,34 @@ runTests {
     expected = ["b" "c"];
   };
 
-  testFold = {
-    expr = fold (builtins.add) 0 (range 0 100);
-    expected = 5050;
-  };
+  testFold =
+    let
+      f = op: fold: fold op 0 (range 0 100);
+      # fold with associative operator
+      assoc = f builtins.add;
+      # fold with non-associative operator
+      nonAssoc = f builtins.sub;
+    in {
+      expr = {
+        assocRight = assoc foldr;
+        # right fold with assoc operator is same as left fold
+        assocRightIsLeft = assoc foldr == assoc foldl;
+        nonAssocRight = nonAssoc foldr;
+        nonAssocLeft = nonAssoc foldl;
+        # with non-assoc operator the fold results are not the same
+        nonAssocRightIsNotLeft = nonAssoc foldl != nonAssoc foldr;
+        # fold is an alias for foldr
+        foldIsRight = nonAssoc fold == nonAssoc foldr;
+      };
+      expected = {
+        assocRight = 5050;
+        assocRightIsLeft = true;
+        nonAssocRight = 50;
+        nonAssocLeft = (-5050);
+        nonAssocRightIsNotLeft = true;
+        foldIsRight = true;
+      };
+    };
 
   testTake = testAllTrue [
     ([] == (take 0 [  1 2 3 ]))