ktec · January 30, 2017 22:38 · Jan 30, 2017 · Jan 30, 2017 · Jan 30, 2017 · Jan 30, 2017
diff --git a/sumFolds.js b/sumFolds.js
@@ -98,8 +98,6 @@ const mempty = Sum.empty
 // [ Sum(0), Sum(1), Sum(2), Sum(3), Sum(4) ]
 
 
-// this is wrong:
-// result = map(Sum, [1, 2, 3, 4])
 result = getSum(foldl(cons, mempty(), map(Sum, [1, 2, 3, 4])))
 
 console.log(result)
diff --git a/sumFolds.js b/sumFolds.js
@@ -5,14 +5,20 @@
 //   inspect: () => `Box(${x})`
 // })
 
-const cons = (x, xs) => [x].concat(xs)
+
+const fmap = f => xs => xs.map(x => f(x))
+
+const cons = (a, b) => a.concat(b)
+// const cons = (x, xs) => [x].concat(xs)
 const car = xs => xs[0] // head
 const cdr = xs => xs.slice(1) // tail
 const foldr = (f, v, xs) => xs.reduceRight(f, v)
 const foldl = (f, v, xs) => xs.reduce(f, v)
 const id = x => x
 
-const map = (f, xs) => foldr((acc, curr) => cons(f(curr), acc), [], xs)
+// const map = (f, xs) => foldr((acc, curr) => cons(f(curr), acc), [], xs)
+const map = (f, xs) => xs.map(f)
+
 
 const Sum = x =>
 ({
@@ -93,7 +99,7 @@ const mempty = Sum.empty
 
 
 // this is wrong:
-result = foldl(cons, mempty(), map(Sum, [1, 2, 3, 4]))
-// [ [ [ [Object], Sum(2) ], Sum(3) ], Sum(4) ]
+// result = map(Sum, [1, 2, 3, 4])
+result = getSum(foldl(cons, mempty(), map(Sum, [1, 2, 3, 4])))
 
 console.log(result)
diff --git a/sumFolds.js b/sumFolds.js
@@ -86,9 +86,14 @@ const mempty = Sum.empty
 
 // result = Sum(0).concat(Sum(1).concat(Sum(2).concat(Sum(3).concat(Sum(4)))))
 // xs = map(Sum, [1, 2, 3, 4]) // [ Sum(1), Sum(2), Sum(3), Sum(4) ]
-result = foldl(cons, mempty, map(Sum, [1, 2, 3, 4]))
+
+// this works:
+// result = cons(mempty(), [ Sum(1), Sum(2), Sum(3), Sum(4) ])
+// [ Sum(0), Sum(1), Sum(2), Sum(3), Sum(4) ]
+
 
 // this is wrong:
+result = foldl(cons, mempty(), map(Sum, [1, 2, 3, 4]))
 // [ [ [ [Object], Sum(2) ], Sum(3) ], Sum(4) ]
 
 console.log(result)
diff --git a/sumFolds.js b/sumFolds.js
@@ -0,0 +1,94 @@
+// const Box = x =>
+// ({
+//   map: f => Box(f(x)),
+//   fold: f => f(x),
+//   inspect: () => `Box(${x})`
+// })
+
+const cons = (x, xs) => [x].concat(xs)
+const car = xs => xs[0] // head
+const cdr = xs => xs.slice(1) // tail
+const foldr = (f, v, xs) => xs.reduceRight(f, v)
+const foldl = (f, v, xs) => xs.reduce(f, v)
+const id = x => x
+
+const map = (f, xs) => foldr((acc, curr) => cons(f(curr), acc), [], xs)
+
+const Sum = x =>
+({
+  x,
+  concat: ({x: y}) => Sum(x + y),
+  inspect: () => `Sum(${x})`
+})
+
+Sum.empty = () => Sum(0)
+
+const getSum = m => m.x
+
+
+// Haskell version:
+// data Fold i o = forall m . Monoid m => Fold (i -> m) (m -> o)
+
+// import Data.Monoid
+// import Prelude hiding (sum)
+//
+// import qualified Data.Foldable
+//
+// data Fold i o = forall m . Monoid m => Fold (i -> m) (m -> o)
+//
+// fold :: Fold i o :: [i] -> o
+// fold (Fold tally summarise) is = summarise ( reduce (map tally is) )
+//   where
+//     reduce = Data.Foldable.foldl' (<>) mempty
+//
+// sum :: Num n => Fold n n
+// sum = Fold Sum getSum
+//
+//
+// >>> fold sum [1..10]
+// 55
+//
+
+// -- sum = Fold Sum getSum
+// = print (fold (Fold Sum getSum) [1, 2, 3, 4])
+//
+// -- fold (Fold tally summarize) is = summarize (reduce (map tally is))
+// = print (getSum (reduce (map Sum [1, 2, 3, 4])))
+//
+// -- reduce = foldl' (<>) mempty
+// = print (getSum (foldl' (<>) mempty (map Sum [1, 2, 3, 4])))
+//
+// -- Definition of `map` (skipping a few steps)
+// = print (getSum (foldl' (<>) mempty [Sum 1, Sum 2, Sum 3, Sum 4]))
+//
+// -- `foldl' (<>) mempty` (skipping a few steps)
+// = print (getSum (mempty <> Sum 1 <> Sum 2 <> Sum 3 <> Sum 4))
+//
+// -- mempty = Sum 0
+// = print (getSum (Sum 0 <> Sum 1 <> Sum 2 <> Sum 3 <> Sum 4))
+//
+// -- Sum x <> Sum y = Sum (x + y)
+// = print (getSum (Sum 10))
+//
+// -- getSum (Sum x) = x
+// = print 10
+
+
+// const result = Sum(1).concat(Sum(2))
+const mempty = Sum.empty
+
+// = print (getSum (Sum 0 <> Sum 1 <> Sum 2 <> Sum 3 <> Sum 4))
+// result = getSum(result)
+// result = getSum(mempty.concat(Sum(1).concat(Sum(2).concat(Sum(3).concat(Sum(4))))))
+
+// map Sum [1, 2, 3, 4] # => [Sum 1, Sum 2, Sum 3, Sum 4]
+// result = foldl(cons, Sum.empty, map(Sum, [1, 2, 3, 4]))
+
+// result = Sum(0).concat(Sum(1).concat(Sum(2).concat(Sum(3).concat(Sum(4)))))
+// xs = map(Sum, [1, 2, 3, 4]) // [ Sum(1), Sum(2), Sum(3), Sum(4) ]
+result = foldl(cons, mempty, map(Sum, [1, 2, 3, 4]))
+
+// this is wrong:
+// [ [ [ [Object], Sum(2) ], Sum(3) ], Sum(4) ]
+
+console.log(result)