diff --git a/src/Data/NumIdr/Array/Array.idr b/src/Data/NumIdr/Array/Array.idr
index b4bc931..1aa37cb 100644
--- a/src/Data/NumIdr/Array/Array.idr
+++ b/src/Data/NumIdr/Array/Array.idr
@@ -31,20 +31,27 @@ data Array : (s : Vect rk Nat) -> (a : Type) -> Type where
   ||| *strides*, which determine how indexes into the internal array should be
   ||| performed. This is how the order of the array is configurable.
   |||
-  ||| @ s   The shape of the array
+  ||| @ ord The order of the elements of the array
   ||| @ sts The strides of the array
-  MkArray : (s : Vect rk Nat) -> (sts : Vect rk Nat) -> PrimArray a -> Array s a
+  ||| @ s   The shape of the array
+  MkArray : (ord : Order) -> (sts : Vect rk Nat) ->
+            (s : Vect rk Nat) -> PrimArray a -> Array s a
 
 
 ||| Extract the primitive array value.
 export
 getPrim : Array s a -> PrimArray a
-getPrim (MkArray _ _ arr) = arr
+getPrim (MkArray _ _ _ arr) = arr
+
+||| The order of the elements of the array
+export
+getOrder : Array s a -> Order
+getOrder (MkArray ord _ _ _) = ord
 
 ||| The strides of the array, returned in the same axis order as in the shape.
 export
 getStrides : Array {rk} s a -> Vect rk Nat
-getStrides (MkArray _ sts _) = sts
+getStrides (MkArray _ sts _ _) = sts
 
 ||| The total number of elements of the array
 ||| This is equivalent to `product s`.
@@ -55,7 +62,7 @@ size = length . getPrim
 ||| The shape of the array
 export
 shape : Array {rk} s a -> Vect rk Nat
-shape (MkArray s _ _) = s
+shape (MkArray _ _ s _) = s
 
 ||| The rank of the array
 export
@@ -69,8 +76,8 @@ rank = length . shape
 ||| @ s   The shape of the constructed array
 ||| @ ord The order to interpret the elements
 export
-fromVect' : (s : Vect rk Nat) -> (ord : Order rk) -> Vect (product s) a -> Array s a
-fromVect' s ord v = MkArray s (calcStrides ord s) (fromList $ toList v)
+fromVect' : (s : Vect rk Nat) -> (ord : Order) -> Vect (product s) a -> Array s a
+fromVect' s ord v = MkArray ord (calcStrides ord s) s (fromList $ toList v)
 
 ||| Create an array given a vector of its elements. The elements of the vector
 ||| are assembled into the provided shape using row-major order (the last axis is the
@@ -88,19 +95,19 @@ fromVect s = fromVect' s COrder
 ||| @ s   The shape of the constructed array
 ||| @ ord The order of the constructed array
 export
-array' : (s : Vect rk Nat) -> (ord : Order rk) -> Vects s a -> Array s a
-array' s ord v = MkArray s sts (unsafeFromIns (product s) ins)
+array' : (s : Vect rk Nat) -> (ord : Order) -> Vects s a -> Array s a
+array' s ord v = MkArray ord sts s (unsafeFromIns (product s) ins)
   where
     sts : Vect rk Nat
     sts = calcStrides ord s
 
     ins : List (Nat, a)
-    ins = collapse $ mapWithIndex (\i,x => (sum $ zipWith (*) i sts, x)) v
+    ins = collapse $ mapWithIndex (\is,x => (getLocation' sts is, x)) v
 
 ||| Construct an array using a structure of nested vectors.
 export
 array : {s : _} -> Vects s a -> Array s a
-array v = MkArray s (calcStrides COrder s) (fromList $ collapse v)
+array v = MkArray COrder (calcStrides COrder s) s (fromList $ collapse v)
 
 
 ||| Reshape the array into the given shape and reinterpret it according to
@@ -109,20 +116,17 @@ array v = MkArray s (calcStrides COrder s) (fromList $ collapse v)
 ||| @ s'  The shape to convert the array to
 ||| @ ord The order to reinterpret the array by
 export
-reshape' : (s' : Vect rk' Nat) -> (ord : Order rk') -> Array {rk} s a ->
+reshape' : (s' : Vect rk' Nat) -> (ord : Order) -> Array {rk} s a ->
              product s = product s' => Array s' a
-reshape' s' ord' arr = MkArray s' (calcStrides ord' s') (getPrim arr)
+reshape' s' ord' arr = MkArray ord' (calcStrides ord' s') s' (getPrim arr)
 
 ||| Reshape the array into the given shape.
 |||
-||| The array is also reinterpreted in row-major order; if this is undesirable,
-||| then `reshape'` must be used instead.
-|||
 ||| @ s' The shape to convert the array to
 export
 reshape : (s' : Vect rk' Nat) -> Array {rk} s a ->
             product s = product s' => Array s' a
-reshape s' = reshape' s' COrder
+reshape s' arr = reshape' s' (getOrder arr) arr
 
 
 ||| Index the array using the given `Coords` object.
diff --git a/src/Data/NumIdr/Array/Coords.idr b/src/Data/NumIdr/Array/Coords.idr
index e47d421..695f3f5 100644
--- a/src/Data/NumIdr/Array/Coords.idr
+++ b/src/Data/NumIdr/Array/Coords.idr
@@ -46,8 +46,12 @@ index []      x = x
 index (i::is) v = index is $ index i v
 
 
+export
+getLocation' : (sts : Vect rk Nat) -> (is : Vect rk Nat) -> Nat
+getLocation' = sum .: zipWith (*)
+
 ||| Compute the memory location of an array element
 ||| given its coordinate and the strides of the array.
 export
 getLocation : Vect rk Nat -> Coords {rk} s -> Nat
-getLocation sts is = sum $ zipWith (*) sts (toNats is)
+getLocation sts is = getLocation' sts (toNats is)
diff --git a/src/Data/NumIdr/Array/Order.idr b/src/Data/NumIdr/Array/Order.idr
index 83ff31f..827ca78 100644
--- a/src/Data/NumIdr/Array/Order.idr
+++ b/src/Data/NumIdr/Array/Order.idr
@@ -1,7 +1,6 @@
 module Data.NumIdr.Array.Order
 
 import Data.Vect
-import Data.Permutation
 
 %default total
 
@@ -10,24 +9,16 @@ import Data.Permutation
 ||| 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.
-|||
-||| @ rk The rank of the array this order applies to
 public export
-data Order : (rk : Nat) -> Type where
+data Order : Type where
 
   ||| C-like order, or contiguous order. This order stores elements in a
   ||| row-major fashion (the last axis is the least significant).
-  COrder : Order rk
+  COrder : Order
 
   ||| Fortran-like order. This order stores elements in a column-major
   ||| fashion (the first axis is the least significant).
-  FOrder : Order rk
-
-
-export
-orderOfShape : (0 s : Vect rk Nat) -> Order (length s) -> Order rk
-orderOfShape s ord = rewrite sym (lengthCorrect s) in ord
-
+  FOrder : Order
 
 
 scanr : (el -> res -> res) -> res -> Vect len el -> Vect (S len) res
@@ -38,7 +29,7 @@ scanr f q0 (x::xs) = f x (head qs) :: qs
 
 ||| Calculate an array's strides given its order and shape.
 export
-calcStrides : Order rk -> Vect rk Nat -> Vect rk Nat
+calcStrides : Order -> Vect rk Nat -> Vect rk Nat
 calcStrides _      []        = []
 calcStrides COrder v@(_::_)  = scanr (*) 1 $ tail v
 calcStrides FOrder v@(_::_)  = scanl (*) 1 $ init v
diff --git a/src/Data/Permutation.idr b/src/Data/Permutation.idr
deleted file mode 100644
index ca3fabe..0000000
--- a/src/Data/Permutation.idr
+++ /dev/null
@@ -1,32 +0,0 @@
-module Data.Permutation
-
-import Data.Vect
-
-%default total
-
-
-||| A permutation of `n` elements represented as a vector of indices.
-||| For example, `[1,2,0]` is a permutation that maps element `0` to
-||| element `1`, element `1` to element `2`, and element `2` to element `0`.
-public export
-Permutation : (n : Nat) -> Type
-Permutation n = Vect n (Fin n)
-
-
-||| The identity permutation.
-public export
-identity : {n : _} -> Permutation n
-identity {n=Z} = []
-identity {n=S n} = FZ :: map FS identity
-
-||| The permutation that reverses the order of elements.
-public export
-reversed : {n : _} -> Permutation n
-reversed {n=Z} = []
-reversed {n=S n} = last :: map weaken reversed
-
-
-||| Apply a permutation to a vector.
-public export
-permuteVect : Permutation n -> Vect n a -> Vect n a
-permuteVect p v = map (\i => index i v) p