モナモナ言うモナド入门.迟补谤.驳锄
- 1. モナモナ言う モナド入門.tar.gz 2012-11-18 hiratara
- 3. 100分で话して来た
- 4. 超短缩版
- 6. 大统一理论２
- 9. そのとき Philip Wadler の脳裏に閃光が走った！ ※この話はフィクションです
- 10. モノイダル圏 双関手□と自然同型α、λ、ρがある圏 A B A□B f g f□g A’ B’ A’□B’
- 11. (モノイダル圏の) モノイド η□M M□η I□M M□M M□I μ λ ρ α M□μ M□M (M□M)□M M□(M□M) M μ□M μ M□M M
- 12. Monoid a(1) prod (id, mappend’) (a, a), a ((x, y), z) -> (x, (y, z)) a, (a, a) (a, a) prod (mappend’, id) mappend’ mappend’ (a, a) prod (f, g) (x, y) = (f x, g y) a mappend’ = uncurry mappend
- 13. Monoid a(1) (x <> y) <> z = x <> (y <> z) prod (id, mappend’) (a, a), a ((x, y), z) -> (x, (y, z)) a, (a, a) (a, a) prod (mappend’, id) mappend’ mappend’ (a, a) prod (f, g) (x, y) = (f x, g y) a mappend’ = uncurry mappend
- 14. Monoid a(2) prod (mempty’, id) prod (id, mempty’) ((), a) (a, a) (a, ()) mappend’ snd fst a mempty’ = const mempty
- 15. Monoid a(2) mempty <> x = x x <> mempty = x prod (mempty’, id) prod (id, mempty’) ((), a) (a, a) (a, ()) mappend’ snd fst a mempty’ = const mempty
- 16. Monoid a(2) mempty <> x = x x <> mempty = x prod (mempty’, id) prod (id, mempty’) ((), a) (a, a) (a, ()) mappend’ snd fst a ”集合” mempty’ = const mempty
- 17. 惭辞苍辞颈诲は 集合圏のモノイド
- 18. モナド則 ? 以下と同値 join . fmap join = join . join join . fmap return = join . return = id ? 証明は http://ja.wikibooks.org/wiki/Haskell/ %E5%9C%8F%E8%AB%96 を参照
- 19. Monad m(1) id fmap join mmma mmma mma join join join mma ma
- 20. Monad m(1) join . fmap join = join . join id fmap join mmma mmma mma join join join mma ma
- 21. Monad m(2) return fmap return ma mma ma join id id ma
- 22. Monad m(2) join . fmap return = id join . return = id return fmap return ma mma ma join id id ma
- 23. Monad m(2) join . fmap return = id join . return = id return fmap return ma mma ma join id id ma ”自己関手”
- 25. まとめ ? 同じ図で法則をまとめれるのはイイ ? 書きかけの検証用ソース https://gist.github.com/4104020