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what-did-category-theory-do-for-us.lyx
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what-did-category-theory-do-for-us.lyx
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#LyX 2.3 created this file. For more info see http://www.lyx.org/
\lyxformat 544
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\title[What did category theory ever do for us]{What did category theory ever do for us (functional programmers)}
\subtitle{An extreme pragmatic un-academic approach}
\author{Sergei Winitzki}
\date{2019-11-15}
\institute[SBTB]{Scale by the Bay}
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\begin_layout Plain Layout
\backslash
frame{
\backslash
titlepage}
\end_layout
\end_inset
\begin_inset Note Note
status collapsed
\begin_layout Plain Layout
Beginning of slides.
\end_layout
\end_inset
\end_layout
\begin_layout Frame
\begin_inset Argument 4
status open
\begin_layout Plain Layout
Functional programming, pragmatically
\end_layout
\end_inset
What do functional programmers do most often (and most benefit from)?
\end_layout
\begin_layout Frame
\begin_inset space ~
\end_inset
\begin_inset Newline newline
\end_inset
\begin_inset VSpace 285baselineskip%
\end_inset
\end_layout
\begin_layout Itemize
Work with collections using methods
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
map
\end_layout
\end_inset
,
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
filter
\end_layout
\end_inset
,
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
fold
\end_layout
\end_inset
,
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
flatMap
\end_layout
\end_inset
\end_layout
\begin_layout Itemize
Use
\series bold
disjunctive types
\series default
(
\begin_inset Quotes eld
\end_inset
case classes
\begin_inset Quotes erd
\end_inset
,
\begin_inset Quotes eld
\end_inset
algebraic data types
\begin_inset Quotes erd
\end_inset
) for domain modeling
\end_layout
\begin_layout Itemize
Use type constructors with arbitrary type parameters
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
Flow[KafkaMessage[MyData], KafkaMessage[MyResult], NotUsed]
\end_layout
\end_inset
\end_layout
\begin_layout Itemize
Use
\series bold
functor blocks
\series default
(
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
for
\end_layout
\end_inset
/
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
yield
\end_layout
\end_inset
syntax,
\begin_inset Quotes eld
\end_inset
for comprehensions
\begin_inset Quotes erd
\end_inset
)
\begin_inset listings
inline false
status open
\begin_layout Plain Layout
for {
\end_layout
\begin_layout Plain Layout
x <- Future(...)
\end_layout
\begin_layout Plain Layout
y <- Future(...)
\end_layout
\begin_layout Plain Layout
} yield f(x, y)
\end_layout
\end_inset
\end_layout
\begin_layout Itemize
Use curried functions (e.g.
\begin_inset space ~
\end_inset
Akka Streams)
\begin_inset listings
inline false
status open
\begin_layout Plain Layout
GraphDSL.create { implicit builder => (source, sink) => ...
}
\end_layout
\end_inset
\end_layout
\begin_layout Standard
No category theory needed so far!
\end_layout
\begin_layout Itemize
Programmers can learn these features of Scala and become productive
\end_layout
\begin_layout Standard
\begin_inset space ~
\end_inset
\end_layout
\begin_layout Standard
\begin_inset Separator parbreak
\end_inset
\end_layout
\begin_layout Frame
\begin_inset Argument 4
status open
\begin_layout Plain Layout
Uses of category theory.
I.
Typeclasses with laws
\end_layout
\end_inset
\begin_inset Separator latexpar
\end_inset
\end_layout
\begin_deeper
\begin_layout Standard
Typeclasses: type constructors with methods
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
map
\end_layout
\end_inset
,
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
filter
\end_layout
\end_inset
,
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
fold
\end_layout
\end_inset
,
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
flatMap
\end_layout
\end_inset
\end_layout
\begin_layout Standard
To be useful for programming, the methods must satisfy certain laws
\end_layout
\begin_layout Itemize
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
map
\end_layout
\end_inset
: identity, composition
\end_layout
\begin_layout Itemize
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
filter
\end_layout
\end_inset
: identity, composition, partial function, naturality
\end_layout
\begin_layout Itemize
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
fold
\end_layout
\end_inset
(traverse): identity, composition, naturality
\end_layout
\begin_layout Itemize
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
flatMap
\end_layout
\end_inset
: identity, composition, naturality
\end_layout
\end_deeper
\begin_layout Standard
\begin_inset Separator parbreak
\end_inset
\end_layout
\begin_layout Standard
Example of incorrect implementation of typeclasses:
\end_layout
\begin_layout Standard
\begin_inset listings
inline false
status open
\begin_layout Plain Layout
case class Bad[A](x: Int, do: A => Int) {
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\begin_layout Plain Layout
def map[B](f: A => B): Bad[B] = Bad(x, _ => x)
\end_layout
\begin_layout Plain Layout
def flatMap[B](f: A => Bad[B]): Bad[B] = Bad(x, _ => x)
\end_layout
\begin_layout Plain Layout
def filter(p: A => Boolean): Bad[A] = this
\end_layout
\begin_layout Plain Layout
}
\end_layout
\end_inset
We can now use
\begin_inset listings
inline true
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for
\end_layout
\end_inset
/
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
yield
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syntax with sources of type
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Bad
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\end_inset
...
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\begin_layout Standard
...but the code will have strange, hard-to-find bugs:
\begin_inset listings
inline false
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val b: Bad[String] = Bad(1, _.length)
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val c: Bad[String] = for {
\end_layout
\begin_layout Plain Layout
x <- b // x : String ??
\end_layout
\begin_layout Plain Layout
y = x
\end_layout
\begin_layout Plain Layout
} yield y
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
scala> b.do(
\begin_inset Quotes eld
\end_inset
abc
\begin_inset Quotes erd
\end_inset
)
\end_layout
\begin_layout Plain Layout
res0: Int = 3
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
scala> c.do("abc")
\end_layout
\begin_layout Plain Layout
res1: Int = 1
\end_layout
\end_inset
\end_layout
\begin_layout Standard
The methods of
\begin_inset listings
inline true
status open
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Bad
\end_layout
\end_inset
are not lawful (and
\emph on
cannot
\emph default
be!)
\end_layout
\begin_layout Standard
\begin_inset Separator parbreak
\end_inset
\end_layout
\begin_layout Frame
\begin_inset Argument 4
status open
\begin_layout Plain Layout
Finding patterns in typeclass laws.
I.
Type signatures
\end_layout
\end_inset
\begin_inset Separator latexpar
\end_inset
\end_layout
\begin_deeper
\begin_layout Standard
One can transform and simplify typeclass laws into a form of
\begin_inset Quotes eld
\end_inset
lifting
\begin_inset Quotes erd
\end_inset
\end_layout
\begin_layout Itemize
Need to derive equivalent formulations of typeclass laws...
\end_layout
\begin_deeper
\begin_layout Itemize
...two months later:
\end_layout
\end_deeper
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\align center
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Typeclass
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\begin_inset Text
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\series bold
Method
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\series bold
Type signature
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
functor
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
fmap
\end_layout
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
(A => B) => F[A] => F[B]
\end_layout
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
contrafunctor
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
cmap
\end_layout
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
(B => A) => F[A] => F[B]
\end_layout
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
filterable functor
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
liftOpt
\end_layout
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset listings
inline true
status open
\begin_layout Plain Layout
(A => Option[B]) => F[A] => F[B]
\end_layout
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
monad
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset listings
inline true
status open
\begin_layout Plain Layout