diff --git a/libs/base/Data/List.idr b/libs/base/Data/List.idr
index a0210ff4c..3f71e7c56 100644
--- a/libs/base/Data/List.idr
+++ b/libs/base/Data/List.idr
@@ -445,6 +445,10 @@ public export
 replaceOn : Eq a => (e : a) -> (b : a) -> (l : List a) -> List a
 replaceOn e = replaceWhen (== e)
 
+replicateTR : List a -> Nat -> a -> List a
+replicateTR as Z     _ = as
+replicateTR as (S n) x = replicateTR (x :: as) n x
+
 ||| Construct a list with `n` copies of `x`.
 |||
 ||| @ n how many copies
@@ -454,6 +458,10 @@ replicate : (n : Nat) -> (x : a) -> List a
 replicate Z     _ = []
 replicate (S n) x = x :: replicate n x
 
+-- Data.List.replicateTRIsReplicate proves these are equivalent.
+%transform "tailRecReplicate" List.replicate = List.replicateTR Nil
+
+
 ||| Compute the intersect of two lists by user-supplied equality predicate.
 export
 intersectBy : (a -> a -> Bool) -> List a -> List a -> List a
@@ -1066,3 +1074,49 @@ export
 mapAppend : (f : a -> b) -> (xs, ys : List a) -> map f (xs ++ ys) = map f xs ++ map f ys
 mapAppend f []      ys = Refl
 mapAppend f (x::xs) ys = rewrite mapAppend f xs ys in Refl
+
+0 mapTRIsMap :  (f : a -> b) -> (as : List a) -> mapTR f as === map f as
+mapTRIsMap f = lemma Lin
+  where lemma :  (sb : SnocList b)
+              -> (as : List a)
+              -> mapAppend sb f as === (sb <>> map f as)
+        lemma sb []        = Refl
+        lemma sb (x :: xs) = lemma (sb :< f x) xs
+
+
+0 mapMaybeTRIsMapMaybe :  (f : a -> Maybe b)
+                       -> (as : List a)
+                       -> mapMaybeTR f as === mapMaybe f as
+mapMaybeTRIsMapMaybe f = lemma Lin
+  where lemma :  (sb : SnocList b)
+              -> (as : List a)
+              -> mapMaybeAppend sb f as === (sb <>> mapMaybe f as)
+        lemma sb []        = Refl
+        lemma sb (x :: xs) with (f x)
+          lemma sb (x :: xs) | Nothing = lemma sb xs
+          lemma sb (x :: xs) | Just v  = lemma (sb :< v) xs
+
+0 filterTRIsFilter :  (f : a -> Bool)
+                   -> (as : List a)
+                   -> filterTR f as === filter f as
+filterTRIsFilter f = lemma Lin
+
+  where lemma :  (sa : SnocList a)
+              -> (as : List a)
+              -> filterAppend sa f as === (sa <>> filter f as)
+        lemma sa []        = Refl
+        lemma sa (x :: xs) with (f x)
+          lemma sa (x :: xs) | False = lemma sa xs
+          lemma sa (x :: xs) | True  = lemma (sa :< x) xs
+
+0 replicateTRIsReplicate : (n : Nat) -> (x : a) -> replicateTR [] n x === replicate n x
+replicateTRIsReplicate n x = trans (lemma [] n) (appendNilRightNeutral _)
+  where lemma1 : (as : List a) -> (m : Nat) -> (x :: replicate m x) ++ as === replicate m x ++ (x :: as)
+        lemma1 as 0     = Refl
+        lemma1 as (S k) = cong (x ::) (lemma1 as k)
+
+        lemma : (as : List a) -> (m : Nat) -> replicateTR as m x === replicate m x ++ as
+        lemma as 0     = Refl
+        lemma as (S k) =
+          let prf := lemma (x :: as) k
+           in trans prf (sym $ lemma1 as k)
diff --git a/libs/base/Data/SnocList.idr b/libs/base/Data/SnocList.idr
index a520755c3..73a35350a 100644
--- a/libs/base/Data/SnocList.idr
+++ b/libs/base/Data/SnocList.idr
@@ -62,9 +62,26 @@ Show a => Show (SnocList a) where
       show' acc (xs :< x) = show' (show x :: acc) xs
 
 public export
+mapImpl : (a -> b) -> SnocList a -> SnocList b
+mapImpl f Lin = Lin
+mapImpl f (sx :< x) = (mapImpl f sx) :< (f x)
+
+-- Utility for implementing `mapTR`
+mapTR' : List b -> (a -> b) -> SnocList a -> SnocList b
+mapTR' xs f (sx :< x) = mapTR' (f x :: xs) f sx
+mapTR' xs f Lin       = Lin <>< xs
+
+-- Tail recursive version of `map`. This is automatically used
+-- at runtime due to a `transform` rule.
+mapTR : (a -> b) -> SnocList a -> SnocList b
+mapTR = mapTR' []
+
+-- mapTRIsMap proves these are equivalent.
+%transform "tailRecMapSnocList" SnocList.mapImpl = SnocList.mapTR
+
+public export %inline
 Functor SnocList where
-  map f Lin = Lin
-  map f (sx :< x) = (map f sx) :< (f x)
+  map = mapImpl
 
 public export
 Semigroup (SnocList a) where
@@ -357,3 +374,75 @@ mapMaybeCast f (x::xs) = do
     mapMaybeStepLemma with (f x)
       _ | Nothing  = rewrite appendLinLeftNeutral $ [<] <>< mapMaybe f xs in Refl
       _ | (Just y) = rewrite fishAsSnocAppend [<y] (mapMaybe f xs) in Refl
+
+0 mapTRIsMap :  (f : a -> b) -> (sa : SnocList a) -> mapTR f sa === map f sa
+mapTRIsMap f = lemma []
+  where lemma :  (bs : List b)
+              -> (sa : SnocList a)
+              -> mapTR' bs f sa === (map f sa <>< bs)
+        lemma bs Lin       = Refl
+        lemma bs (sx :< x) = lemma (f x :: bs) sx
+
+
+0 mapMaybeTRIsMapMaybe :  (f : a -> Maybe b)
+                       -> (sa : SnocList a)
+                       -> mapMaybeTR f sa === mapMaybe f sa
+mapMaybeTRIsMapMaybe f = lemma []
+  where lemma :  (bs : List b)
+              -> (sa : SnocList a)
+              -> mapMaybeAppend bs f sa === (mapMaybe f sa <>< bs)
+        lemma bs Lin = Refl
+        lemma bs (sx :< x) with (f x)
+          lemma bs (sx :< x) | Nothing = lemma bs sx
+          lemma bs (sx :< x) | Just v  = lemma (v :: bs) sx
+
+0 filterTRIsFilter :  (f : a -> Bool)
+                   -> (sa : SnocList a)
+                   -> filterTR f sa === filter f sa
+filterTRIsFilter f = lemma []
+  where lemma :  (as : List a)
+              -> (sa : SnocList a)
+              -> filterAppend as f sa === (filter f sa <>< as)
+        lemma as Lin = Refl
+        lemma as (sx :< x) with (f x)
+          lemma as (sx :< x) | False = lemma as sx
+          lemma as (sx :< x) | True  = lemma (x :: as) sx
+
+-- SnocList `reverse` applied to `reverseOnto` is equivalent to swapping the
+-- arguments of `reverseOnto`.
+reverseReverseOnto : (l, r : SnocList a) ->
+                     reverse (reverseOnto l r) = reverseOnto r l
+reverseReverseOnto _ Lin = Refl
+reverseReverseOnto l (sx :< x) = reverseReverseOnto (l :< x) sx
+
+||| SnocList `reverse` applied twice yields the identity function.
+export
+reverseInvolutive : (sx : SnocList a) -> reverse (reverse sx) = sx
+reverseInvolutive = reverseReverseOnto Lin
+
+-- Appending `x` to `l` and then reversing the result onto `r` is the same as
+-- using (::) with `x` and the result of reversing `l` onto `r`.
+snocReverse : (x : a) -> (l, r : SnocList a) ->
+              reverseOnto r l :< x = reverseOnto r (reverseOnto [<x] (reverse l))
+snocReverse _ Lin _ = Refl
+snocReverse x (sy :< y) r
+  = rewrite snocReverse x sy (r :< y) in
+      rewrite cong (reverseOnto r . reverse) $ snocReverse x sy [<y] in
+        rewrite reverseInvolutive (reverseOnto [<x] (reverse sy) :< y) in
+          Refl
+
+-- Proof that it is safe to lift a (::) out of the first `tailRecAppend`
+-- argument.
+snocTailRecAppend : (x : a) -> (l, r : SnocList a) ->
+                    tailRecAppend l (r :< x) = (tailRecAppend l r) :< x
+snocTailRecAppend x l r =
+  rewrite snocReverse x (reverse r) l in
+    rewrite reverseInvolutive r in
+       Refl
+
+-- Proof that `(++)` and `tailRecAppend` do the same thing, so the %transform
+-- directive is safe.
+tailRecAppendIsAppend : (sx, sy : SnocList a) -> tailRecAppend sx sy = sx ++ sy
+tailRecAppendIsAppend sx Lin = Refl
+tailRecAppendIsAppend sx (sy :< y) =
+  trans (snocTailRecAppend y sx sy) (cong (:< y) $ tailRecAppendIsAppend sx sy)
diff --git a/libs/prelude/Prelude/Types.idr b/libs/prelude/Prelude/Types.idr
index dbe5981d1..d3b7d6096 100644
--- a/libs/prelude/Prelude/Types.idr
+++ b/libs/prelude/Prelude/Types.idr
@@ -392,6 +392,119 @@ Ord a => Ord (List a) where
             EQ => compare xs ys
             c => c
 
+namespace SnocList
+
+  infixl 7 <><
+  infixr 6 <>>
+
+  ||| 'fish': Action of lists on snoc-lists
+  public export
+  (<><) : SnocList a -> List a -> SnocList a
+  sx <>< [] = sx
+  sx <>< (x :: xs) = sx :< x <>< xs
+
+  ||| 'chips': Action of snoc-lists on lists
+  public export
+  (<>>) : SnocList a -> List a -> List a
+  Lin       <>> xs = xs
+  (sx :< x) <>> xs = sx <>> x :: xs
+
+  public export
+  (++) : (sx, sy : SnocList a) -> SnocList a
+  (++) sx Lin = sx
+  (++) sx (sy :< y) = (sx ++ sy) :< y
+
+  public export
+  length : SnocList a -> Nat
+  length Lin = Z
+  length (sx :< x) = S $ length sx
+
+  ||| Filters a snoc-list according to a simple classifying function
+  public export
+  filter : (a -> Bool) -> SnocList a -> SnocList a
+  filter f [<]     = [<]
+  filter f (xs:<x) = let rest = filter f xs in if f x then rest :< x else rest
+
+  ||| Apply a partial function to the elements of a list, keeping the ones at which
+  ||| it is defined.
+  public export
+  mapMaybe : (a -> Maybe b) -> SnocList a -> SnocList b
+  mapMaybe f [<]       = [<]
+  mapMaybe f (sx :< x) = case f x of
+    Nothing => mapMaybe f sx
+    Just j  => mapMaybe f sx :< j
+
+  ||| Reverse the second snoclist, prepending its elements to the first.
+  public export
+  reverseOnto : SnocList a -> SnocList a -> SnocList a
+  reverseOnto acc Lin       = acc
+  reverseOnto acc (sx :< x) = reverseOnto (acc :< x) sx
+
+  ||| Reverses the given list.
+  public export
+  reverse : SnocList a -> SnocList a
+  reverse = reverseOnto Lin
+
+  ||| Tail-recursive append. Uses of (++) are automatically transformed to
+  ||| this. The only reason this is exported is that the proof of equivalence
+  ||| lives in a different module.
+  public export
+  tailRecAppend : (sx, sy : SnocList a) -> SnocList a
+  tailRecAppend sx sy = reverseOnto sx (reverse sy)
+
+  -- Always use tailRecAppend at runtime. Data.SnocList.tailRecAppendIsAppend
+  -- proves these are equivalent.
+  %transform "tailRecAppendSnocList" SnocList.(++) = SnocList.tailRecAppend
+
+  ||| Returns the first argument plus the length of the second.
+  public export
+  lengthPlus : Nat -> SnocList a -> Nat
+  lengthPlus n Lin       = n
+  lengthPlus n (sx :< _) = lengthPlus (S n) sx
+
+  ||| `length` implementation that uses tail recursion. Exported so
+  ||| lengthTRIsLength can see it.
+  public export
+  lengthTR : SnocList a -> Nat
+  lengthTR = lengthPlus Z
+
+  -- Data.List.lengthTRIsLength proves these are equivalent.
+  %transform "tailRecLengthSnocList" SnocList.length = SnocList.lengthTR
+
+  ||| Utility for implementing `mapMaybeTR`
+  public export
+  mapMaybeAppend : List b -> (a -> Maybe b) -> SnocList a -> SnocList b
+  mapMaybeAppend xs f (sx :< x) = case f x of
+    Just v  => mapMaybeAppend (v :: xs) f sx
+    Nothing => mapMaybeAppend xs f sx
+  mapMaybeAppend xs f Lin       = Lin <>< xs
+
+  ||| Tail recursive version of `mapMaybe`. This is automatically used
+  ||| at runtime due to a `transform` rule.
+  public export %inline
+  mapMaybeTR : (a -> Maybe b) -> SnocList a -> SnocList b
+  mapMaybeTR = mapMaybeAppend []
+
+  -- Data.List.mapMaybeTRIsMapMaybe proves these are equivalent.
+  %transform "tailRecMapMaybeSnocList" SnocList.mapMaybe = SnocList.mapMaybeTR
+
+  ||| Utility for implementing `filterTR`
+  public export
+  filterAppend : List a -> (a -> Bool) -> SnocList a -> SnocList a
+  filterAppend xs f (sx :< x) = case f x of
+    True  => filterAppend (x :: xs) f sx
+    False => filterAppend xs f sx
+  filterAppend xs f Lin       = Lin <>< xs
+
+  ||| Tail recursive version of `filter`. This is automatically used
+  ||| at runtime due to a `transform` rule.
+  public export %inline
+  filterTR : (a -> Bool) -> SnocList a -> SnocList a
+  filterTR = filterAppend []
+
+  -- Data.List.listTRIsList proves these are equivalent.
+  %transform "tailRecFilterSnocList" SnocList.filter = SnocList.filterTR
+
 namespace List
 
   ||| Concatenate one list with another.
@@ -445,7 +558,7 @@ namespace List
 
   -- Always use tailRecAppend at runtime. Data.List.tailRecAppendIsAppend
   -- proves these are equivalent.
-  %transform "tailRecAppend" (++) = tailRecAppend
+  %transform "tailRecAppend" List.(++) = List.tailRecAppend
 
   ||| Returns the first argument plus the length of the second.
   public export
@@ -460,12 +573,65 @@ namespace List
   lengthTR = lengthPlus Z
 
   -- Data.List.lengthTRIsLength proves these are equivalent.
-  %transform "tailRecLength" length = lengthTR
+  %transform "tailRecLength" List.length = List.lengthTR
 
-public export
+  public export
+  mapImpl : (a -> b) -> List a -> List b
+  mapImpl f [] = []
+  mapImpl f (x :: xs) = f x :: mapImpl f xs
+
+  ||| Utility for implementing `mapTR`
+  public export
+  mapAppend : SnocList b -> (a -> b) -> List a -> List b
+  mapAppend sx f (x :: xs) = mapAppend (sx :< f x) f xs
+  mapAppend sx f []        = sx <>> []
+
+  ||| Tail recursive version of `map`. This is automatically used
+  ||| at runtime due to a `transform` rule.
+  public export %inline
+  mapTR : (a -> b) -> List a -> List b
+  mapTR = mapAppend Lin
+
+  -- Data.List.mapTRIsMap proves these are equivalent.
+  %transform "tailRecMap" mapImpl = List.mapTR
+
+  ||| Utility for implementing `mapMaybeTR`
+  public export
+  mapMaybeAppend : SnocList b -> (a -> Maybe b) -> List a -> List b
+  mapMaybeAppend sx f (x :: xs) = case f x of
+    Just v  => mapMaybeAppend (sx :< v) f xs
+    Nothing => mapMaybeAppend sx f xs
+  mapMaybeAppend sx f []        = sx <>> []
+
+  ||| Tail recursive version of `mapMaybe`. This is automatically used
+  ||| at runtime due to a `transform` rule.
+  public export %inline
+  mapMaybeTR : (a -> Maybe b) -> List a -> List b
+  mapMaybeTR = mapMaybeAppend Lin
+
+  -- Data.List.mapMaybeTRIsMapMaybe proves these are equivalent.
+  %transform "tailRecMapMaybe" List.mapMaybe = List.mapMaybeTR
+
+  ||| Utility for implementing `filterTR`
+  public export
+  filterAppend : SnocList a -> (a -> Bool) -> List a -> List a
+  filterAppend sx f (x :: xs) = case f x of
+    True  => filterAppend (sx :< x) f xs
+    False => filterAppend sx f xs
+  filterAppend sx f []        = sx <>> []
+
+  ||| Tail recursive version of `filter`. This is automatically used
+  ||| at runtime due to a `transform` rule.
+  public export %inline
+  filterTR : (a -> Bool) -> List a -> List a
+  filterTR = filterAppend Lin
+
+  -- Data.List.listTRIsList proves these are equivalent.
+  %transform "tailRecFilter" List.filter = List.filterTR
+
+public export %inline
 Functor List where
-  map f [] = []
-  map f (x :: xs) = f x :: map f xs
+  map = mapImpl
 
 public export
 Semigroup (List a) where
@@ -519,48 +685,6 @@ Traversable List where
   traverse f [] = pure []
   traverse f (x::xs) = [| f x :: traverse f xs |]
 
-namespace SnocList
-
-  infixl 7 <><
-  infixr 6 <>>
-
-  ||| 'fish': Action of lists on snoc-lists
-  public export
-  (<><) : SnocList a -> List a -> SnocList a
-  sx <>< [] = sx
-  sx <>< (x :: xs) = sx :< x <>< xs
-
-  ||| 'chips': Action of snoc-lists on lists
-  public export
-  (<>>) : SnocList a -> List a -> List a
-  Lin       <>> xs = xs
-  (sx :< x) <>> xs = sx <>> x :: xs
-
-  public export
-  (++) : (sx, sy : SnocList a) -> SnocList a
-  (++) sx Lin = sx
-  (++) sx (sy :< y) = (sx ++ sy) :< y
-
-  public export
-  length : SnocList a -> Nat
-  length Lin = Z
-  length (sx :< x) = S $ length sx
-
-  ||| Filters a snoc-list according to a simple classifying function
-  public export
-  filter : (a -> Bool) -> SnocList a -> SnocList a
-  filter f [<]     = [<]
-  filter f (xs:<x) = let rest = filter f xs in if f x then rest :< x else rest
-
-  ||| Apply a partial function to the elements of a list, keeping the ones at which
-  ||| it is defined.
-  public export
-  mapMaybe : (a -> Maybe b) -> SnocList a -> SnocList b
-  mapMaybe f [<]       = [<]
-  mapMaybe f (sx :< x) = case f x of
-    Nothing => mapMaybe f sx
-    Just j  => mapMaybe f sx :< j
-
 public export
 Eq a => Eq (SnocList a) where
   (==) Lin Lin = True
diff --git a/src/Core/Env.idr b/src/Core/Env.idr
index 11cdf135b..a27938412 100644
--- a/src/Core/Env.idr
+++ b/src/Core/Env.idr
@@ -72,7 +72,7 @@ bindEnv loc (b :: env) tm
                                         Explicit
                                         (binderType b)) tm)
 
-revOnto : (xs, vs : _) -> reverseOnto xs vs = reverse vs ++ xs
+revOnto : (xs, vs : List a) -> reverseOnto xs vs = reverse vs ++ xs
 revOnto xs [] = Refl
 revOnto xs (v :: vs)
     = rewrite revOnto (v :: xs) vs in
diff --git a/tests/ideMode/ideMode005/expectedJ b/tests/ideMode/ideMode005/expectedJ
index cb1ff81fd..e23c1e7a2 100644
--- a/tests/ideMode/ideMode005/expectedJ
+++ b/tests/ideMode/ideMode005/expectedJ
@@ -48,7 +48,7 @@
 0000cf(:return (:ok "   n : Nat
 ------------------------------
 prf : [2, 1, 0] = ?a" ((7 3 ((:decor :type))) (49 1 ((:decor :data))) (52 1 ((:decor :data))) (55 1 ((:decor :data))) (58 1 ((:decor :keyword))))) 2)
-0000f6(:return (:ok "   xs : List Nat
+0000fa(:return (:ok "   xs : List Nat
 ------------------------------
-prf2 : map S xs = ?lgjgk" ((8 4 ((:decor :type))) (13 3 ((:decor :type))) (55 3 ((:decor :function))) (59 1 ((:decor :data))) (61 2 ((:decor :bound))) (64 1 ((:decor :keyword))))) 3)
+prf2 : mapImpl S xs = ?lgjgk" ((8 4 ((:decor :type))) (13 3 ((:decor :type))) (55 7 ((:decor :function))) (63 1 ((:decor :data))) (65 2 ((:decor :bound))) (68 1 ((:decor :keyword))))) 3)
 Alas the file is done, aborting
diff --git a/tests/node/tailrec_libs/expected b/tests/node/tailrec_libs/expected
index 68a2516bf..f051743fb 100644
--- a/tests/node/tailrec_libs/expected
+++ b/tests/node/tailrec_libs/expected
@@ -1 +1,8 @@
 50001
+50000
+50000
+50000
+50001
+50000
+50000
+50000
diff --git a/tests/node/tailrec_libs/tailrec.idr b/tests/node/tailrec_libs/tailrec.idr
index 20f523962..6e675a68c 100644
--- a/tests/node/tailrec_libs/tailrec.idr
+++ b/tests/node/tailrec_libs/tailrec.idr
@@ -9,14 +9,22 @@ So far, only Prelude.List.++ is tested.
 
 module Main
 
--- Until replicate is tail recursive, we roll our own for this test.
+import Data.List
+import Data.SnocList
 
-replicateOnto : List a -> Nat -> a -> List a
-replicateOnto acc Z x = acc
-replicateOnto acc (S n) x = replicateOnto (x :: acc) n x
+values : List Nat
+values = replicate 50000 1
 
-tailRecReplicate : Nat -> a -> List a
-tailRecReplicate = replicateOnto []
+seulav : SnocList Nat
+seulav = Lin <>< values
 
 main : IO ()
-main = putStrLn $ show $ length $ tailRecReplicate 50000 () ++ [()]
+main = do
+  printLn $ length $ values ++ [1]
+  printLn $ length $ map Just values
+  printLn $ length $ mapMaybe Just values
+  printLn $ length $ filter (const True) values
+  printLn $ length $ seulav ++ [<1]
+  printLn $ length $ map Just seulav
+  printLn $ length $ mapMaybe Just seulav
+  printLn $ length $ filter (const True) seulav