This document presents a detailed exploration of first-class patterns and pattern matching techniques in programming, particularly focusing on their implementation in languages like Haskell and Scala. It discusses the definitions, examples, limitations, and exercises related to pattern matching and first-class patterns, emphasizing their significance for abstraction and composition. Additionally, the document outlines magical patterns and their drawbacks in contrast to first-class patterns, reinforcing the importance of proper design in programming constructs.

1. First-Class Patterns
John A. De Goes - @jdegoes
Frontier Developers, February 26

2. Agenda
●
●
●
●
●
●
Intro
Pattern Matching 101
First-Class-ness 101
Magical Patterns
First-Class Patterns
Exercises

3. Intro
Pattern Matching
● Divides a (possibly infinite) set of values into
a discrete number of cases, where each case
can be handled in a uniform way
● “if” on steroids
○ Sometimes strictly more powerful (e.g. Haskell)

4. Intro - Examples
-- sign of a number
sign x |
|
|
x > 0
x == 0
x < 0
=
=
=
1
0
-1
-- take the first n elements from a list
take
take
take
0
_
n
_
[]
(x:xs)
=
=
=
[]
[]
x : take (n-1) xs
-- generate some javascript
valueToJs
valueToJs
valueToJs
valueToJs
...
:: Options -> ModuleName -> Environment -> Value -> JS
_ _ _ (NumericLiteral n) = JSNumericLiteral n
_ _ _ (StringLiteral s) = JSStringLiteral s
_ _ _ (BooleanLiteral b) = JSBooleanLiteral b

5. Intro - Examples
sealed trait Level
case object Level1 extends Level
case object Level2 extends Level
sealed trait Title
case object DBAdmin extends Title
case class SWEngineer(level: Level) extends Title
case class Employee(manager: Option[Employee], name: String, title: Title)
val employees = ???
val selfManagedLevel2Engineers = employees.collect {
case Employee(None, name, SWEngineer(Level2)) => name
}

6. Pattern Matching 101
Filter
Does it have the structure I
want? [Yes/No]
If so, extract out the pieces
that are relevant to me.
Extract

7. Pattern Matching 101
-- take the first n elements from a list
take 0
_
= []
take _
[]
= []
take n
(x:xs)
= x : take (n-1) xs
Filter - does it have non-empty list structure?
Extract - Give me ‘head’ and ‘tail’

8. Pattern Matching 101
Products
Sums
case class Employee(
sealed trait Title
manager: Option[Employee],
name:
String,
title:
case object DBAdmin extends Title
terms
Title
case class SWEngineer(level: Level)
extends Title
)
class Account {
interface Shape { }
...
class Rect extends Shape { … }
public Account(BigDecimal balance, User holder) {
class Ellipse extends Shape { … }
...
}
}
class Pentagon extends Shape { … }
terms

9. First-Class-ness 101
data Maybe a = Nothing | Just a deriving (Eq, Ord)
class Person {
public Person(String name, int age) {
...
}
}

10. First-Class-ness 101
Magic interferes with your ability to
abstract and compose.

11. Magical Patterns
Ordinary Duplication
sealed
object
…
case
case
trait Provenance
Provenance {
class Either(left: Provenance, right: Provenance) extends Provenance
class Both(left: Provenance, right: Provenance) extends Provenance
def allOf(xs: Seq[Provenance]): Provenance = {
if (xs.length == 0) Unknown
else if (xs.length == 1) xs.head
else xs.reduce(Both.apply)
}
def anyOf(xs: Seq[Provenance]): Provenance = {
if (xs.length == 0) Unknown
else if (xs.length == 1) xs.head
else xs.reduce(Either.apply)
}
}

12. Magical Patterns
Factoring
sealed
object
case
case
case
case
case
trait Provenance
Provenance {
object Unknown extends Provenance
object Value extends Provenance
class Relation(value: SqlRelation) extends Provenance
class Either(left: Provenance, right: Provenance) extends Provenance
class Both(left: Provenance, right: Provenance) extends Provenance
def allOf(xs: Seq[Provenance]): Provenance = reduce(xs)(Both.apply)
def anyOf(xs: Seq[Provenance]): Provenance = reduce(xs)(Either.apply)
private def reduce(xs: Seq[Provenance])(
f: (Provenance, Provenance) => Provenance): Provenance = {
if (xs.length == 0) Unknown
else if (xs.length == 1) xs.head
else xs.reduce(f)
}
}

13. Magical Patterns
Factoringz
sealed
object
case
case
case
case
case
trait Provenance
Provenance {
object Unknown extends Provenance
object Value extends Provenance
class Relation(value: SqlRelation) extends Provenance
class Either(left: Provenance, right: Provenance) extends Provenance
class Both(left: Provenance, right: Provenance) extends Provenance
private def strict[A, B, C](f: (A, B) => C): (A, => B) => C = (a, b) => f(a, b)
val BothMonoid
= Monoid.instance(strict[Provenance, Provenance, Provenance](Both.apply), Unknown)
val EitherMonoid = Monoid.instance(strict[Provenance, Provenance, Provenance](Either.apply), Unknown)
def allOf(xs: List[Provenance]): Provenance = Foldable[List].foldMap(xs)(identity)(BothMonoid)
def anyOf(xs: List[Provenance]): Provenance = Foldable[List].foldMap(xs)(identity)(EitherMonoid)
}

14. Magical Patterns
Toxic Duplication - Abstraction Fail
val Add = Mapping(
"(+)", "Adds two numeric values" NumericDomain,
,
(partialTyper {
case Type.Const(Data.Number(v1)) :: v2 :: Nil if (v1.signum == 0) => v2
case v1 :: Type.Const(Data.Number(v2)) :: Nil if (v2.signum == 0) => v1
case Type.Const(Data.
Int(v1)) :: Type.Const(Data.
Int(v2)) :: Nil =>
Type.Const(Data.
Int(v1 + v2))
case Type.Const(Data.Number(v1)) :: Type.Const(Data.Number(v2)) ::
Nil =>
Type.Const(Data.Dec(v1 + v2))
}) ||| numericWidening
)

15. Magical Patterns
Pattern Combinators - Composition Fail
● Product & sum
○ PartialFunction.orElse
● Negation
● Defaults
● Use-case specific

16. Magical Patterns
Magical patterns limit your ability
to abstract over patterns and to
compose them together to create new
patterns.

17. First-Class Patterns
First-class patterns are built using
other language features so you can
abstract and compose them.

18. First-Class Patterns
Haskell Example
ex4 :: Either (Int,Int) Int -> Int
ex4 a = match a $
(1+) <$> (left (pair var (cst 4)) ->> id
<|>
right var
->> id)
<|> left (pair __ var) ->> id
http://hackage.haskell.org/package/first-class-patterns

19. First-Class Patterns
“For the rest of us”
X match {
case Y => Z
}
type Pattern???

20. First-Class Patterns
Structure
Input
X match {
Output
case Y => Z
}
type Pattern???
Extraction

21. First-Class Patterns
One ‘Option’
Input
X match {
Output
case Y => Z
}
Extraction
type Pattern[X, Z] = X => Option[Z]

22. First-Class Patterns
Basic Patterns
def some[A, B](p: Pattern[A, B]): Pattern[Option[A], B] = _.flatMap(p)
def none[A, B]: Pattern[A, B] = Function.const( None)
def k[A](v0: A): Pattern[A, A] = v => if (v == v0) Some(v0) else None
def or[A, B](p1: Pattern[A, B], p2: Pattern[A, B]): Pattern[A, B] =
v => p1(v).orElse(p2(v))
scala> or(none, some(k( 2)))(Some(2))
res3: Option[Int] = Some(2)
https://gist.github.com/jdegoes/9240971

23. First-Class Patterns - JS
And Now in JavaScript….Because
http://jsfiddle.net/AvL4V/

24. First-Class Patterns
Limitations
● Extractors cannot throw away information,
leading to ‘dummy parameters’
● Negation not possible under any
circumstances
● No partiality warnings or built-in catch all

25. Exercises
1. Define a Pattern Combinator to Fix:
val Add = Mapping(
"(+)", "Adds two numeric values" NumericDomain,
,
(partialTyper {
case Type.Const(Data.Number(v1)) :: v2 :: Nil if (v1.signum == 0) => v2
case v1 :: Type.Const(Data.Number(v2)) :: Nil if (v2.signum == 0) => v1
case Type.Const(Data.
Int(v1)) :: Type.Const(Data.
Int(v2)) :: Nil =>
Type.Const(Data.
Int(v1 + v2))
case Type.Const(Data.Number(v1)) :: Type.Const(Data.Number(v2)) ::
Nil =>
Type.Const(Data.Dec(v1 + v2))
}) ||| numericWidening
)
EASY

26. Exercises
2. Define ‘Pattern’ and some core
patterns in the language of your choice
EASY

27. Exercises
3. Define an ‘And’ pattern that requires
both inputs match
EASY

28. Exercises
4. Define an alternate definition of
pattern (along with a few core patterns)
that permits pattern negation
4.b Optional: Use this to allow catch-alls
MODERATE

29. Exercises
5. Define an alternate definition of
pattern (along with a few core patterns)
that permits extractors to throw away
information
HARD

30. THANK YOU
First-Class Patterns
John A. De Goes - @jdegoes
Frontier Developers, February 26