The document provides a historical overview and examples of local functions across various programming languages, starting from ALGOL 60 to contemporary uses in C# and F#. It includes references to significant philosophical quotes and timelines of programming developments, particularly focusing on factorial implementations and pattern matching techniques. Various programming paradigms and their evolution with respect to local functions are illustrated through code snippets.

3. 88
mph

5. YEAR
2016
GitHub

8. YEAR
440 BCE
Herodotus

9. “Herodotus of
Halicarnassus here
presents his research
so that human events
do not fade with
time.”
Herodotus, The Histories
Book I, Proem
trans. Andrea L. Purvis

11. YEAR
404 BCE
Lysander

12. “[Sparta] they would never
reduce to slavery a city
which was itself an integral
portion of Hellas, and had
performed a great and
noble service to Hellas in
the most perilous of
emergencies.”
Xenophon, Hellenica
Book 2, 2.20
trans. H. G. Dakyns

14. YEAR
399 BCE
Socrates

15. “[Writing offers readers] the
appearance of wisdom, not true
wisdom, for they will read many
things without instruction and
will therefore seem to know
many things, when they are for
the most part ignorant and hard
to get along with, since they are
not wise, but only appear wise.”
Plato, Phaedrus
275a-b
trans. Harold N. Fowler

17. YEAR
1822
Hegel

18. “World history is
the record of the
spirit's efforts to
attain knowledge of
what it is in itself.”
Hegel, Lectures on the
Philosophy of World History
Introduction
trans. Johannes Hoffmeister

20. Timeline
• Local Functions
• Tuples
• Records
• Pattern Matching
• Ref Locals / Ref Returns
• Binary Literals / Digit Separators

21. Timeline
• Local Functions
• Tuples
• Pattern Matching

23. Timeline
• Local Functions
• Tuples
• Pattern Matching

25. YEAR
1960
Algol 60

26. Local Functions
{Algol 60}
begin
comment classic recursive procedure;
integer nn, nf;
integer procedure factorial(n); value n; integer n;
begin
if n <= 1 then factorial := 1
else factorial := n * factorial(n-1)
end;
nn := 5;
nf := factorial(nn);
outinteger ( 1 , nf)
end
taken from: http://algol60.org/lego/procedure11.a60Algol 60

27. Local Functions
{Algol 60}
integer procedure factorial(n); value n; integer n;
begin
if n <= 1 then factorial := 1
else factorial := n * factorial(n-1)
end;
nn := 5;
nf := factorial(nn);
taken from: http://algol60.org/lego/procedure11.a60Algol 60

29. YEAR
2015
C# 6

30. Local Functions
{without language support}
private struct locals
{
public int x;
}
static void Main(string[] args)
{
var x = 42;
var local = new locals {x = x};
AddOne(ref local);
x = local.x;
WriteLine($"x + 1 = {x}");
}
private static void AddOne(ref locals implicits)
{
implicits.x += 1;
}
C# 6

32. YEAR
2017
C# 7

33. Local Functions
{with language support}
static void Main(string[] args)
{
var x = 42;
void AddOne()
{
x += 1;
}
AddOne();
WriteLine($"x + 1 = {x}");
}
C# 7

34. Functions

35. Functions
{basic}
function outputinput

36. Functions
{real world}
function
outputinput
effect
side
effect

37. Functions
{basic}
Hello Lengthname

38. Functions
{basic}
public int Hello(string name)
{
var time = DateTime.Now;
Console.Write($"Hello {name} it is now {time}");
return name.Length;
}
C# 6

39. Functions
{real world}
Hello
Lengthname
DateTime Console

40. Functions
{real world}
public int Hello(string name)
{
var time = DateTime.Now;
Console.Write($"Hello {name} it is now {time}");
return name.Length;
}
C# 6

42. YEAR
2017
C# 7

43. Local Functions
{“realistic”}
static void Main(string[] args)
{
var program = new Program();
IEnumerable<int> values = new[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
string FormatValues()
{
return string.Join(",", values);
}
Console.WriteLine($"before: {FormatValues()}");
values = program.RealistCode(values);
Console.WriteLine($"after: {FormatValues()}");
}
public IEnumerable<int> RealistCode(IEnumerable<int> values)
{
if (values == null)
throw new ArgumentException("values cannot be null");
if (!values.Any())
throw new ArgumentException("must have at least one element in values");
IEnumerable <int> Rules()
{
return values
.Where(x => x > 2)
.Where(x => x%2 == 1);
}
return Rules();
}
C# 7

44. Local Functions
{“realistic”}
static void Main(string[] args)
{
var program = new Program();
IEnumerable<int> values = new[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
string FormatValues()
{
return string.Join(",", values);
}
Console.WriteLine($"before: {FormatValues()}");
values = program.RealistCode(values);
Console.WriteLine($"after: {FormatValues()}");
}
C# 7

45. Local Functions
{really “realistic”}
public IEnumerable<int> RealistCode(IEnumerable<int> values)
{
if (values == null)
throw new ArgumentException("values cannot be null");
if (!values.Any())
throw new ArgumentException(
"must have at least one element in values");
IEnumerable <int> Rules()
{
return values
.Where(x => x > 2)
.Where(x => x%2 == 1);
}
return Rules();
}
C# 7

46. Local Functions
{really “realistic”}
public IEnumerable<int> RealistCode(IEnumerable<int> values)
{
Precondition();
return values
.Where(x => x > 2)
.Where(x => x%2 == 1);
void Precondition()
{
if (values == null)
throw new ArgumentException("values cannot be null");
if (!values.Any())
throw new ArgumentException("must have at least one element in values");
}
}
C# 7

47. Design
By Contract

48. YEAR
1985
Eiffel

49. Local Functions
{design by contract}
note
description : "example of factorial"
class
APPLICATION
create
make
feature -- Initialization
make
local
n: NATURAL
do
n := 3
print ("%NFactorial of " + n.out + " = ")
print (recursive_factorial (n))
end
feature -- Access
recursive_factorial (n: NATURAL): NATURAL
require
n >= 0
do
if n = 0 then
Result := 1
else
Result := n * recursive_factorial (n - 1)
end
end
end
Eiffel

50. Local Functions
{design by contract}
feature -- Access
recursive_factorial (n: NATURAL): NATURAL
require
n >= 0
do
if n = 0 then
Result := 1
else
Result := n * recursive_factorial (n - 1)
end
end
end
Eiffel

52. YEAR
2009
Clojure

53. Local Functions
{design by contract}
(ns com.blogspot.comp-phil.factorial)
;; no tail call optimization
(defn factorial [n]
{:pre [((comp not neg?) n)]}
(if (= n 0)
1
(* n (factorial (dec n)))))
(factorial 1)
(factorial 5)
Clojure

54. Local Functions
{design by contract}
(defn factorial [n]
{:pre [((comp not neg?) n)]}
(if (= n 0)
1
(* n (factorial (dec n)))))
Clojure

56. YEAR
2017
C# 7

57. Local Functions
{design by contract}
static void Main(string[] args)
{
// no tail call optimization
long Factorial(int x)
{
if (x < 0)
throw new ArgumentException(“value < 0”);
if (x <= 1) return 1;
return x * Factorial(x-1);
}
Console.WriteLine($"1! = {Factorial(1)}");
Console.WriteLine($"3! = {Factorial(3)}");
Console.WriteLine($"20! = {Factorial(20)}");
}
C# 7

58. Tail Call
Optimization

59. YEAR
2017
C# 7

60. Local Functions
{no tail call}
static void Main(string[] args)
{
// no tail call optimization
long Factorial(int x)
{
if (x <= 1) return 1;
return x * Factorial(x-1);
}
Console.WriteLine($"1! = {Factorial(1)}");
Console.WriteLine($"3! = {Factorial(3)}");
Console.WriteLine($"20! = {Factorial(20)}");
}
C# 7

61. Console.WriteLine($"3! = {Factorial(3)}");
long Factorial(int x)
{
if (x <= 1) return x;
return x * Factorial(x-1);
}
x = 3
3 * ?
C# 7

62. Console.WriteLine($"3! = {Factorial(3)}");
long Factorial(int x)
{
if (x <= 1) return x;
return x * Factorial(x-1);
}
x = 3
3 *
x = 2
2 * ?
C# 7

63. Console.WriteLine($"3! = {Factorial(3)}");
x = 3
3 *
long Factorial(int x)
{
if (x <= 1) return x;
return x * Factorial(x-1);
}
x = 2
2 *
x = 1
1
C# 7

64. Console.WriteLine($"3! = {Factorial(3)}");
x = 3
3 *
long Factorial(int x)
{
if (x <= 1) return x;
return x * Factorial(x-1);
}
x = 2
2
C# 7

65. Console.WriteLine($"3! = {Factorial(3)}");
x = 3
6
long Factorial(int x)
{
if (x <= 1) return x;
return x * Factorial(x-1);
}
C# 7

67. Local Functions
{tail call}
static void Main(string[] args)
{
// would have tail call optimization if supported
long Factorial(int x)
{
long Aux(long acc, int n)
{
if (n <= 1) return acc;
return Aux(acc * n, n - 1);
}
return Aux(1, x);
}
Console.WriteLine($"1! = {Factorial(1)}");
Console.WriteLine($"3! = {Factorial(3)}");
Console.WriteLine($"20! = {Factorial(20)}");
}
C# 7

68. Console.WriteLine($"3! = {Factorial(3)}");
acc = 1
n = 3
long Aux(long acc, int n)
{
if (n <= 1) return acc;
return Aux(acc * n, n - 1);
}
C# 7

69. Console.WriteLine($"3! = {Factorial(3)}");
acc = 1
n = 3
acc = 3
n = 2
long Aux(long acc, int n)
{
if (n <= 1) return acc;
return Aux(acc * n, n - 1);
}
C# 7

70. Console.WriteLine($"3! = {Factorial(3)}");
acc = 1
n = 3
acc = 3
n = 2
acc = 6
n = 1
long Aux(long acc, int n)
{
if (n <= 1) return acc;
return Aux(acc * n, n - 1);
}
C# 7

72. Local Functions
{“tail call optimization”}
static void Main(string[] args)
{
// simulated tail call optimization
long Factorial(int n)
{
long acc = 1;
top:
if (n <= 1) return acc;
acc *= n;
n--;
goto top;
}
Console.WriteLine($"1! = {Factorial(1)}");
Console.WriteLine($"3! = {Factorial(3)}");
Console.WriteLine($"20! = {Factorial(20)}");
}
C# 7

73. Local Functions
{“tail call optimization”}
static void Main(string[] args)
{
// simulated tail call optimization
long Factorial(int n)
{
long acc = 1;
top:
if (n <= 1) return acc;
acc *= n;
n--;
goto top;
}
Console.WriteLine($"1! = {Factorial(1)}");
Console.WriteLine($"3! = {Factorial(3)}");
Console.WriteLine($"20! = {Factorial(20)}");
}
C# 7

74. Console.WriteLine($"3! = {Factorial(3)}");
acc = 1
n = 3
long Factorial(int n)
{
long acc = 1;
top:
if (n <= 1) return acc;
acc *= n;
n--;
goto top;
}C# 7

75. Console.WriteLine($"3! = {Factorial(3)}");
acc = 3
n = 2
long Factorial(int n)
{
long acc = 1;
top:
if (n <= 1) return acc;
acc *= n;
n--;
goto top;
}C# 7

76. Console.WriteLine($"3! = {Factorial(3)}");
acc = 6
n = 1
long Factorial(int n)
{
long acc = 1;
top:
if (n <= 1) return acc;
acc *= n;
n--;
goto top;
}C# 7

78. YEAR
2010
F#

79. Local Functions
{tail call optimization}
F#
module Factorial =
let factorial x =
let rec aux m x =
match x with
| 0 -> m
| _ -> aux (m*x) (x-1)
aux 1 x

81. Timeline
• Local Functions
• Tuples
• Pattern Matching

82. Tuples
tuple
item 1 item 2

83. Tuples
“Hello” 42

85. YEAR
2010
C# 4.0

86. Tuple
{mostly everything}
static void Main(string[] args)
{
Console.WriteLine("1! = “ + Factorial(1));
Console.WriteLine("5! = “ + Factorial(5));
Console.WriteLine("20! = “ + Factorial(20));
}
private static long Factorial(int x)
{
return FactorialAux(new Tuple<int, int>(1, x));
}
private static long FactorialAux(Tuple<int, int> t)
{
if (t.Item2 <= 1) return t.Item1;
var r = new Tuple<int, int>(t.Item1*t.Item2, t.Item2 - 1);
return FactorialAux(r);
}
C# 4.0

88. YEAR
2017
C# 7

89. Tuple
{mostly everything}
static void Main(string[] args)
{
long Factorial(int x)
{
long Aux((int acc, int n) a)
{
if (a.n <= 1) return a.acc;
var r = (a.acc * a.n, a.n - 1);
return Aux(r);
}
(int, int) t = (1, x);
return Aux(t);
}
Console.WriteLine($"1! = {Factorial(1)}");
Console.WriteLine($"3! = {Factorial(3)}");
Console.WriteLine($"20! = {Factorial(20)}");
}
C# 7

91. Timeline
• Local Functions
• Tuples
• Pattern Matching

92. Pattern Matching
type 1
type 2
other
type 2 Matcher

94. YEAR
2010
C# 4.0

95. Pattern Matching
{types}
static void Main(string[] args)
{
var values = new List<object>
{1, (short) 2,
(Int32) 3, null,
new {}, "no", 1.2d};
foreach (var value in values)
{
var x = value as int;
if (x != null)
Console.WriteLine("got “ + x);
}
}
C# 4.0

97. YEAR
2017
C# 7

98. Pattern Matching
{types}
static void Main(string[] args)
{
var values = new List<object>
{1, (short) 2,
(Int32) 3, null,
new {}, "no", 1.2d};
foreach (var value in values)
{
if (value is int x)
Console.WriteLine($"got {x}");
}
}
C# 7

99. Function
Pattern
Matching

100. YEAR
1973
ML

101. Pattern Matching
{functional pattern matching}
fun factorial(0) = 1
| factorial(n) = n * factorial(n-1);
print(
"5! =" ^ (Int.toString (factorial(5))) ^ "n");
ML

103. YEAR
2004
Scala

104. Pattern Matching
{functional pattern matching}
import scala.annotation.tailrec
object factorial {
def apply(x: Int): Int = {
@tailrec
def go(m: Int, x: Int): Int = x match {
case 0 => m
case _ => go(x*m, x-1)
}
go(1, x)
}
}
println(s"5! = ${factorial(5)}")
Scala

106. YEAR
2018
C# 8

107. Pattern Matching
{functional pattern matching}
long Factorial(int x)
{
long Aux(int m, int x)
{
match(x)
{
case 0: return m;
default: return Aux(x*m, x-1);
}
}
return Aux(1, x);
}
Console.WriteLine($"5! = {Factorial(5)}");
C# 8

109. YEAR
2018
C# 8

110. Pattern Matching
{types}
static void Main(string[] args)
{
var values = new List<object>
{1, (short) 2,
(Int32) 3, null,
new {}, "no", 1.2d};
foreach (var value in values)
{
t = match(x)
{
case int _: "int";
case short _: "short";
case object _: "object";
case string _: "string";
default: "something";
}
Console.WriteLine("got “ + t);
}
}
C# 8

111. Pattern Matching
{types}
foreach (var value in values)
{
t = match(x)
{
case int _: "int";
case short _: "short";
case object _: "object";
case string _: "string";
default: "something";
}
Console.WriteLine("got “ + t);
}
C# 8

113. Thank you!
Mike Harris
@MikeMKH
http://comp-phil.blogspot.com/

115. Biography
• Tomas Petricek - "Coeffects: Context-aware programming
languages" http://tomasp.net/coeffects/
• https://github.com/dotnet/roslyn/blob/features/patterns/
docs/features/local-functions.md
• https://github.com/dotnet/roslyn/issues/347
• https://github.com/dotnet/roslyn/blob/features/patterns/
docs/features/patterns.md
• https://github.com/dotnet/roslyn/blob/master/docs/
Language%20Feature%20Status.md

116. Images
• DeLorean DMC-12 by en:user:Grenex - Wikipedia en, CC BY-SA 3.0,
https://commons.wikimedia.org/w/index.php?curid=2500249
• Herodotos by © Marie-Lan Nguyen / Wikimedia Commons, Public
Domain, https://commons.wikimedia.org/w/index.php?curid=12886457
• Lysander by Walter Crane - The story of Greece : told to boys and girls
(191-?) by Macgregor, Mary, Public Domain, https://
commons.wikimedia.org/w/index.php?curid=32804563
• Socrates by Walter Crane - The story of Greece : told to boys and girls
(191-?) by Macgregor, Mary, Public Domain, https://
commons.wikimedia.org/w/index.php?curid=32804549
• Hegel by Unknown - http://portrait.kaar.at/, Public Domain, https://
commons.wikimedia.org/w/index.php?curid=3308762