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Highlights of my experiences in the programming world
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Stefan Dresselhaus
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Studium generale / University-Life
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Work-Experience
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Android
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Einrichtung Android-Smartphones
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Haskell
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Code-Snippets
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*-Morpisms
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TODO: Use < details > to toggle visibility?
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<!-- Variable bindings for this tree -->
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Monoid? Da war doch was…
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TODO: Use < details > to toggle visibility?
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< / div >
< / div >
<!-- Variable bindings for this tree -->
<!-- Rendering of this tree -->
< div class = 'pl-2' >
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< / path >
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< a class = 'hover:underline truncate' title = 'Fortgeschrittene funktionale Programmierung in Haskell' href = 'Haskell/FFPiH' >
Fortgeschrittene funktionale Programmierung in Haskell
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<!-- Node's children forest, displayed only on active trees
TODO: Use < details > to toggle visibility?
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Lenses
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<!-- Node's children forest, displayed only on active trees
TODO: Use < details > to toggle visibility?
-->
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<!-- Variable bindings for this tree -->
<!-- Rendering of this tree -->
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<!-- Node's rootLabel -->
< div class = 'flex items-center my-2 space-x-2 justify-left' >
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< / path >
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< a class = 'hover:underline truncate' title = 'Webapp-Example: Main.hs' href = 'Haskell/Webapp-Example/Main.hs' >
Webapp-Example: Main.hs
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< a class = 'hover:underline truncate' title = 'Webapp-Example: MyService/Types.hs' href = 'Haskell/Webapp-Example/MyService_Types.hs' >
Webapp-Example: MyService/Types.hs
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Logik für Dummies
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< a class = 'font-bold hover:underline truncate' title = 'Uni' href = 'Uni' >
Uni
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< a class = 'hover:underline truncate' title = 'Wie lerne ich richtig an der Uni?' href = 'Uni/Lernerfolg_an_der_Uni' >
Wie lerne ich richtig an der Uni?
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< path d = 'M6 12a2 2 0 012-2h8a2 2 0 012 2v2a2 2 0 01-2 2H2h2a2 2 0 002-2v-2z' > < / path >
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< a class = 'font-bold hover:underline truncate' title = 'Unix' href = 'Unix' >
Unix
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< a class = 'hover:underline truncate' title = 'SSH-Filter' href = 'Unix/SSH-Filter' >
SSH-Filter
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< div class = 'text-gray-900 forest-link' >
< a href = 'Haskell/Advantages' >
Talks und Posts zu Haskell
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< div class = 'text-gray-900 forest-link' >
< a href = 'Haskell' >
Haskell
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Home
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< a href = 'Haskell/FFPiH' >
Fortgeschrittene funktionale Programmierung in Haskell
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Stefan Dresselhaus
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About
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< div class = 'text-gray-900 forest-link' >
< a href = 'About/Extracurricular' >
Studium generale / University-Life
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< h1 class = 'flex items-end justify-center mb-4 p-3 bg-red-100 text-5xl font-extrabold text-black rounded' >
< a class = 'z-40 tracking-tighter ' >
Lenses
< / a >
< / h1 >
< article class = 'overflow-auto' >
<!-- What goes in this file will appear on top of note body -->
< h2 id = 'wofür-brauchen-wir-das-überhaupt' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Wofür brauchen wir das überhaupt?< / h2 >
< p class = 'mb-3' >
Die Idee dahinter ist, dass man Zugriffsabstraktionen über Daten verknüpfen kann. Als einfachen Datenstruktur kann man einen Record mit der entsprechenden Syntax nehmen.
< / p >
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< h3 id = 'beispiel' class = 'mt-6 mb-2 text-3xl font-bold text-gray-700' > Beispiel< / h3 > < div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data Person = P { name :: String
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, addr :: Address
, salary :: Int }
data Address = A { road :: String
, city :: String
, postcode :: String }
-- autogeneriert unten anderem: addr :: Person -> Address
setName :: String -> Person -> Person
setName n p = p { name = n } --record update notation
setPostcode :: String -> Person -> Person
setPostcode pc p
= p { addr = addr p { postcode = pc } }
-- update of a record inside a record< / code > < / pre > < / div > < h3 id = 'probleme' class = 'mt-6 mb-2 text-3xl font-bold text-gray-700' > Probleme< / h3 >
< p class = 'mb-3' >
Probleme mit diesem Code:
< / p >
< ul class = 'my-3 ml-6 space-y-1 list-disc' >
< li >
für 1-Dimensionale Felder ist die record-syntax ok.
< / li >
< li >
tiefere Ebenen nur umständlich zu erreichen
< / li >
< li >
eigentlich wollen wir nur pe in p setzen, müssen aber über addr etc. gehen.
< / li >
< li >
wir brauchen wissen über die “Zwischenstrukturen”, an denen wir nicht interessiert sind
< / li >
< / ul >
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< h3 id = 'was-wir-gern-hätten' class = 'mt-6 mb-2 text-3xl font-bold text-gray-700' > Was wir gern hätten< / h3 > < div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data Person = P { name :: String
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, addr :: Address
, salary :: Int }
-- a lens for each field
lname :: Lens' Person String
laddr :: Lens' Person Adress
lsalary :: Lens' Person Int
-- getter/setter for them
view :: Lens' s a -> s -> a
set :: Lens' s a -> a -> s -> s
-- lens-composition
composeL :: Lens' s1 s2 -> Lens s2 a -> Lens' s1 a< / code > < / pre > < / div > < h3 id = 'wie-uns-das-hilft' class = 'mt-6 mb-2 text-3xl font-bold text-gray-700' > Wie uns das hilft< / h3 >
< p class = 'mb-3' >
Mit diesen Dingen (wenn wir sie hätten) könnte man dann
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data Person = P { name :: String
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, addr :: Address
, salary :: Int }
data Address = A { road :: String
, city :: String
, postcode :: String }
setPostcode :: String -> Person -> Person
setPostcode pc p
= set (laddr `composeL` lpostcode) pc p< / code > < / pre > < / div >
< p class = 'mb-3' >
machen und wäre fertig.
< / p >
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< h2 id = 'trivialer-ansatz' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Trivialer Ansatz< / h2 > < h3 id = 'gettersetter-als-lens-methoden' class = 'mt-6 mb-2 text-3xl font-bold text-gray-700' > Getter/Setter als Lens-Methoden< / h3 > < div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data LensR s a = L { viewR :: s -> a
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, setR :: a -> s -> s }
composeL (L v1 u1) (L v2 u2)
= L (\s -> v2 (v1 s))
(\a s -> u1 (u2 a (v1 s)) s)< / code > < / pre > < / div > < h3 id = 'wieso-ist-das-schlecht' class = 'mt-6 mb-2 text-3xl font-bold text-gray-700' > Wieso ist das schlecht?< / h3 >
< ul class = 'my-3 ml-6 space-y-1 list-disc' >
< li >
extrem ineffizient
< / li >
< / ul >
< p class = 'mb-3' >
Auslesen traversiert die Datenstruktur, dann wird die Funktion angewendet und zum setzen wird die Datenstruktur erneut traversiert:
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > over :: LensR s a -> (a -> a) -> s -> s
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over ln f s = setR l (f (viewR l s)) s< / code > < / pre > < / div >
< ul class = 'my-3 ml-6 space-y-1 list-disc' >
< li >
Lösung: modify-funktion hinzufügen
< / li >
< / ul >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data LensR s a
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= L { viewR :: s -> a
, setR :: a -> s -> s
, mod :: (a-> a) -> s -> s
, modM :: (a-> Maybe a) -> s -> Maybe s
, modIO :: (a-> IO a) -> s -> IO s }< / code > < / pre > < / div >
< p class = 'mb-3' >
Neues Problem: Für jeden Spezialfall muss die Lens erweitert werden.
< / p >
< h3 id = 'something-in-common' class = 'mt-6 mb-2 text-3xl font-bold text-gray-700' > Something in common< / h3 >
< p class = 'mb-3' >
Man kann alle Monaden abstrahieren. Functor reicht schon:
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data LensR s a
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= L { viewR :: s -> a
, setR :: a -> s -> s
, mod :: (a-> a) -> s -> s
, modF :: Functor f => (a-> f a) -> s -> f s }< / code > < / pre > < / div >
< p class = 'mb-3' >
Idee: Die 3 darüberliegenden durch modF ausdrücken.
< / p >
< h3 id = 'typ-einer-lens' class = 'mt-6 mb-2 text-3xl font-bold text-gray-700' > Typ einer Lens< / h3 >
< p class = 'mb-3' >
Wenn man das berücksichtigt, dann hat einen Lens folgenden Typ:
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > type Lens' s a = forall f. Functor f
=> (a -> f a) -> s -> f s< / code > < / pre > < / div >
< p class = 'mb-3' >
Allerdings haben wir dann noch unseren getter/setter:
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data LensR s a = L { viewR :: s -> a
, setR :: a -> s -> s }< / code > < / pre > < / div >
< p class = 'mb-3' >
Stellt sich raus: Die sind isomorph! Auch wenn die von den Typen her komplett anders aussehen.
< / p >
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< h2 id = 'benutzen-einer-lens-als-setter' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Benutzen einer Lens als Setter< / h2 > < div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > set :: Lens' s a -> (a -> s -> s)
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set ln a s = --...umm...
--:t ln => (a -> f a) -> s -> f s
-- => get s out of f s to return it< / code > < / pre > < / div >
< p class = 'mb-3' >
Wir können für f einfach die “Identity”-Monade nehmen, die wir nachher wegcasten können.
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > newtype Identity a = Identity a
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-- Id :: a -> Identity a
runIdentity :: Identity s -> s
runIdentity (Identity x) = x
instance Functor Identity where
fmap f (Identity x) = Identity (f x)< / code > < / pre > < / div >
< p class = 'mb-3' >
somit ist set einfach nur
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > set :: Lens' s a -> (a -> s -> s)
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set ln x s
= runIdentity (ls set_fld s)
where
set_fld :: a -> Identity a
set_fld _ = Identity x
-- a was the OLD value.
-- We throw that away and set the new value< / code > < / pre > < / div >
< p class = 'mb-3' >
oder kürzer (für nerds wie den Autor der Lens-Lib)
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > set :: Lens' s a -> (a -> s -> s)
set ln x = runIdentity . ln (Identity . const x)< / code > < / pre > < / div > < h2 id = 'benutzen-einer-lens-als-modify' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Benutzen einer Lens als Modify< / h2 >
< p class = 'mb-3' >
Dasselbe wie Set, nur dass wir den Parameter nicht entsorgen, sondern in die mitgelieferte Funktion stopfen.
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > over :: Lens' s a -> (a -> a) -> s -> s
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over ln f = runIdentity . ln (Identity . f)< / code > < / pre > < / div > < h2 id = 'benutzen-einer-lens-als-getter' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Benutzen einer Lens als Getter< / h2 > < div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > view :: Lens' s a -> (s -> a)
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view ln s = --...umm...
--:t ln => (a -> f a) -> s -> f s
-- => get a out of the (f s) return-value
-- Wait, WHAT?< / code > < / pre > < / div >
< p class = 'mb-3' >
Auch hier gibt es einen netten Funktor. Wir packen das “a” einfach in das “f” und werfen das “s” am Ende weg.
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > newtype Const v a = Const v
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getConst :: Const v a -> v
getConst (Const x) = x
instance Functor (Const v) where
fmap f (Const x) = Const x
-- throw f away. Nothing changes our const!< / code > < / pre > < / div >
< p class = 'mb-3' >
somit ergibt sich
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > view :: Lens' s a -> (s -> a)
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view ln s
= getConst (ln Const s)
-- Const :: s -> Const a s< / code > < / pre > < / div >
< p class = 'mb-3' >
oder nerdig
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > view :: Lens' s a -> (s -> a)
view ln = getConst . ln Const< / code > < / pre > < / div > < h2 id = 'lenses-bauen' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Lenses bauen< / h2 >
< p class = 'mb-3' >
Nochmal kurz der Typ:
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > type Lens' s a = forall f. Functor f
=> (a -> f a) -> s -> f s< / code > < / pre > < / div >
< p class = 'mb-3' >
Für unser Personen-Beispiel vom Anfang:
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data Person = P { _name :: String, _salary :: Int }
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name :: Lens' Person String
-- name :: Functor f => (String -> f String)
-- -> Person -> f Person
name elt_fn (P n s)
= fmap (\n' -> P n' s) (elt_fn n)
-- fmap :: Functor f => (a-> b) -> f a -> f b - der Funktor, der alles verknüpft
-- \n' -> .. :: String -> Person - Funktion um das Element zu lokalisieren (WO wird ersetzt/gelesen/...)
-- elt_fn n :: f String - Funktion um das Element zu verändern (setzen, ändern, ...)< / code > < / pre > < / div >
< p class = 'mb-3' >
Die Lambda-Funktion ersetzt einfach den Namen. Häufig sieht man auch
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > name elt_fn (P n s)
= (\n' -> P n' s) < $> (elt_fn n)
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-- | Focus | |Function|< / code > < / pre > < / div > < h2 id = 'wie-funktioniert-das-intern' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Wie funktioniert das intern?< / h2 > < div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > view name (P {_name="Fred", _salary=100})
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-- inline view-function
= getConst (name Const (P {_name="Fred", _salary=100})
-- inline name
= getConst (fmap (\n' -> P n' 100) (Const "Fred"))
-- fmap f (Const x) = Const x - Definition von Const
= getConst (Const "Fred")
-- getConst (Const x) = x
= "Fred"< / code > < / pre > < / div >
< p class = 'mb-3' >
Dieser Aufruf hat KEINE Runtime-Kosten, weil der Compiler direkt die Adresse des Feldes einsetzen kann. Der gesamte Boilerplate-Code wird vom Compiler wegoptimiert.
< / p >
< p class = 'mb-3' >
Dies gilt für jeden Funktor mit newtype, da das nur ein Typalias ist.
< / p >
< h2 id = 'composing-lenses-und-deren-benutzung' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Composing Lenses und deren Benutzung< / h2 >
< p class = 'mb-3' >
Wie sehen denn die Typen aus?
< / p >
< p class = 'mb-3' >
Wir wollen ein
< / p >
< blockquote class = 'py-0.5 px-4 mb-3 italic border-l-4 bg-gray-50 text-gray-600 border-gray-400 quote' >
< p class = 'mb-3' >
Lens’ > Lens’ > Lens’
< / p >
< / blockquote >
< p class = 'mb-3' >
Wir haben 2 Lenses
< / p >
< blockquote class = 'py-0.5 px-4 mb-3 italic border-l-4 bg-gray-50 text-gray-600 border-gray-400 quote' >
< p class = 'mb-3' >
ln1 :: (s2 -> f s2) -> (s1 -> f s1) ln2 :: (a -> f a) -> (s2 -> f s2)
< / p >
< / blockquote >
< p class = 'mb-3' >
wenn man scharf hinsieht, kann man die verbinden
< / p >
< blockquote class = 'py-0.5 px-4 mb-3 italic border-l-4 bg-gray-50 text-gray-600 border-gray-400 quote' >
< p class = 'mb-3' >
ln1 . ln2 :: (a -> f s) -> (s1 -> f s1)
< / p >
< / blockquote >
< p class = 'mb-3' >
und erhält eine Lens. Sogar die Gewünschte!< br / > Somit ist Lens-Composition einfach nur Function-Composition (.).
< / p >
< h2 id = 'automatisieren-mit-template-haskell' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Automatisieren mit Template-Haskell< / h2 >
< p class = 'mb-3' >
Der Code um die Lenses zu bauen ist für records immer Identisch:
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data Person = P { _name :: String, _salary :: Int }
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name :: Lens' Person String
name elt_fn (P n s) = (\n' -> P n' s) < $> (elt_fn n)< / code > < / pre > < / div >
< p class = 'mb-3' >
Daher kann man einfach
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > import Control.Lens.TH
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data Person = P { _name :: String, _salary :: Int }
$(makeLenses ''Person)< / code > < / pre > < / div >
< p class = 'mb-3' >
nehmen, was einem eine Lens für “name” und eine Lens für “salary” generiert.< br / > Mit anderen Templates kann man auch weitere Dinge steuern (etwa wofür Lenses generiert werden, welches Prefix (statt _) man haben will etc. pp.).
< / p >
< p class = 'mb-3' >
Will man das aber haben, muss man selbst in den Control.Lens.TH-Code schauen.
< / p >
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< h2 id = 'lenses-für-den-beispielcode' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Lenses für den Beispielcode< / h2 > < div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > import Control.Lens.TH
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data Person = P { _name :: String
, _addr :: Address
, _salary :: Int }
data Address = A { _road :: String
, _city :: String
, _postcode :: String }
$(makeLenses ''Person)
$(makeLenses ''Address)
setPostcode :: String -> Person -> Person
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setPostcode pc p = set (addr . postcode) pc p< / code > < / pre > < / div > < h2 id = 'shortcuts-mit-line-noise' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Shortcuts mit “Line-Noise”< / h2 > < div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > -- ...
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setPostcode :: String -> Person -> Person
setPostcode pc p = addr . postcode .~ pc $ p
-- | Focus |set|to what|in where
getPostcode :: Person -> String
getPostcode p = p ^. $ addr . postcode
-- |from|get| Focus |< / code > < / pre > < / div >
< p class = 'mb-3' >
Es gibt drölf-zillionen weitere Infix-Operatoren (für Folds, Listenkonvertierungen, -traversierungen, …)
< / p >
< h2 id = 'virtuelle-felder' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Virtuelle Felder< / h2 >
< p class = 'mb-3' >
Man kann mit Lenses sogar Felder emulieren, die gar nicht da sind. Angenommen folgender Code:
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data Temp = T { _fahrenheit :: Float }
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$(makeLenses ''Temp)
-- liefert Lens: fahrenheit :: Lens Temp Float
centigrade :: Lens Temp Float
centigrade centi_fn (T faren)
= (\centi' -> T (cToF centi'))
< $> (centi_fn (fToC faren))
-- cToF & fToC as Converter-Functions defined someplace else< / code > < / pre > < / div >
< p class = 'mb-3' >
Hiermit kann man dann auch Funktionen, die auf Grad-Celsius rechnen auf Daten anwenden, die eigenlich nur Fahrenheit speichern, aber eine Umrechnung bereitstellen. Analog kann man auch einen Zeit-Datentypen definieren, der intern mit Sekunden rechnet (und somit garantiert frei von Fehlern wie -3 Minuten oder 37 Stunden ist)
< / p >
< h2 id = 'non-record-strukturen' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Non-Record Strukturen< / h2 >
< p class = 'mb-3' >
Das ganze kann man auch parametrisieren und auf Non-Record-Strukturen anwenden. Beispielhaft an einer Map verdeutlicht:
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > -- from Data.Lens.At
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at :: Ord k => k -> Lens' (Map k v) (Maybe v)
-- oder identisch, wenn man die Lens' auflöst:
at :: Ord k, forall f. Functor f => k -> (Maybe v -> f Maybe v) -> Map k v -> f Map k v
at k mb_fn m
= wrap < $> (mb_fn mv)
where
mv = Map.lookup k m
wrap :: Maybe v -> Map k v
wrap (Just v') = Map.insert k v' m
wrap Nothing = case mv of
Nothing -> m
Just _ -> Map.delete k m
-- mb_fn :: Maybe v -> f Maybe v< / code > < / pre > < / div > < h2 id = 'weitere-beispiele' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Weitere Beispiele< / h2 >
< ul class = 'my-3 ml-6 space-y-1 list-disc' >
< li >
< p class = 'mb-3' >
Bitfields auf Strukturen die Bits haben (Ints, …) in Data.Bits.Lens
< / p >
< / li >
< li >
< p class = 'mb-3' >
Web-scraper in Package hexpat-lens
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > p ^.. _HTML' . to allNodes
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. traverse . named "a"
. traverse . ix "href"
. filtered isLocal
. to trimSpaces< / code > < / pre > < / div >
< p class = 'mb-3' >
Zieht alle externen Links aus dem gegebenen HTML-Code in p um weitere ziele fürs crawlen zu finden.
< / p >
< / li >
< / ul >
< h2 id = 'erweiterungen' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Erweiterungen< / h2 >
< p class = 'mb-3' >
Bisher hatten wir Lenses nur auf Funktoren F. Die nächstmächtigere Klasse ist Applicative.
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > type Traversal' s a = forall f. Applicative f
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=> (a -> f a) -> (s -> f s)< / code > < / pre > < / div >
< p class = 'mb-3' >
Da wir den Container identisch lassen (weder s noch a wurde angefasst) muss sich etwas anderes ändern. Statt eines einzelnen Focus erhalten wir viele Foci.
< / p >
< p class = 'mb-3' >
Was ist ein Applicative überhaupt? Eine schwächere Monade (nur 1x Anwendung und kein Bind - dafür kann man die beliebig oft hintereinanderhängen).
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > class Functor f => Applicative f where
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pure :: a -> f a
(< *> ) :: f (a -> b) -> f a -> f b
-- Monade als Applicative:
pure = return
mf < *> mx = do { f < - mf; x < - mx; return (f x) }< / code > < / pre > < / div >
< p class = 'mb-3' >
Recap: Was macht eine Lens:
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > data Adress = A { _road :: String
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, _city :: String
, _postcode :: String }
road :: Lens' Adress String
road elt_fn (A r c p) = (\r' -> A r' c p) < $> (elt_fn r)
-- | "Hole" | | Thing to put in|< / code > < / pre > < / div >
< p class = 'mb-3' >
Wenn man nun road & city gleichzeitig bearbeiten will:
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > addr_strs :: Traversal' Address String
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addr_strs elt_fn (A r c p)
= ... (\r' c' -> A r' c' p) .. (elt_fn r) .. (elt_fn c) ..
-- | function with 2 "Holes"| first Thing | second Thing< / code > < / pre > < / div >
< p class = 'mb-3' >
fmap kann nur 1 Loch stopfen, aber nicht mit n Löchern umgehen. Applicative mit < *> kann das.< br / > Somit gibt sich
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > addr_strs :: Traversal' Address String
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addr_strs elt_fn (A r c p)
= pure (\r' c' -> A r' c' p) < *> (elt_fn r) < *> (elt_fn c)
-- lift in Appl. | function with 2 "Holes"| first Thing | second Thing
-- oder kürzer
addr_strs :: Traversal' Address String
addr_strs elt_fn (A r c p)
= (\r' c' -> A r' c' p) < $> (elt_fn r) < *> (elt_fn c)
-- pure x < *> y == x < $> y< / code > < / pre > < / div >
< p class = 'mb-3' >
Wie würd eine modify-funktion aussehen?
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > over :: Lens' s a -> (a -> a) -> s -> s
over ln f = runIdentity . ln (Identity . f)
over :: Traversal' s a -> (a -> a) -> s -> s
over ln f = runIdentity . ln (Identity . f)< / code > < / pre > < / div >
< p class = 'mb-3' >
Der Code ist derselbe - nur der Typ ist generischer. Auch die anderen Dinge funktioniert diese Erweiterung (für Identity und Const muss man noch ein paar dummy-Instanzen schreiben um sie von Functor auf Applicative oder Monad zu heben
< / p >
< ul class = 'my-3 ml-6 space-y-1 list-disc' >
< li >
konkret reicht hier die Instanzierung von Monoid). In der Lens-Library ist daher meist Monad m statt Functor f gefordert.
< / li >
< / ul >
< h2 id = 'wozu-dienen-die-erweiterungen' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Wozu dienen die Erweiterungen?< / h2 >
< p class = 'mb-3' >
Man kann mit Foci sehr selektiv vorgehen. Auch kann man diese durch Funktionen steuern. Beispisweise eine Funktion anwenden auf
< / p >
< ul class = 'my-3 ml-6 space-y-1 list-disc' >
< li >
Jedes 2. Listenelement
< / li >
< li >
Alle graden Elemente in einem Baum
< / li >
< li >
Alle Namen in einer Tabelle, deren Gehalt > 10.000€ ist
< / li >
< / ul >
< p class = 'mb-3' >
Traversals und Lenses kann man trivial kombinieren (< code class = 'py-0.5 px-0.5 bg-gray-100' > lens . lens< / code > => < code class = 'py-0.5 px-0.5 bg-gray-100' > lens< / code > , < code class = 'py-0.5 px-0.5 bg-gray-100' > lens . traversal< / code > => < code class = 'py-0.5 px-0.5 bg-gray-100' > traversal< / code > etc.)
< / p >
< h2 id = 'wie-es-in-lens-wirklich-aussieht' class = 'inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2' > Wie es in Lens wirklich aussieht< / h2 >
< p class = 'mb-3' >
In diesem Artikel wurde nur auf Monomorphic Lenses eingegangen. In der richtigen Library ist eine Lens
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > type Lens' s a = Lens s s a a
type Lens s t a b = forall f. Functor f => (a -> f b) -> (s -> f t)< / code > < / pre > < / div >
< p class = 'mb-3' >
sodass sich auch die Typen ändern können um z.B. automatisch einen Konvertierten (sicheren) Typen aus einer unsicheren Datenstruktur zu geben.
< / p >
< p class = 'mb-3' >
Die modify-Funktion over ist auch
< / p >
< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > > over :: Profunctor p => Setting p s t a b -> p a b -> s -> t< / code > < / pre > < / div >
< blockquote class = 'py-0.5 px-4 mb-3 italic border-l-4 bg-gray-50 text-gray-600 border-gray-400 quote' >
< p class = 'mb-3' >
< em > Edward is deeply in thrall to abstractionitis< / em > - Simon Peyton Jones
< / p >
< / blockquote >
< p class = 'mb-3' >
Lens alleine definiert 39 newtypes, 34 data-types und 194 Typsynonyme…< br / > Ausschnitt
< / p >
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< div class = 'py-0.5 mb-3 text-sm' > < pre > < code class = 'haskell language-haskell' > -- traverseOf :: Functor f => Iso s t a b -> (a -> f b) -> s -> f t
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-- traverseOf :: Functor f => Lens s t a b -> (a -> f b) -> s -> f t
-- traverseOf :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t
traverseOf :: Over p f s t a b -> p a (f b) -> s -> f t< / code > < / pre > < / div >
< p class = 'mb-3' >
dafuq?
< / p >
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Fortgeschrittene funktionale Programmierung in Haskell
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< div class = 'fixed w-screen h-screen inset-0' onclick = 'window.emanote.stork.toggleSearch()' > < / div >
< div class = 'container mx-auto p-10 mt-10' >
< div class = 'stork-wrapper-flat container mx-auto' >
< input id = 'stork-search-input' data-stork = 'emanote-search' class = 'stork-input' placeholder = 'Search (Ctrl+K) ...' / >
< div data-stork = 'emanote-search-output' class = 'stork-output' > < / div >
< / div >
< / div >
< / div >
< / body >
< / html >
