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Document the laws of the -WithIndex classes #58

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ced30ee
Document the laws of the -WithIndex classes
jozanek Jun 9, 2026
447907b
Drop the index-uniqueness claim and the lens issue reference per review
jozanek Jun 19, 2026
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6 changes: 6 additions & 0 deletions indexed-traversable/Changelog.md
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Original file line number Diff line number Diff line change
@@ -1,3 +1,9 @@
# 0.1.6 [unreleased]

- Document the laws of `FunctorWithIndex`, `FoldableWithIndex`, and
`TraversableWithIndex`: the `fmap`/`foldMap`/`traverse` compatibility laws
and agreement with `imapDefault`/`ifoldMapDefault`.

# 0.1.5 [2026-05-07]

- Use automatic flags for compatibility conditionals
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35 changes: 35 additions & 0 deletions indexed-traversable/src/WithIndex.hs
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Expand Up @@ -68,6 +68,13 @@ import CoerceCompat
-- 'imap' f '.' 'imap' g ≡ 'imap' (\\i -> f i '.' g i)
-- 'imap' (\\_ a -> a) ≡ 'id'
-- @
--
-- The index must be compatible with the underlying 'Functor': forgetting the
-- index recovers 'fmap'.
--
-- @
-- 'fmap' f ≡ 'imap' ('const' f)
-- @
class Functor f => FunctorWithIndex i f | f -> i where
-- | Map with access to the index.
imap :: (i -> a -> b) -> f a -> f b
Expand All @@ -86,6 +93,16 @@ imapDefault f = runIdentity #. itraverse (Identity #.. f)
-------------------------------------------------------------------------------

-- | A container that supports folding with an additional index.
--
-- The index must be compatible with the underlying 'Foldable': forgetting the
-- index recovers 'foldMap'.
--
-- @
-- 'foldMap' f ≡ 'ifoldMap' ('const' f)
-- @
--
-- When the same type is also a 'FunctorWithIndex' or 'TraversableWithIndex',
-- all three agree on the index assigned to each element.
class Foldable f => FoldableWithIndex i f | f -> i where
--
-- | Fold a container by mapping value to an arbitrary 'Monoid' with access to the index @i@.
Expand Down Expand Up @@ -230,6 +247,24 @@ class (Foldable1 f, FoldableWithIndex i f) => Foldable1WithIndex i f | f -> i wh
-- 'itraverse' ('const' 'Identity') ≡ 'Identity'
-- 'fmap' ('itraverse' f) '.' 'itraverse' g ≡ 'Data.Functor.Compose.getCompose' '.' 'itraverse' (\\i -> 'Data.Functor.Compose.Compose' '.' 'fmap' (f i) '.' g i)
-- @
--
-- The index must be compatible with the underlying 'Traversable': forgetting
-- the index recovers 'traverse'.
--
-- @
-- 'traverse' f ≡ 'itraverse' ('const' f)
-- @
--
-- The 'FunctorWithIndex' and 'FoldableWithIndex' instances must agree with the
-- ones induced by 'itraverse':
--
-- @
-- 'imap' ≡ 'imapDefault'
-- 'ifoldMap' ≡ 'ifoldMapDefault'
-- @
--
-- so 'itraverse' visits every element exactly once, in order, pairing it with
-- the same index used by 'imap' and 'ifoldMap'.
class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i t | t -> i where
-- | Traverse an indexed container.
--
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