2 files changed, 30 insertions, 3 deletions

diff --git a/std/List.bruijn b/std/List.bruijn
index 1f3d8f7..19fac6b 100644
--- a/std/List.bruijn
+++ b/std/List.bruijn
@@ -58,7 +58,7 @@ length z [[[rec]]] (+0) ⧗ (List a) → Number
 :test (∀((+1) : {}(+2))) ((+2))
 :test (∀empty) ((+0))
 
-# applies each element of a list to a function
+# applies each element of a list to a function (left-associative)
 apply z [[[rec]]] ⧗ (a* → b) → (List a) → b
 	rec 0 [[[case-app]]] case-end
 		case-app 5 (4 2) 1
@@ -68,13 +68,23 @@ apply z [[[rec]]] ⧗ (a* → b) → (List a) → b
 
 :test (…+… <! ((+1) : {}(+2))) ((+3))
 
-# applies each element of the tail to the head
+# applies each element of the tail to the head (left-associative)
 eval [0 apply] ⧗ (Pair (a → b) (List a)) → b
 
 !‣ eval
 
 :test (!(…+… : ((+1) : {}(+2)))) ((+3))
 
+# applies each element of the tail to the head (right-associative)
+eval-r z [[rec]]
+	rec 0 [[[case-app]]] case-end
+		case-app ∅?1 2 (2 (4 1))
+		case-end 1
+
+~!‣ eval-r
+
+:test (~!(inc : (inc : {}(+1)))) ((+3))
+
 # returns the element at index in list
 index z [[[rec]]] ⧗ (List a) → Number → a
 	rec 0 [[[case-index]]] case-end
diff --git a/std/Monad.bruijn b/std/Monad.bruijn
index e015efa..97291eb 100644
--- a/std/Monad.bruijn
+++ b/std/Monad.bruijn
@@ -2,7 +2,7 @@
 # monadic interface for anything based on lists (e.g. IO, strings)
 # afaik originally proposed by John Tromp and inspired by Haskell
 
-:import std/Pair .
+:import std/List .
 :import std/Combinator .
 
 read [0] ⧗ a → (M a)
@@ -25,3 +25,20 @@ pure return ⧗ a → (M a)
 …>>… [[1 >>= [1]]] ⧗ (M a) → (M b) → (M b)
 
 :test ((read >> (return 'a')) "hah") ("aah")
+
+# monadifies a list
+lift-m map ⧗ (a → b) → (M a) → (M b)
+
+# monadifies a list with two monadic arguments
+lift-m2 [[[concat ([[4 1 0] <$> 1] <$> 1)]]] ⧗ (a → b → c) → (M a) → (M b) → (M c)
+
+# evaluates monadic actions
+sequence foldr (lift-m2 cons) {}empty ⧗ (List (M a)) → (M (List a))
+
+>‣ [sequence ∘∘ 0]
+
+# performs action n times
+replicate-m >replicate ⧗ Number → (M a) → (M (List a))
+
+# maps elements to a monadic action
+map-m >map ⧗ (a → (M b)) → (List a) → (M (List b))