diff --git a/CHANGELOG_NEXT.md b/CHANGELOG_NEXT.md
index ebfcf88fc..e3fe342c2 100644
--- a/CHANGELOG_NEXT.md
+++ b/CHANGELOG_NEXT.md
@@ -60,24 +60,24 @@ This CHANGELOG describes the merged but unreleased changes. Please see [CHANGELO
   is dropped as soon as possible. This allows you to reuse unique variables and
   optimize memory consumption.
 
-* Fix invalid memory read onf strSubStr.
+* Fix invalid memory read on `strSubStr`.
 
-* Fix memory leaks of IORef. Now that IORef holds values by itself,
-  global_IORef_Storage is no longer needed.
+* Fix memory leaks of `IORef`. Now that `IORef` holds values by itself,
+  `global_IORef_Storage` is no longer needed.
 
-* Pattern matching generates simpler code. This reduces malloc/free and memory
+* Pattern matching generates simpler code. This reduces `malloc`/`free` and memory
   consumption. It also makes debugging easier.
 
 * Stopped useless string copying in the constructor to save memory. Also, name
   generation was stopped for constructors that have tags.
 
-* Special constructors such as Nil and Nothing were eliminated and assigned to
-  NULL.
+* Special constructors such as `Nil` and `Nothing` were eliminated and assigned to
+  `NULL`.
 
-* Unbox Bits32,Bits16,Bits8,Int32,Int16,Int8. These types are now packed into
+* Unbox `Bits32`, `Bits16`, `Bits8`, `Int32`, `Int16`, `Int8`. These types are now packed into
   Value*. Now, RefC backend requires at least 32 bits for pointers.
   16-bit CPUs are no longer supported. And we expect the address returned by
-  malloc to be aligned with at least 32 bits. Otherwise it cause a runtime error.
+  `malloc` to be aligned with at least 32 bits. Otherwise it cause a runtime error.
 
 * Rename C function to avoid confliction. But only a part.
 
@@ -144,6 +144,9 @@ This CHANGELOG describes the merged but unreleased changes. Please see [CHANGELO
 * Added `funExt0` and `funExt1`, functions analogous to `funExt` but for functions
   with quantities 0 and 1 respectively.
 
+* `SortedSet`, `SortedMap` and `SortedDMap` modules were extended with flipped variants
+  of functions like `lookup`, `contains`, `update` and `insert`.
+
 * Moved definition of `Data.Vect.nubBy` to the global scope as `nubByImpl` to
   allow compile time proofs on `nubBy` and `nub`.
 
@@ -160,4 +163,4 @@ This CHANGELOG describes the merged but unreleased changes. Please see [CHANGELO
 
 #### Network
 
-* Add a missing function parameter (the flag) in the C implementation of idrnet_recv_bytes
+* Add a missing function parameter (the flag) in the C implementation of `idrnet_recv_bytes`
diff --git a/libs/base/Data/SortedMap.idr b/libs/base/Data/SortedMap.idr
index 6f20f4f9a..84eedb21c 100644
--- a/libs/base/Data/SortedMap.idr
+++ b/libs/base/Data/SortedMap.idr
@@ -22,22 +22,38 @@ export
 lookup : k -> SortedMap k v -> Maybe v
 lookup k = map snd . lookup k . unM
 
+public export %inline
+lookup' : SortedMap k v -> k -> Maybe v
+lookup' = flip lookup
+
 export
 insert : k -> v -> SortedMap k v -> SortedMap k v
 insert k v = M . insert k v . unM
 
+public export %inline
+insert' : SortedMap k v -> (k, v) -> SortedMap k v
+insert' = flip $ uncurry insert
+
 export
 singleton : Ord k => k -> v -> SortedMap k v
 singleton = M .: singleton
 
 export
 insertFrom : Foldable f => f (k, v) -> SortedMap k v -> SortedMap k v
-insertFrom = flip $ foldl $ flip $ uncurry insert
+insertFrom = flip $ foldl insert'
+
+public export %inline
+insertFrom' : Foldable f => SortedMap k v -> f (k, v) -> SortedMap k v
+insertFrom' = flip insertFrom
 
 export
 delete : k -> SortedMap k v -> SortedMap k v
 delete k = M . delete k . unM
 
+public export %inline
+delete' : SortedMap k v -> k -> SortedMap k v
+delete' = flip delete
+
 ||| Updates or deletes a value based on the decision function
 |||
 ||| The decision function takes information about the presence of the value,
@@ -51,6 +67,10 @@ update f k m = case f $ lookup k m of
   Just v  => insert k v m
   Nothing => delete k m
 
+public export %inline
+update' : SortedMap k v -> (Maybe v -> Maybe v) -> k -> SortedMap k v
+update' m f x = update f x m
+
 ||| Updates existing value, if it is present, and does nothing otherwise
 |||
 ||| The current implementation performs up to two traversals of the original map
@@ -60,9 +80,13 @@ updateExisting f k m = case lookup k m of
   Just v  => insert k (f v) m
   Nothing => m
 
+public export %inline
+updateExisting' : SortedMap k v -> (v -> v) -> k -> SortedMap k v
+updateExisting' m f x = updateExisting f x m
+
 export
 fromList : Ord k => List (k, v) -> SortedMap k v
-fromList = flip insertFrom empty
+fromList = insertFrom' empty
 
 export
 toList : SortedMap k v -> List (k, v)
diff --git a/libs/base/Data/SortedMap/Dependent.idr b/libs/base/Data/SortedMap/Dependent.idr
index 9233c7075..6bc33ea63 100644
--- a/libs/base/Data/SortedMap/Dependent.idr
+++ b/libs/base/Data/SortedMap/Dependent.idr
@@ -219,6 +219,10 @@ lookup : (x : k) -> SortedDMap k v -> Maybe (y : k ** v y) -- could return also
 lookup _ Empty = Nothing
 lookup k (M _ t) = treeLookup k t
 
+public export %inline
+lookup' : SortedDMap k v -> (x : k) -> Maybe (y : k ** v y)
+lookup' = flip lookup
+
 export
 lookupPrecise : DecEq k => (x : k) -> SortedDMap k v -> Maybe (v x)
 lookupPrecise x = lookup x >=> \(y ** v) =>
@@ -226,6 +230,10 @@ lookupPrecise x = lookup x >=> \(y ** v) =>
     Yes Refl => Just v
     No _     => Nothing
 
+public export %inline
+lookupPrecise' : DecEq k => SortedDMap k v -> (x : k) -> Maybe (v x)
+lookupPrecise' m x = lookupPrecise x m
+
 export
 insert : (x : k) -> v x -> SortedDMap k v -> SortedDMap k v
 insert k v Empty = M Z (Leaf k v)
@@ -234,13 +242,21 @@ insert k v (M _ t) =
     Left t' => (M _ t')
     Right t' => (M _ t')
 
+public export %inline
+insert' : SortedDMap k v -> (x : k ** v x) -> SortedDMap k v
+insert' m (x ** v) = insert x v m
+
 export
 singleton : Ord k => (x : k) -> v x -> SortedDMap k v
 singleton k v = insert k v empty
 
 export
 insertFrom : Foldable f => f (x : k ** v x) -> SortedDMap k v -> SortedDMap k v
-insertFrom = flip $ foldl $ flip $ uncurry insert
+insertFrom = flip $ foldl insert'
+
+public export %inline
+insertFrom' : Foldable f => SortedDMap k v -> f (x : k ** v x) -> SortedDMap k v
+insertFrom' = flip insertFrom
 
 export
 delete : k -> SortedDMap k v -> SortedDMap k v
@@ -254,6 +270,10 @@ delete k (M (S n) t) =
     Left t' => (M _ t')
     Right t' => (M _ t')
 
+public export %inline
+delete' : SortedDMap k v -> k -> SortedDMap k v
+delete' = flip delete
+
 ||| Updates or deletes a value based on the decision function
 |||
 ||| The decision function takes information about the presence of the value,
@@ -267,6 +287,10 @@ update k f m = case f $ lookupPrecise k m of
   Just v  => insert k v m
   Nothing => delete k m
 
+public export %inline
+update' : DecEq k => SortedDMap k v -> (x : k ** Maybe (v x) -> Maybe (v x)) -> SortedDMap k v
+update' m (x ** f) = update x f m
+
 ||| Updates existing value, if it is present, and does nothing otherwise
 |||
 ||| The current implementation performs up to two traversals of the original map
@@ -276,9 +300,13 @@ updateExisting k f m = case lookupPrecise k m of
   Just v  => insert k (f v) m
   Nothing => m
 
+public export %inline
+updateExisting' : DecEq k => SortedDMap k v -> (x : k ** v x -> v x) -> SortedDMap k v
+updateExisting' m (x ** f) = updateExisting x f m
+
 export
 fromList : Ord k => List (x : k ** v x) -> SortedDMap k v
-fromList = foldl (flip (uncurry insert)) empty
+fromList = foldl insert' empty
 
 export
 toList : SortedDMap k v -> List (x : k ** v x)
@@ -346,6 +374,10 @@ traverse : Applicative f => ({x : k} -> v x -> f (w x)) -> SortedDMap k v -> f (
 traverse _ Empty = pure Empty
 traverse f (M _ t) = M _ <$> treeTraverse f t
 
+public export %inline
+for : Applicative f => SortedDMap k v -> ({x : k} -> v x -> f (w x)) -> f (SortedDMap k w)
+for = flip traverse
+
 ||| Merge two maps. When encountering duplicate keys, using a function to combine the values.
 ||| Uses the ordering of the first map given.
 export
diff --git a/libs/base/Data/SortedSet.idr b/libs/base/Data/SortedSet.idr
index 25611af80..a90d4a791 100644
--- a/libs/base/Data/SortedSet.idr
+++ b/libs/base/Data/SortedSet.idr
@@ -17,14 +17,26 @@ export
 insert : k -> SortedSet k -> SortedSet k
 insert k (SetWrapper m) = SetWrapper (Data.SortedMap.insert k () m)
 
+public export %inline
+insert' : SortedSet k -> k -> SortedSet k
+insert' = flip insert
+
 export
 delete : k -> SortedSet k -> SortedSet k
 delete k (SetWrapper m) = SetWrapper (Data.SortedMap.delete k m)
 
+public export %inline
+delete' : SortedSet k -> k -> SortedSet k
+delete' = flip delete
+
 export
 contains : k -> SortedSet k -> Bool
 contains k (SetWrapper m) = isJust (Data.SortedMap.lookup k m)
 
+public export %inline
+contains' : SortedSet k -> k -> Bool
+contains' = flip contains
+
 export
 fromList : Ord k => List k -> SortedSet k
 fromList l = SetWrapper (Data.SortedMap.fromList (map (\i => (i, ())) l))
@@ -100,4 +112,4 @@ namespace Dependent
 
 export
 singleton : Ord k => k -> SortedSet k
-singleton k = insert k empty
+singleton = insert' empty