refactor list functions

sml/week3/card.sml

@@ -31,7 +31,7 @@ val remove_card: remove_card = fn (cards, to_remove, exp) =>
             then (found, card :: acc)
             else (true orelse found, acc)
     in
-        case fold filter (false, []) cards of
+        case foldl filter (false, []) cards of
         (true, filtered) => filtered
         | (false, _) => raise exp
     end
@@ -47,10 +47,11 @@ val rec all_same_color: all_same_color = fn cards =>
 
 type sum_cards = card list -> int
 val sum_cards: sum_cards = fn cards =>
-    cards |> fold (fn card => fn sum => card_value card + sum) 0 
+    cards |> foldl (fn card => fn sum => card_value card + sum) 0 
 
+fun sum a b = a + b
 (* even shorter via partial application :) *)
-val sum_cards: sum_cards = fold (fn card => fn sum => card_value card + sum) 0 
+val sum_cards: sum_cards = foldl (card_value >> sum) 0 
 
 type score = card list * int -> int
 val score: score = fn (cards, goal) =>
@@ -83,5 +84,5 @@ val officiate: officiate = fn (deck, moves, goal) =>
         
         fun round hand = score (hand, goal)
     in
-        moves |> fold play (deck, []) |> #2 |> round 
+        moves |> foldl play (deck, []) |> #2 |> round 
     end

sml/week3/card_tests.sml

@@ -212,4 +212,11 @@ val 0 =
                 |> (fn _ => expected)
     end
 
+fun by2 a = a * 2 
+
+val () =
+    assert
+    $ map by2 [1, 2, 3] = [2, 4, 6]
+    $ "map test"
+
 val () = complete ()

sml/week3/list.sml

@@ -2,23 +2,22 @@ use "operators.sml";
 
 fun cons head tail = head :: tail
 
-fun fold f acc lst =
+fun foldl f acc lst =
     case lst of
     [] => acc
-    | head :: tail => fold f (f head acc) tail
+    | head :: tail => foldl f (f head acc) tail
 
-fun reverse lst =
-    let
-        fun f elm acc = elm :: acc
-    in
-        fold f [] lst
-    end
+fun reverse lst = foldl cons [] lst
+
+fun foldr f acc = foldl f acc >> reverse    
+
+fun map f = foldr (f >> cons) []
 
 fun filter predicate lst =
     let
         fun f elm acc = if predicate elm then elm :: acc else acc
     in
-        lst |> fold f [] |> reverse
+        foldr f [] lst
     end
 
 fun empty lst = lst = []
@@ -27,4 +26,5 @@ fun empty lst = lst = []
 fun exists elem lst =
      lst 
      |> filter (fn needle => elem = needle) 
-     |> not o empty
+     |> empty
+     |> not