std/Monad/List.bruijn


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# MIT License, Copyright (c) 2023 Marvin Borner
# monadic interface for anything based on lists (e.g. IO, strings)
# afaik originally proposed by John Tromp and inspired by Haskell

:import std/List .
:import std/Combinator .

read [0] ⧗ a → (M a)

return [[1 : 0]] ⧗ a → (M a)

pure return ⧗ a → (M a)

# monadic bind operator
bind [[[2 0 1]]] ⧗ (M a) → (a → (M b)) → (M a)

…>>=… bind

:test ((read >>= return) "woa") ("woa")

# monadic reverse bind operator
…=<<… \…>>=… ⧗ (a → (M b)) → (M a) → (M b)

:test ((return =<< read) "woa") ("woa")

# monadic compose operator
…>>… [[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]

# traverses list based on modifier
traverse sequence ∘∘ map ⧗ (a → (M b)) → (N a) → (M (N b))

# 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))