diff --git a/src/Data/NumIdr/Array/Array.idr b/src/Data/NumIdr/Array/Array.idr
index 8b55505..e9ec0d9 100644
--- a/src/Data/NumIdr/Array/Array.idr
+++ b/src/Data/NumIdr/Array/Array.idr
@@ -13,6 +13,8 @@ import Data.NumIdr.Array.Coords
 %default total
 
 
+||| The type of an array.
+|||
 ||| Arrays are the central data structure of NumIdr. They are an `n`-dimensional
 ||| grid of values, where `n` is a value known as the *rank* of the array. Arrays
 ||| of rank 0 are single values, arrays of rank 1 are vectors, and arrays of rank
@@ -23,22 +25,18 @@ import Data.NumIdr.Array.Coords
 ||| array's total size.
 |||
 ||| Arrays are indexed by row first, as in the standard mathematical notation for
-||| matrices. This is independent of the actual order in which they are stored; the
-||| default order is row-major, but this is configurable.
+||| matrices.
 |||
 ||| @ rk The rank of the array
 ||| @ s The shape of the array
 ||| @ a The type of the array's elements
 export
 data Array : (s : Vect rk Nat) -> (a : Type) -> Type where
-  ||| Internally, arrays are stored using Idris's primitive array type. This is
-  ||| stored along with the array's shape, and a vector of values called the
-  ||| *strides*, which determine how indexes into the internal array should be
-  ||| performed. This is how the order of the array is configurable.
+  ||| Internally, arrays are stored via one of a handful of representations.
   |||
-  ||| @ ord The order of the elements of the array
-  ||| @ sts The strides of the array
   ||| @ s   The shape of the array
+  ||| @ rep The internal representation of the array
+  ||| @ rc  A witness that the element type satisfies the representation constraint
   MkArray : (rep : Rep) -> (rc : RepConstraint rep a) => (s : Vect rk Nat) ->
                PrimArray rep s a @{rc} -> Array s a
 
@@ -56,24 +54,27 @@ unsafeMkArray = MkArray
 --------------------------------------------------------------------------------
 
 
-||| The shape of the array
+||| The shape of the array.
 export
 shape : Array {rk} s a -> Vect rk Nat
 shape (MkArray _ s _) = s
 
-||| The rank of the array
+||| The rank of the array.
 export
 rank : Array s a -> Nat
 rank = length . shape
 
+||| The internal representation of the array.
 export
 getRep : Array s a -> Rep
 getRep (MkArray rep _ _) = rep
 
+||| The representation constraint of the array.
 export
 getRepC : (arr : Array s a) -> RepConstraint (getRep arr) a
 getRepC (MkArray _ @{rc} _ _) = rc
 
+||| Extract the primitive backend array.
 export
 getPrim : (arr : Array s a) -> PrimArray (getRep arr) s a @{getRepC arr}
 getPrim (MkArray _ _ pr) = pr
@@ -340,14 +341,26 @@ arr !#.. is = indexRangeUnsafe is arr
 -- Operations on arrays
 --------------------------------------------------------------------------------
 
+||| Map a function over an array.
+|||
+||| You should almost always use `map` instead; only use this function if you
+||| know what you are doing!
 export
 mapArray' : (a -> a) -> Array s a -> Array s a
 mapArray' f (MkArray rep _ arr) = MkArray rep _ (mapPrim f arr)
 
+||| Map a function over an array.
+|||
+||| You should almost always use `map` instead; only use this function if you
+||| know what you are doing!
 export
 mapArray : (a -> b) -> (arr : Array s a) -> RepConstraint (getRep arr) b => Array s b
 mapArray f (MkArray rep _ arr) @{rc} = MkArray rep @{rc} _ (mapPrim f arr)
 
+||| Combine two arrays of the same element type using a binary function.
+|||
+||| You should almost always use `zipWith` instead; only use this function if
+||| you know what you are doing!
 export
 zipWithArray' : (a -> a -> a) -> Array s a -> Array s a -> Array s a
 zipWithArray' {s} f a b with (viewShape a)
@@ -356,6 +369,10 @@ zipWithArray' {s} f a b with (viewShape a)
                           $ PrimArray.fromFunctionNB @{mergeRepConstraint (getRepC a) (getRepC b)} _
                               (\is => f (a !# is) (b !# is))
 
+||| Combine two arrays using a binary function.
+|||
+||| You should almost always use `zipWith` instead; only use this function if
+||| you know what you are doing!
 export
 zipWithArray : (a -> b -> c) -> (arr : Array s a) -> (arr' : Array s b) ->
                 RepConstraint (mergeRep (getRep arr) (getRep arr')) c => Array s c
@@ -446,6 +463,7 @@ stack axis arrs = rewrite sym (lengthCorrect arrs) in
     getAxisInd FZ (i :: is) = (i, is)
     getAxisInd {s=_::_} (FS ax) (i :: is) = mapSnd (i::) (getAxisInd ax is)
 
+||| Join the axes of a nested array structure to form a single array.
 export
 joinAxes : {s' : _} -> Array s (Array s' a) -> Array (s ++ s') a
 joinAxes {s} arr with (viewShape arr)
@@ -460,6 +478,7 @@ joinAxes {s} arr with (viewShape arr)
     dropUpTo (x::xs) (y::ys) = dropUpTo xs ys
 
 
+||| Split an array into a nested array structure along the specified axes.
 export
 splitAxes : (rk : Nat) -> {0 rk' : Nat} -> {s : _} ->
             Array {rk=rk+rk'} s a -> Array (take {m=rk'} rk s) (Array (drop {m=rk'} rk s) a)
@@ -577,7 +596,8 @@ export
 
 
 -- Foldable and Traversable operate on the primitive array directly. This means
--- that their operation is dependent on the order of the array.
+-- that their operation is dependent on the internal representation of the
+-- array.
 
 export
 Foldable (Array s) where
diff --git a/src/Data/NumIdr/Array/Rep.idr b/src/Data/NumIdr/Array/Rep.idr
index 3410d13..c673c14 100644
--- a/src/Data/NumIdr/Array/Rep.idr
+++ b/src/Data/NumIdr/Array/Rep.idr
@@ -12,10 +12,10 @@ import Data.Buffer
 --------------------------------------------------------------------------------
 
 
-||| An order is an abstract representation of the way in which array
-||| elements are stored in memory. Orders are used to calculate strides,
-||| which provide a method of converting an array coordinate into a linear
-||| memory location.
+||| An order is an abstract representation of the way in which contiguous array
+||| elements are stored in memory. Orders are used to calculate strides, which
+||| provide a method of converting an array coordinate into a linear memory
+||| location.
 public export
 data Order : Type where
   ||| C-like order, or contiguous order. This order stores elements in a
@@ -49,24 +49,57 @@ calcStrides FOrder v@(_::_)  = scanl (*) 1 $ init v
 --------------------------------------------------------------------------------
 
 
+||| An internal representation of an array.
+|||
+||| Each array internally stores its values based on one of these
+||| representations.
 public export
 data Rep : Type where
-  Bytes : Order -> Rep
-  Boxed : Order -> Rep
+  ||| Byte-buffer array representation.
+  |||
+  ||| This representations stores elements by converting them into byte values
+  ||| storing them in a `Buffer`. Use of this representation is only valid if
+  ||| the element type implements `ByteRep`.
+  |||
+  ||| @ o The order to store array elements in
+  Bytes : (o : Order) -> Rep
+
+  ||| Boxed array representation.
+  |||
+  ||| This representation uses a boxed array type to store its elements.
+  |||
+  ||| @ o The order to store array elements in
+  Boxed : (o : Order) -> Rep
+
+  ||| Linked list array representation.
+  |||
+  ||| This representation uses Idris's standard linked list types to store its
+  ||| elements.
   Linked : Rep
+
+  ||| Delayed/Lazy array representation.
+  |||
+  ||| This representation delays the computation of the array's elements, which
+  ||| may be useful in writing efficient algorithms.
   Delayed : Rep
 
 %name Rep rep
 
 
+||| An alias for the representation `Boxed COrder`, the C-like boxed array
+||| representation.
+|||
+||| This representation is the default for all newly created arrays.
 public export
 B : Rep
 B = Boxed COrder
 
+||| An alias for the representation `Linked COrder`.
 public export
 L : Rep
 L = Linked
 
+||| An alias for the representation `Delayed`.
 public export
 D : Rep
 D = Delayed
@@ -80,6 +113,8 @@ Eq Rep where
   Delayed == Delayed = True
   _ == _ = False
 
+||| A predicate on representations for those that store their elements
+||| linearly.
 public export
 data LinearRep : Rep -> Type where
   BytesIsL : LinearRep (Bytes o)
@@ -140,11 +175,19 @@ forceRepNCCorrect Delayed = DelayedNC
 --------------------------------------------------------------------------------
 
 
+||| An interface for elements that can be converted into raw bytes.
+|||
+||| An implementation of this interface is required to use the `Bytes` array
+||| representation.
 public export
 interface ByteRep a where
+  ||| The number of bytes used to store each value.
   bytes : Nat
 
+  ||| Convert a value into a list of bytes.
   toBytes : a -> Vect bytes Bits8
+
+  ||| Convert a list of bytes into a value.
   fromBytes : Vect bytes Bits8 -> a
 
 export
@@ -294,6 +337,11 @@ export
     in  fromBytes bs1 :: fromBytes bs2
 
 
+||| The constraint that each array representation requires.
+|||
+||| Currently, only the `Bytes` representation has a constraint, requiring an
+||| implementation of `ByteRep`. All other representations can be used without
+||| constraint.
 public export
 RepConstraint : Rep -> Type -> Type
 RepConstraint (Bytes _) a = ByteRep a