From e4e67f0427d93b3686366ffe9f14a4751690101e Mon Sep 17 00:00:00 2001
From: Eduardo Julian
Date: Wed, 2 May 2018 00:09:35 -0400
Subject: - Moved the "wrap" function into Monad, and removed Applicative from
 Monad's family tree. - Moved the Free monad to its own module.

---
 stdlib/source/lux/concurrency/frp.lux      | 12 ++---
 stdlib/source/lux/concurrency/promise.lux  | 11 ++---
 stdlib/source/lux/concurrency/stm.lux      |  8 ++--
 stdlib/source/lux/concurrency/task.lux     | 12 ++---
 stdlib/source/lux/control/applicative.lux  | 18 ++++---
 stdlib/source/lux/control/codec.lux        |  3 +-
 stdlib/source/lux/control/continuation.lux |  8 ++--
 stdlib/source/lux/control/monad.lux        | 77 ++++--------------------------
 stdlib/source/lux/control/monad/free.lux   | 66 +++++++++++++++++++++++++
 stdlib/source/lux/control/parser.lux       | 10 ++--
 stdlib/source/lux/control/reader.lux       | 26 ++++++----
 stdlib/source/lux/control/region.lux       | 14 +++---
 stdlib/source/lux/control/state.lux        | 36 +++++++++-----
 stdlib/source/lux/control/thread.lux       | 10 ++--
 stdlib/source/lux/control/writer.lux       | 34 ++++++++-----
 stdlib/source/lux/data/coll/list.lux       | 15 ++++--
 stdlib/source/lux/data/coll/sequence.lux   | 19 ++++----
 stdlib/source/lux/data/error.lux           | 14 ++++--
 stdlib/source/lux/data/identity.lux        |  7 +--
 stdlib/source/lux/data/lazy.lux            |  8 +---
 stdlib/source/lux/data/maybe.lux           | 14 ++++--
 stdlib/source/lux/io.lux                   | 16 +++----
 stdlib/source/lux/lang/type/check.lux      | 10 ++--
 stdlib/source/lux/macro.lux                | 10 ++--
 stdlib/source/lux/math/random.lux          | 10 ++--
 25 files changed, 253 insertions(+), 215 deletions(-)
 create mode 100644 stdlib/source/lux/control/monad/free.lux

(limited to 'stdlib/source')

diff --git a/stdlib/source/lux/concurrency/frp.lux b/stdlib/source/lux/concurrency/frp.lux
index a8c017a90..93d3498d4 100644
--- a/stdlib/source/lux/concurrency/frp.lux
+++ b/stdlib/source/lux/concurrency/frp.lux
@@ -106,11 +106,6 @@
 (struct: #export _ (Applicative Channel)
   (def: functor Functor<Channel>)
 
-  (def: (wrap a)
-    (let [output (channel [])]
-      (exec (io.run (publish output a))
-        output)))
-
   (def: (apply ff fa)
     (let [output (channel [])]
       (exec (io.run (listen (function (_ f)
@@ -120,7 +115,12 @@
         output))))
 
 (struct: #export _ (Monad Channel)
-  (def: applicative Applicative<Channel>)
+  (def: functor Functor<Channel>)
+
+  (def: (wrap a)
+    (let [output (channel [])]
+      (exec (io.run (publish output a))
+        output)))
 
   (def: (join mma)
     (let [output (channel [])]
diff --git a/stdlib/source/lux/concurrency/promise.lux b/stdlib/source/lux/concurrency/promise.lux
index 8b7849c93..30895098f 100644
--- a/stdlib/source/lux/concurrency/promise.lux
+++ b/stdlib/source/lux/concurrency/promise.lux
@@ -82,20 +82,19 @@
 (struct: #export _ (Applicative Promise)
   (def: functor Functor<Promise>)
 
-  (def: (wrap a)
-    (promise (#.Some a)))
-
   (def: (apply ff fa)
     (let [fb (promise #.None)]
       (exec (await (function (_ f)
                      (io (await (function (_ a) (resolve (f a) fb))
                                 fa)))
                    ff)
-        fb))
-    ))
+        fb))))
 
 (struct: #export _ (Monad Promise)
-  (def: applicative Applicative<Promise>)
+  (def: functor Functor<Promise>)
+
+  (def: (wrap a)
+    (promise (#.Some a)))
 
   (def: (join mma)
     (let [ma (promise #.None)]
diff --git a/stdlib/source/lux/concurrency/stm.lux b/stdlib/source/lux/concurrency/stm.lux
index cdafbc686..6c86af772 100644
--- a/stdlib/source/lux/concurrency/stm.lux
+++ b/stdlib/source/lux/concurrency/stm.lux
@@ -136,9 +136,6 @@
 (struct: #export _ (Applicative STM)
   (def: functor Functor<STM>)
 
-  (def: (wrap a)
-    (function (_ tx) [tx a]))
-
   (def: (apply ff fa)
     (function (_ tx)
       (let [[tx' f] (ff tx)
@@ -146,7 +143,10 @@
         [tx'' (f a)]))))
 
 (struct: #export _ (Monad STM)
-  (def: applicative Applicative<STM>)
+  (def: functor Functor<STM>)
+
+  (def: (wrap a)
+    (function (_ tx) [tx a]))
 
   (def: (join mma)
     (function (_ tx)
diff --git a/stdlib/source/lux/concurrency/task.lux b/stdlib/source/lux/concurrency/task.lux
index edb72ca6f..1ebfa181c 100644
--- a/stdlib/source/lux/concurrency/task.lux
+++ b/stdlib/source/lux/concurrency/task.lux
@@ -15,16 +15,16 @@
 
 (def: #export (fail error)
   (All [a] (-> Text (Task a)))
-  (:: P.Applicative<Promise> wrap (#E.Error error)))
+  (:: P.Monad<Promise> wrap (#E.Error error)))
 
 (def: #export (throw exception message)
   (All [e a] (-> (Exception e) e (Task a)))
-  (:: P.Applicative<Promise> wrap
+  (:: P.Monad<Promise> wrap
       (ex.throw exception message)))
 
 (def: #export (return value)
   (All [a] (-> a (Task a)))
-  (:: P.Applicative<Promise> wrap (#E.Success value)))
+  (:: P.Monad<Promise> wrap (#E.Success value)))
 
 (def: #export (try computation)
   (All [a] (-> (Task a) (Task (E.Error a))))
@@ -45,8 +45,6 @@
 (struct: #export _ (A.Applicative Task)
   (def: functor Functor<Task>)
 
-  (def: wrap return)
-
   (def: (apply ff fa)
     (do P.Monad<Promise>
       [ff' ff
@@ -57,7 +55,9 @@
               (wrap (f a)))))))
 
 (struct: #export _ (Monad Task)
-  (def: applicative Applicative<Task>)
+  (def: functor Functor<Task>)
+
+  (def: wrap return)
 
   (def: (join mma)
     (do P.Monad<Promise>
diff --git a/stdlib/source/lux/control/applicative.lux b/stdlib/source/lux/control/applicative.lux
index a827a06d3..2a926cc20 100644
--- a/stdlib/source/lux/control/applicative.lux
+++ b/stdlib/source/lux/control/applicative.lux
@@ -1,36 +1,34 @@
 (.module:
   lux
-  (// [functor #+ Functor]))
+  (// [functor #+ Functor]
+      [monad #+ Monad]))
 
 (sig: #export (Applicative f)
   {#.doc "Applicative functors."}
   (: (Functor f)
      functor)
-  (: (All [a]
-       (-> a (f a)))
-     wrap)
   (: (All [a b]
        (-> (f (-> a b)) (f a) (f b)))
      apply))
 
-(struct: #export (compose Applicative<F> Applicative<G>)
+(struct: #export (compose Monad<F> Applicative<F> Applicative<G>)
   {#.doc "Applicative functor composition."}
-  (All [F G] (-> (Applicative F) (Applicative G) (Applicative (All [a] (F (G a))))))
+  (All [F G]
+    (-> (Monad F) (Applicative F) (Applicative G)
+        (Applicative (All [a] (F (G a))))))
   
   (def: functor (functor.compose (get@ #functor Applicative<F>)
                                  (get@ #functor Applicative<G>)))
-  (def: wrap
-    (|>> (:: Applicative<G> wrap) (:: Applicative<F> wrap)))
   (def: (apply fgf fgx)
     ## TODO: Switch from this version to the one below (in comments) ASAP.
     (let [fgf' (:: Applicative<F> apply
-                   (:: Applicative<F> wrap (:: Applicative<G> apply))
+                   (:: Monad<F> wrap (:: Applicative<G> apply))
                    fgf)]
       (:: Applicative<F> apply fgf' fgx))
     ## (let [applyF (:: Applicative<F> apply)
     ##       applyG (:: Applicative<G> apply)]
     ##   ($_ applyF
-    ##       (:: Applicative<F> wrap applyG)
+    ##       (:: Monad<F> wrap applyG)
     ##       fgf
     ##       fgx))
     ))
diff --git a/stdlib/source/lux/control/codec.lux b/stdlib/source/lux/control/codec.lux
index b1b6df5d9..0630a11d1 100644
--- a/stdlib/source/lux/control/codec.lux
+++ b/stdlib/source/lux/control/codec.lux
@@ -24,5 +24,4 @@
   (def: (decode cy)
     (do e.Monad<Error>
       [by (:: Codec<c,b> decode cy)]
-      (:: Codec<b,a> decode by)))
-  )
+      (:: Codec<b,a> decode by))))
diff --git a/stdlib/source/lux/control/continuation.lux b/stdlib/source/lux/control/continuation.lux
index 35f549ee7..2a145ae5a 100644
--- a/stdlib/source/lux/control/continuation.lux
+++ b/stdlib/source/lux/control/continuation.lux
@@ -29,9 +29,6 @@
 (struct: #export Applicative<Cont> (All [o] (Applicative (All [i] (Cont i o))))
   (def: functor Functor<Cont>)
 
-  (def: (wrap value)
-    (function (_ k) (k value)))
-
   (def: (apply ff fv)
     (function (_ k)
       (|> (k (f v))
@@ -39,7 +36,10 @@
           (function (_ f)) ff))))
 
 (struct: #export Monad<Cont> (All [o] (Monad (All [i] (Cont i o))))
-  (def: applicative Applicative<Cont>)
+  (def: functor Functor<Cont>)
+
+  (def: (wrap value)
+    (function (_ k) (k value)))
 
   (def: (join ffa)
     (function (_ k)
diff --git a/stdlib/source/lux/control/monad.lux b/stdlib/source/lux/control/monad.lux
index 2e4045f3a..9a1ceb3b9 100644
--- a/stdlib/source/lux/control/monad.lux
+++ b/stdlib/source/lux/control/monad.lux
@@ -1,7 +1,6 @@
 (.module:
   lux
-  (// (functor #as F)
-      (applicative #as A)))
+  (// [functor #+ Functor]))
 
 ## [Utils]
 (def: (list/fold f init xs)
@@ -43,8 +42,11 @@
 
 ## [Signatures]
 (sig: #export (Monad m)
-  (: (A.Applicative m)
-     applicative)
+  (: (Functor m)
+     functor)
+  (: (All [a]
+       (-> a (m a)))
+     wrap)
   (: (All [a]
        (-> (m (m a)) (m a)))
      join))
@@ -64,7 +66,6 @@
       (let [g!_ (: Code [_cursor (#.Symbol ["" " _ "])])
             g!map (: Code [_cursor (#.Symbol ["" " map "])])
             g!join (: Code [_cursor (#.Symbol ["" " join "])])
-            g!apply (: Code [_cursor (#.Symbol ["" " apply "])])
             body' (list/fold (: (-> [Code Code] Code Code)
                                 (function (_ binding body')
                                   (let [[var value] binding]
@@ -80,10 +81,9 @@
         (#.Right [state (#.Cons (` ("lux case" (~ monad)
                                     {(~' @)
                                      ("lux case" (~' @)
-                                      {{#applicative {#A.functor {#F.map (~ g!map)}
-                                                      #A.wrap (~' wrap)
-                                                      #A.apply (~ g!apply)}
-                                        #join (~ g!join)}
+                                      {{#..functor {#functor.map (~ g!map)}
+                                        #..wrap (~' wrap)
+                                        #..join (~ g!join)}
                                        (~ body')})}))
                                 #.Nil)]))
       (#.Left "'do' bindings must have an even number of parts."))
@@ -144,62 +144,3 @@
     (do Monad<M>
       [a ma]
       (wrap (f a)))))
-
-## [Free Monads]
-(type: #export (Free F a)
-  {#.doc "The Free Monad."}
-  (#Pure a)
-  (#Effect (F (Free F a))))
-
-(struct: #export (Functor<Free> dsl)
-  (All [F] (-> (F.Functor F) (F.Functor (Free F))))
-  (def: (map f ea)
-    (case ea
-      (#Pure a)
-      (#Pure (f a))
-      
-      (#Effect value)
-      (#Effect (:: dsl map (map f) value)))))
-
-(struct: #export (Applicative<Free> dsl)
-  (All [F] (-> (F.Functor F) (A.Applicative (Free F))))
-  (def: functor (Functor<Free> dsl))
-
-  (def: (wrap a)
-    (#Pure a))
-  
-  (def: (apply ef ea)
-    (case [ef ea]
-      [(#Pure f) (#Pure a)]
-      (#Pure (f a))
-
-      [(#Pure f) (#Effect fa)]
-      (#Effect (:: dsl map
-                   (:: (Functor<Free> dsl) map f)
-                   fa))
-
-      [(#Effect ff) _]
-      (#Effect (:: dsl map
-                   (function (_ f) (apply f ea))
-                   ff))
-      )))
-
-(struct: #export (Monad<Free> dsl)
-  (All [F] (-> (F.Functor F) (Monad (Free F))))
-  (def: applicative (Applicative<Free> dsl))
-
-  (def: (join efefa)
-    (case efefa
-      (#Pure efa)
-      (case efa
-        (#Pure a)
-        (#Pure a)
-
-        (#Effect fa)
-        (#Effect fa))
-      
-      (#Effect fefa)
-      (#Effect (:: dsl map
-                   (:: (Monad<Free> dsl) join)
-                   fefa))
-      )))
diff --git a/stdlib/source/lux/control/monad/free.lux b/stdlib/source/lux/control/monad/free.lux
new file mode 100644
index 000000000..7a41b3e9f
--- /dev/null
+++ b/stdlib/source/lux/control/monad/free.lux
@@ -0,0 +1,66 @@
+(.module:
+  lux
+  (/// [functor #+ Functor]
+       [applicative #+ Applicative]
+       [monad #+ Monad]))
+
+(type: #export (Free F a)
+  {#.doc "The Free Monad."}
+  (#Pure a)
+  (#Effect (F (Free F a))))
+
+(struct: #export (Functor<Free> dsl)
+  (All [F] (-> (Functor F) (Functor (Free F))))
+  
+  (def: (map f ea)
+    (case ea
+      (#Pure a)
+      (#Pure (f a))
+      
+      (#Effect value)
+      (#Effect (:: dsl map (map f) value)))))
+
+(struct: #export (Applicative<Free> dsl)
+  (All [F] (-> (Functor F) (Applicative (Free F))))
+  
+  (def: functor (Functor<Free> dsl))
+
+  (def: (apply ef ea)
+    (case [ef ea]
+      [(#Pure f) (#Pure a)]
+      (#Pure (f a))
+
+      [(#Pure f) (#Effect fa)]
+      (#Effect (:: dsl map
+                   (:: (Functor<Free> dsl) map f)
+                   fa))
+
+      [(#Effect ff) _]
+      (#Effect (:: dsl map
+                   (function (_ f) (apply f ea))
+                   ff))
+      )))
+
+(struct: #export (Monad<Free> dsl)
+  (All [F] (-> (Functor F) (Monad (Free F))))
+
+  (def: functor (Functor<Free> dsl))
+
+  (def: (wrap a)
+    (#Pure a))
+
+  (def: (join efefa)
+    (case efefa
+      (#Pure efa)
+      (case efa
+        (#Pure a)
+        (#Pure a)
+
+        (#Effect fa)
+        (#Effect fa))
+      
+      (#Effect fefa)
+      (#Effect (:: dsl map
+                   (:: (Monad<Free> dsl) join)
+                   fefa))
+      )))
diff --git a/stdlib/source/lux/control/parser.lux b/stdlib/source/lux/control/parser.lux
index c33c17d72..c4aaf35e3 100644
--- a/stdlib/source/lux/control/parser.lux
+++ b/stdlib/source/lux/control/parser.lux
@@ -26,10 +26,6 @@
 (struct: #export Applicative<Parser> (All [s] (Applicative (Parser s)))
   (def: functor Functor<Parser>)
 
-  (def: (wrap x)
-    (function (_ input)
-      (#e.Success [input x])))
-
   (def: (apply ff fa)
     (function (_ input)
       (case (ff input)
@@ -45,7 +41,11 @@
         (#e.Error msg)))))
 
 (struct: #export Monad<Parser> (All [s] (Monad (Parser s)))
-  (def: applicative Applicative<Parser>)
+  (def: functor Functor<Parser>)
+
+  (def: (wrap x)
+    (function (_ input)
+      (#e.Success [input x])))
 
   (def: (join mma)
     (function (_ input)
diff --git a/stdlib/source/lux/control/reader.lux b/stdlib/source/lux/control/reader.lux
index ed974ee46..fc2d6540b 100644
--- a/stdlib/source/lux/control/reader.lux
+++ b/stdlib/source/lux/control/reader.lux
@@ -10,23 +10,29 @@
   (-> r a))
 
 ## [Structures]
-(struct: #export Functor<Reader> (All [r] (F.Functor (Reader r)))
+(struct: #export Functor<Reader>
+  (All [r] (F.Functor (Reader r)))
+  
   (def: (map f fa)
     (function (_ env)
       (f (fa env)))))
 
-(struct: #export Applicative<Reader> (All [r] (A.Applicative (Reader r)))
+(struct: #export Applicative<Reader>
+  (All [r] (A.Applicative (Reader r)))
+  
   (def: functor Functor<Reader>)
 
-  (def: (wrap x)
-    (function (_ env) x))
-
   (def: (apply ff fa)
     (function (_ env)
       ((ff env) (fa env)))))
 
-(struct: #export Monad<Reader> (All [r] (Monad (Reader r)))
-  (def: applicative Applicative<Reader>)
+(struct: #export Monad<Reader>
+  (All [r] (Monad (Reader r)))
+  
+  (def: functor Functor<Reader>)
+
+  (def: (wrap x)
+    (function (_ env) x))
 
   (def: (join mma)
     (function (_ env)
@@ -50,7 +56,11 @@
 (struct: #export (ReaderT Monad<M>)
   {#.doc "Monad transformer for Reader."}
   (All [M] (-> (Monad M) (All [e] (Monad (All [a] (Reader e (M a)))))))
-  (def: applicative (A.compose Applicative<Reader> (get@ #monad.applicative Monad<M>)))
+
+  (def: functor (F.compose Functor<Reader> (get@ #monad.functor Monad<M>)))
+
+  (def: wrap (|>> (:: Monad<M> wrap) (:: Monad<Reader> wrap)))
+  
   (def: (join eMeMa)
     (function (_ env)
       (do Monad<M>
diff --git a/stdlib/source/lux/control/region.lux b/stdlib/source/lux/control/region.lux
index 83afbbdc6..1e2b4a47b 100644
--- a/stdlib/source/lux/control/region.lux
+++ b/stdlib/source/lux/control/region.lux
@@ -86,12 +86,7 @@
         (All [r] (Applicative (Region r m)))))
 
   (def: functor
-    (Functor<Region> (get@ [#monad.applicative #applicative.functor]
-                           Monad<m>)))
-
-  (def: (wrap value)
-    (function (_ [region cleaners])
-      (:: Monad<m> wrap [cleaners (#e.Success value)])))
+    (Functor<Region> (get@ #monad.functor Monad<m>)))
 
   (def: (apply ff fa)
     (function (_ [region cleaners])
@@ -111,7 +106,12 @@
     (-> (Monad m)
         (All [r] (Monad (Region r m)))))
 
-  (def: applicative (Applicative<Region> Monad<m>))
+  (def: functor
+    (Functor<Region> (get@ #monad.functor Monad<m>)))
+
+  (def: (wrap value)
+    (function (_ [region cleaners])
+      (:: Monad<m> wrap [cleaners (#e.Success value)])))
 
   (def: (join ffa)
     (function (_ [region cleaners])
diff --git a/stdlib/source/lux/control/state.lux b/stdlib/source/lux/control/state.lux
index cf65ae6a7..86813bf69 100644
--- a/stdlib/source/lux/control/state.lux
+++ b/stdlib/source/lux/control/state.lux
@@ -10,27 +10,33 @@
   (-> s [s a]))
 
 ## [Structures]
-(struct: #export Functor<State> (All [s] (F.Functor (State s)))
+(struct: #export Functor<State>
+  (All [s] (F.Functor (State s)))
+  
   (def: (map f ma)
     (function (_ state)
       (let [[state' a] (ma state)]
         [state' (f a)]))))
 
-(struct: #export Applicative<State> (All [s] (A.Applicative (State s)))
+(struct: #export Applicative<State>
+  (All [s] (A.Applicative (State s)))
+  
   (def: functor Functor<State>)
 
-  (def: (wrap a)
-    (function (_ state)
-      [state a]))
-
   (def: (apply ff fa)
     (function (_ state)
       (let [[state' f] (ff state)
             [state'' a] (fa state')]
         [state'' (f a)]))))
 
-(struct: #export Monad<State> (All [s] (Monad (State s)))
-  (def: applicative Applicative<State>)
+(struct: #export Monad<State>
+  (All [s] (Monad (State s)))
+  
+  (def: functor Functor<State>)
+
+  (def: (wrap a)
+    (function (_ state)
+      [state a]))
 
   (def: (join mma)
     (function (_ state)
@@ -76,6 +82,7 @@
 
 (struct: (Functor<StateT> Functor<M>)
   (All [M s] (-> (F.Functor M) (F.Functor (All [a] (-> s (M [s a]))))))
+  
   (def: (map f sfa)
     (function (_ state)
       (:: Functor<M> map (function (_ [s a]) [s (f a)])
@@ -83,12 +90,9 @@
 
 (struct: (Applicative<StateT> Monad<M>)
   (All [M s] (-> (Monad M) (A.Applicative (All [a] (-> s (M [s a]))))))
+  
   (def: functor (Functor<StateT> (:: Monad<M> functor)))
 
-  (def: (wrap a)
-    (function (_ state)
-      (:: Monad<M> wrap [state a])))
-
   (def: (apply sFf sFa)
     (function (_ state)
       (do Monad<M>
@@ -108,7 +112,13 @@
 (struct: #export (StateT Monad<M>)
   {#.doc "A monad transformer to create composite stateful computations."}
   (All [M s] (-> (Monad M) (Monad (State' M s))))
-  (def: applicative (Applicative<StateT> Monad<M>))
+
+  (def: functor (Functor<StateT> (:: Monad<M> functor)))
+
+  (def: (wrap a)
+    (function (_ state)
+      (:: Monad<M> wrap [state a])))
+  
   (def: (join sMsMa)
     (function (_ state)
       (do Monad<M>
diff --git a/stdlib/source/lux/control/thread.lux b/stdlib/source/lux/control/thread.lux
index 84bc33501..9848ed5bc 100644
--- a/stdlib/source/lux/control/thread.lux
+++ b/stdlib/source/lux/control/thread.lux
@@ -46,10 +46,6 @@
 
   (def: functor Functor<Thread>)
 
-  (def: (wrap value)
-    (function (_ !)
-      value))
-  
   (def: (apply ff fa)
     (function (_ !)
       ((ff !) (fa !)))))
@@ -57,7 +53,11 @@
 (struct: #export Monad<Thread>
   (All [!] (Monad (Thread !)))
 
-  (def: applicative Applicative<Thread>)
+  (def: functor Functor<Thread>)
+
+  (def: (wrap value)
+    (function (_ !)
+      value))
 
   (def: (join ffa)
     (function (_ !)
diff --git a/stdlib/source/lux/control/writer.lux b/stdlib/source/lux/control/writer.lux
index 7f8299100..5022620c8 100644
--- a/stdlib/source/lux/control/writer.lux
+++ b/stdlib/source/lux/control/writer.lux
@@ -10,27 +10,33 @@
   {#log l
    #value a})
 
-(struct: #export Functor<Writer> (All [l]
-                                   (F.Functor (Writer l)))
+(struct: #export Functor<Writer>
+  (All [l]
+    (F.Functor (Writer l)))
+  
   (def: (map f fa)
     (let [[log datum] fa]
       [log (f datum)])))
 
-(struct: #export (Applicative<Writer> mon) (All [l]
-                                             (-> (Monoid l) (A.Applicative (Writer l))))
+(struct: #export (Applicative<Writer> mon)
+  (All [l]
+    (-> (Monoid l) (A.Applicative (Writer l))))
+  
   (def: functor Functor<Writer>)
 
-  (def: (wrap x)
-    [(:: mon identity) x])
-
   (def: (apply ff fa)
     (let [[log1 f] ff
           [log2 a] fa]
       [(:: mon compose log1 log2) (f a)])))
 
-(struct: #export (Monad<Writer> mon) (All [l]
-                                       (-> (Monoid l) (Monad (Writer l))))
-  (def: applicative (Applicative<Writer> mon))
+(struct: #export (Monad<Writer> mon)
+  (All [l]
+    (-> (Monoid l) (Monad (Writer l))))
+  
+  (def: functor Functor<Writer>)
+
+  (def: (wrap x)
+    [(:: mon identity) x])
 
   (def: (join mma)
     (let [[log1 [log2 a]] mma]
@@ -43,7 +49,13 @@
 
 (struct: #export (WriterT Monoid<l> Monad<M>)
   (All [l M] (-> (Monoid l) (Monad M) (Monad (All [a] (M (Writer l a))))))
-  (def: applicative (A.compose (get@ #monad.applicative Monad<M>) (Applicative<Writer> Monoid<l>)))
+
+  (def: functor (F.compose (get@ #monad.functor Monad<M>) Functor<Writer>))
+
+  (def: wrap
+    (let [monad (Monad<Writer> Monoid<l>)]
+      (|>> (:: monad wrap) (:: Monad<M> wrap))))
+  
   (def: (join MlMla)
     (do Monad<M>
       [## TODO: Remove once new-luxc is the standard compiler.
diff --git a/stdlib/source/lux/data/coll/list.lux b/stdlib/source/lux/data/coll/list.lux
index 943743018..e558c592e 100644
--- a/stdlib/source/lux/data/coll/list.lux
+++ b/stdlib/source/lux/data/coll/list.lux
@@ -271,9 +271,6 @@
 (struct: #export _ (Applicative List)
   (def: functor Functor<List>)
 
-  (def: (wrap a)
-    (#.Cons a #.Nil))
-
   (def: (apply ff fa)
     (case ff
       #.Nil
@@ -283,7 +280,10 @@
       (compose (map f fa) (apply ff' fa)))))
 
 (struct: #export _ (Monad List)
-  (def: applicative Applicative<List>)
+  (def: functor Functor<List>)
+
+  (def: (wrap a)
+    (#.Cons a #.Nil))
 
   (def: join (|>> reverse (fold compose identity))))
 
@@ -478,10 +478,15 @@
 
 (struct: #export (ListT Monad<M>)
   (All [M] (-> (Monad M) (Monad (All [a] (M (List a))))))
-  (def: applicative (applicative.compose (get@ #monad.applicative Monad<M>) Applicative<List>))
+
+  (def: functor (functor.compose (get@ #monad.functor Monad<M>) Functor<List>))
+
+  (def: wrap (|>> (:: Monad<List> wrap) (:: Monad<M> wrap)))
+  
   (def: (join MlMla)
     (do Monad<M>
       [lMla MlMla
+       ## TODO: Remove this version ASAP and use one below.
        lla (: (($ +0) (List (List ($ +1))))
               (monad.seq @ lMla))
        ## lla (monad.seq @ lMla)
diff --git a/stdlib/source/lux/data/coll/sequence.lux b/stdlib/source/lux/data/coll/sequence.lux
index b109e460c..0c3156f7f 100644
--- a/stdlib/source/lux/data/coll/sequence.lux
+++ b/stdlib/source/lux/data/coll/sequence.lux
@@ -204,10 +204,10 @@
             ## If so, a brand-new root must be established, that is
             ## 1-level taller.
             (|> vec
-                (set@ #root (|> ## (new-hierarchy [])
-                                ## TODO: Remove once new-luxc becomes the standard compiler.
-                                (: (Hierarchy ($ +0))
+                (set@ #root (|> (: (Hierarchy ($ +0))
                                    (new-hierarchy []))
+                                ## TODO: Remove version above once new-luxc becomes the standard compiler.
+                                ## (new-hierarchy [])
                                 (array.write +0 (#Hierarchy (get@ #root vec)))
                                 (array.write +1 (new-path (get@ #level vec) (get@ #tail vec)))))
                 (update@ #level level-up))
@@ -413,26 +413,23 @@
 (struct: #export _ (Applicative Sequence)
   (def: functor Functor<Sequence>)
 
-  (def: (wrap x)
-    (sequence x))
-  
   (def: (apply ff fa)
     (let [(^open) Functor<Sequence>
           (^open) Fold<Sequence>
           (^open) Monoid<Sequence>
           results (map (function (_ f) (map f fa))
                        ff)]
-      (fold compose identity results)))
-  )
+      (fold compose identity results))))
 
 (struct: #export _ (Monad Sequence)
-  (def: applicative Applicative<Sequence>)
+  (def: functor Functor<Sequence>)
+
+  (def: wrap (|>> sequence))
 
   (def: join
     (let [(^open) Fold<Sequence>
           (^open) Monoid<Sequence>]
-      (fold (function (_ post pre) (compose pre post)) identity)))
-  )
+      (fold (function (_ post pre) (compose pre post)) identity))))
 
 (def: #export (reverse xs)
   (All [a] (-> (Sequence a) (Sequence a)))
diff --git a/stdlib/source/lux/data/error.lux b/stdlib/source/lux/data/error.lux
index b619dc1ad..64cb5618e 100644
--- a/stdlib/source/lux/data/error.lux
+++ b/stdlib/source/lux/data/error.lux
@@ -19,9 +19,6 @@
 (struct: #export _ (A.Applicative Error)
   (def: functor Functor<Error>)
 
-  (def: (wrap a)
-    (#Success a))
-
   (def: (apply ff fa)
     (case ff
       (#Success f)
@@ -37,7 +34,10 @@
     ))
 
 (struct: #export _ (Monad Error)
-  (def: applicative Applicative<Error>)
+  (def: functor Functor<Error>)
+
+  (def: (wrap a)
+    (#Success a))
 
   (def: (join mma)
     (case mma
@@ -46,7 +46,11 @@
 
 (struct: #export (ErrorT Monad<M>)
   (All [M] (-> (Monad M) (Monad (All [a] (M (Error a))))))
-  (def: applicative (A.compose (get@ #M.applicative Monad<M>) Applicative<Error>))
+  
+  (def: functor (F.compose (get@ #M.functor Monad<M>) Functor<Error>))
+
+  (def: wrap (|>> (:: Monad<Error> wrap) (:: Monad<M> wrap)))
+  
   (def: (join MeMea)
     (do Monad<M>
       [eMea MeMea]
diff --git a/stdlib/source/lux/data/identity.lux b/stdlib/source/lux/data/identity.lux
index 919c2385f..51198d11c 100644
--- a/stdlib/source/lux/data/identity.lux
+++ b/stdlib/source/lux/data/identity.lux
@@ -15,15 +15,12 @@
 
 (struct: #export _ (A.Applicative Identity)
   (def: functor Functor<Identity>)
-
-  (def: wrap id)
-
   (def: (apply ff fa)
     (ff fa)))
 
 (struct: #export _ (Monad Identity)
-  (def: applicative Applicative<Identity>)
-  
+  (def: functor Functor<Identity>)
+  (def: wrap id)
   (def: join id))
 
 (struct: #export _ (CoMonad Identity)
diff --git a/stdlib/source/lux/data/lazy.lux b/stdlib/source/lux/data/lazy.lux
index 8b4a75d1d..adcc1234e 100644
--- a/stdlib/source/lux/data/lazy.lux
+++ b/stdlib/source/lux/data/lazy.lux
@@ -39,14 +39,10 @@
 
 (struct: #export _ (Applicative Lazy)
   (def: functor Functor<Lazy>)
-
-  (def: (wrap a)
-    (freeze a))
-
   (def: (apply ff fa)
     (freeze ((thaw ff) (thaw fa)))))
 
 (struct: #export _ (Monad Lazy)
-  (def: applicative Applicative<Lazy>)
-
+  (def: functor Functor<Lazy>)
+  (def: wrap (|>> freeze))
   (def: join thaw))
diff --git a/stdlib/source/lux/data/maybe.lux b/stdlib/source/lux/data/maybe.lux
index 02d109981..e42af460f 100644
--- a/stdlib/source/lux/data/maybe.lux
+++ b/stdlib/source/lux/data/maybe.lux
@@ -28,9 +28,6 @@
 (struct: #export _ (A.Applicative Maybe)
   (def: functor Functor<Maybe>)
 
-  (def: (wrap x)
-    (#.Some x))
-
   (def: (apply ff fa)
     (case [ff fa]
       [(#.Some f) (#.Some a)]
@@ -40,7 +37,10 @@
       #.None)))
 
 (struct: #export _ (Monad Maybe)
-  (def: applicative Applicative<Maybe>)
+  (def: functor Functor<Maybe>)
+
+  (def: (wrap x)
+    (#.Some x))
 
   (def: (join mma)
     (case mma
@@ -61,7 +61,11 @@
 
 (struct: #export (MaybeT Monad<M>)
   (All [M] (-> (Monad M) (Monad (All [a] (M (Maybe a))))))
-  (def: applicative (A.compose (get@ #monad.applicative Monad<M>) Applicative<Maybe>))
+
+  (def: functor (F.compose (get@ #monad.functor Monad<M>) Functor<Maybe>))
+
+  (def: wrap (|>> (:: Monad<Maybe> wrap) (:: Monad<M> wrap)))
+  
   (def: (join MmMma)
     (do Monad<M>
       [mMma MmMma]
diff --git a/stdlib/source/lux/io.lux b/stdlib/source/lux/io.lux
index ca9d7b608..6e038aa7c 100644
--- a/stdlib/source/lux/io.lux
+++ b/stdlib/source/lux/io.lux
@@ -32,14 +32,14 @@
 (struct: #export _ (Applicative IO)
   (def: functor Functor<IO>)
 
-  (def: (wrap x)
-    (io x))
-
   (def: (apply ff fa)
     (io ((ff (:! Void [])) (fa (:! Void []))))))
 
 (struct: #export _ (Monad IO)
-  (def: applicative Applicative<IO>)
+  (def: functor Functor<IO>)
+
+  (def: (wrap x)
+    (io x))
   
   (def: (join mma)
     (io ((mma (:! Void [])) (:! Void [])))))
@@ -60,14 +60,14 @@
 (struct: #export _ (Applicative Process)
   (def: functor Functor<Process>)
 
-  (def: (wrap x)
-    (io (:: e.Applicative<Error> wrap x)))
-
   (def: (apply ff fa)
     (io (:: e.Applicative<Error> apply (run ff) (run fa)))))
 
 (struct: #export _ (Monad Process)
-  (def: applicative Applicative<Process>)
+  (def: functor Functor<Process>)
+
+  (def: (wrap x)
+    (io (:: e.Monad<Error> wrap x)))
   
   (def: (join mma)
     (case (run mma)
diff --git a/stdlib/source/lux/lang/type/check.lux b/stdlib/source/lux/lang/type/check.lux
index 09af682ca..cea574d0c 100644
--- a/stdlib/source/lux/lang/type/check.lux
+++ b/stdlib/source/lux/lang/type/check.lux
@@ -60,10 +60,6 @@
 (struct: #export _ (Applicative Check)
   (def: functor Functor<Check>)
 
-  (def: (wrap x)
-    (function (_ context)
-      (#e.Success [context x])))
-
   (def: (apply ff fa)
     (function (_ context)
       (case (ff context)
@@ -81,7 +77,11 @@
   )
 
 (struct: #export _ (Monad Check)
-  (def: applicative Applicative<Check>)
+  (def: functor Functor<Check>)
+
+  (def: (wrap x)
+    (function (_ context)
+      (#e.Success [context x])))
 
   (def: (join ffa)
     (function (_ context)
diff --git a/stdlib/source/lux/macro.lux b/stdlib/source/lux/macro.lux
index 0e2c60959..4c56e9184 100644
--- a/stdlib/source/lux/macro.lux
+++ b/stdlib/source/lux/macro.lux
@@ -29,10 +29,6 @@
 (struct: #export _ (Applicative Meta)
   (def: functor Functor<Meta>)
 
-  (def: (wrap x)
-    (function (_ compiler)
-      (#e.Success [compiler x])))
-
   (def: (apply ff fa)
     (function (_ compiler)
       (case (ff compiler)
@@ -48,7 +44,11 @@
         (#e.Error msg)))))
 
 (struct: #export _ (Monad Meta)
-  (def: applicative Applicative<Meta>)
+  (def: functor Functor<Meta>)
+
+  (def: (wrap x)
+    (function (_ compiler)
+      (#e.Success [compiler x])))
   
   (def: (join mma)
     (function (_ compiler)
diff --git a/stdlib/source/lux/math/random.lux b/stdlib/source/lux/math/random.lux
index 60f9b729d..2b7c6598d 100644
--- a/stdlib/source/lux/math/random.lux
+++ b/stdlib/source/lux/math/random.lux
@@ -37,10 +37,6 @@
 (struct: #export _ (Applicative Random)
   (def: functor Functor<Random>)
 
-  (def: (wrap a)
-    (function (_ state)
-      [state a]))
-
   (def: (apply ff fa)
     (function (_ state)
       (let [[state' f] (ff state)
@@ -48,7 +44,11 @@
         [state'' (f a)]))))
 
 (struct: #export _ (Monad Random)
-  (def: applicative Applicative<Random>)
+  (def: functor Functor<Random>)
+
+  (def: (wrap a)
+    (function (_ state)
+      [state a]))
 
   (def: (join ffa)
     (function (_ state)
-- 
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