Declarative Thinking, Declarative Practice

declarative thinking,
declarative practice
@KevlinHenney

Computer Science in the 1960s to 80s
spent a lot of effort making languages
which were as powerful as possible.
Nowadays we have to appreciate the
reasons for picking not the most
powerful solution but the least powerful.
Tim Berners-Lee
https://www.w3.org/DesignIssues/Principles.html

The reason for this is that the less
powerful the language, the more you can
do with the data stored in that language.
If you write it in a simple declarative
form, anyone can write a program to
analyze it in many ways.
Tim Berners-Lee
https://www.w3.org/DesignIssues/Principles.html

The makefile language is similar
to declarative programming.
This class of language, in which
necessary end conditions are
described but the order in
which actions are to be taken is
not important, is sometimes
confusing to programmers used
to imperative programming.
http://en.wikipedia.org/wiki/Make_(software)

Representation
Is the Essence of
Programming

Show me your flowcharts and
conceal your tables, and I
shall continue to be mystified.
Show me your tables, and I
won’t usually need your
flowcharts; they’ll be obvious.

Excel is the world's
most popular
functional language.
Simon Peyton-Jones

try {
Integer.parseInt(time.substring(0, 2));
}
catch (Exception x) {
return false;
}
if (Integer.parseInt(time.substring(0, 2)) > 12) {
return false;
}
...
if (!time.substring(9, 11).equals("AM") &
!time.substring(9, 11).equals("PM")) {
return false;
}
Burk Hufnagel
"Put the Mouse Down and Step Away from the Keyboard"

Burk Hufnagel
"Put the Mouse Down and Step Away from the Keyboard"
public static boolean validateTime(String time) {
return time.matches("(0[1-9]|1[0-2]):[0-5][0-9]:[0-5][0-9] ([AP]M)");
}

Many programming languages support
programming in both functional and
imperative style but the syntax and
facilities of a language are typically
optimised for only one of these styles,
and social factors like coding conventions
and libraries often force the programmer
towards one of the styles.
https://wiki.haskell.org/Functional_programming

intension, n. (Logic)
 the set of characteristics or properties by which
the referent or referents of a given expression is
determined; the sense of an expression that
determines its reference in every possible world,
as opposed to its actual reference. For example,
the intension of prime number may be having
non-trivial integral factors, whereas its extension
would be the set {2, 3, 5, 7, ...}.
E J Borowski and J M Borwein
Dictionary of Mathematics

{ x2 | x  , x ≥ 1  x ≤ 100 }
select from where

A list comprehension is a syntactic
construct available in some programming
languages for creating a list based on
existing lists. It follows the form of the
mathematical set-builder notation (set
comprehension) as distinct from the use
of map and filter functions.
http://en.wikipedia.org/wiki/List_comprehension

https://twitter.com/richardadalton/status/591534529086693376

def fizzbuzz(n):
result = ''
if n % 3 == 0:
result += 'Fizz'
if n % 5 == 0:
result += 'Buzz'
if not result:
result = str(n)
return result

def fizzbuzz(n):
if n % 15 == 0:
return 'FizzBuzz'
elif n % 3 == 0:
return 'Fizz'
elif n % 5 == 0:
return 'Buzz'
else:
return str(n)

def fizzbuzz(n):
return (
'FizzBuzz' if n % 15 == 0 else
'Fizz' if n % 3 == 0 else
'Buzz' if n % 5 == 0 else
str(n))

def fizzbuzz(n):
return (
'FizzBuzz' if n in range(0, 101, 15) else
'Fizz' if n in range(0, 101, 3) else
'Buzz' if n in range(0, 101, 5) else
str(n))

fizzes = [''] + ([''] * 2 + ['Fizz']) * 33 + ['']
buzzes = [''] + ([''] * 4 + ['Buzz']) * 20
numbers = list(map(str, range(0, 101)))
def fizzbuzz(n):
return fizzes[n] + buzzes[n] or numbers[n]

actual = [fizzbuzz(n) for n in range(1, 101)]
truths = [
every result is 'Fizz', 'Buzz', 'FizzBuzz' or a decimal string,
every decimal result corresponds to its ordinal position,
every third result contains 'Fizz',
every fifth result contains 'Buzz',
every fifteenth result is 'FizzBuzz',
the ordinal position of every 'Fizz' result is divisible by 3,
the ordinal position of every 'Buzz' result is divisible by 5,
the ordinal position of every 'FizzBuzz' result is divisible by 15
]
all(truths)

actual = [fizzbuzz(n) for n in range(1, 101)]
truths = [
all(a in {'Fizz', 'Buzz', 'FizzBuzz'} or a.isdecimal() for a in actual),
all(int(a) == n for n, a in enumerate(actual, 1) if a.isdecimal()),
all('Fizz' in a for a in actual[2::3]),
all('Buzz' in a for a in actual[4::5]),
all(a == 'FizzBuzz' for a in actual[14::15]),
all(n % 3 == 0 for n, a in enumerate(actual, 1) if a == 'Fizz'),
all(n % 5 == 0 for n, a in enumerate(actual, 1) if a == 'Buzz'),
all(n % 15 == 0 for n, a in enumerate(actual, 1) if a == 'FizzBuzz')
]
all(truths)

https://twitter.com/wm/status/7206700352

bi-quinary coded decimal, noun
 A system of representing numbers based on
counting in fives, with an additional indicator to
show whether the count is in the first or second half
of the decimal range, i.e., whether the number
represented is in the range 0–4 or 5–9.
 This system is found in many abacus systems, with
paired columns of counters (normally aligned)
representing each bi-quinary range.
 The Roman numeral system is also a form of bi-
quinary coded decimal.

// Get the unique surnames in uppercase of the
// first 15 book authors that are 50 years old
// or older?
library.stream()
.map(book -> book.getAuthor())
.filter(author -> author.getAge() >= 50)
.limit(15)
.map(Author::getSurname)
.map(String::toUpperCase)
.distinct()
.collect(toList()))

// Get the first 15 unique surnames in
// uppercase of the book authors that are 50
// years old or older.
library.stream()
.distinct()
.limit(15)
.collect(toList()))

// Get the unique surnames in uppercase of the
// first 15 book authors that are 50 years old
// or older.
library.stream()
.distinct()
.limit(15)
.distinct()
.collect(toList()))

Simple filters that can be arbitrarily
chained are more easily re-used,
and more robust, than almost any
other kind of code.
Brandon Rhodes
http://rhodesmill.org/brandon/slides/2012-11-pyconca/

paraskevidekatriaphobia, noun
 The superstitious fear of Friday 13th.
 Contrary to popular myth, this superstition is
relatively recent (19th century) and did not originate
during or before the medieval times.
 Paraskevidekatriaphobia also reflects a particularly
egocentric attributional bias: the universe is
prepared to rearrange causality and probability
around the believer based on an arbitrary and
changeable calendar system, in a way that is
sensitive to geography, culture and time zone.

function NextFriday13thAfter($from) {
(1..500) |
%{ $from.AddDays($_) } |
?{ $_.Day -eq 13} |
?{ $_.DayOfWeek -eq [DayOfWeek]::Friday } |
select –first 1
}

Stack[T]
{
push(T),
pop(),
depth() : Integer,
top() : T
}

An interface is a contract to deliver
a certain amount of service.
Clients of the interface depend on
the contract, which is usually
documented in the interface
specification.
Butler W Lampson
"Hints for Computer System Design"

Stack[T]
{
push(T item),
pop(),
depth() : Integer,
top() : T
}
given:
before = depth()
postcondition:
depth() = before + 1 ∧ top() = item
precondition:
depth() > 0
given:
before = depth()
precondition:
before > 0
postcondition:
depth() = before – 1
given:
result = depth()
postcondition:
result ≥ 0

alphabet(Stack) =
{push, pop, depth, top}

trace(Stack) =
{⟨ ⟩,
⟨push⟩, ⟨depth⟩,
⟨push, pop⟩, ⟨push, top⟩,
⟨push, depth⟩, ⟨push, push⟩,
⟨depth, push⟩, ⟨depth, depth⟩,
⟨push, push, pop⟩,
...}

Non-EmptyEmpty
depth depth
top
push
pop [depth > 1]
push
pop [depth = 1]

public class Stack_spec
{
public static class A_new_stack
{
@Test
public void has_no_depth() 
@Test()
public void has_no_top() 
}
public static class An_empty_stack
{
@Test()
public void throws_when_popped() 
@Test
public void acquires_depth_by_retaining_a_pushed_item_as_its_top() 
}
public static class A_non_empty_stack
{
@Test
public void becomes_deeper_by_retaining_a_pushed_item_as_its_top() 
@Test
public void on_popping_reveals_tops_in_reverse_order_of_pushing() 
}
}

public class
Stack_spec
{
public static class
A_new_stack
{
@Test
public void has_no_depth() 
@Test()
public void has_no_top() 
}
public static class
An_empty_stack
{
@Test()
public void throws_when_popped() 
@Test
public void acquires_depth_by_retaining_a_pushed_item_as_its_top() 
}
public static class
A_non_empty_stack
{
@Test
public void becomes_deeper_by_retaining_a_pushed_item_as_its_top() 
@Test
public void on_popping_reveals_tops_in_reverse_order_of_pushing() 
}
}

Propositions
are vehicles
for stating
how things are
or might be.

Thus only indicative
sentences which it
makes sense to think
of as being true or as
being false are
capable of expressing
propositions.










Are human beings
"noble in reason" and
"infinite in faculty" as
William Shakespeare
famously wrote?
Perfect, "in God's
image," as some
biblical scholars have
asserted?

def is_leap_year(year):
...
# What is the postcondition?

...
# Given
# result = is_leap_year(year)
# Then
# result == (
# year % 4 == 0 and
# year % 100 != 0 or
# year % 400 == 0)

return (
year % 4 == 0 and
year % 100 != 0 or
year % 400 == 0)

def test_is_leap_year_works():
...

Express intention
of code usage
with respect to data

class LeapYearSpec:
@test
def years_not_divisible_by_4_are_not_leap_years(self):
assert not is_leap_year(2015)
@test
def years_divisible_by_4_but_not_by_100_are_leap_years(self):
assert is_leap_year(2016)
@test
def years_divisible_by_100_but_not_by_400_are_not_leap_years(self):
@test
def years_divisible_by_400_are_leap_years(self):

def test(function):
function.is_test = True
return function
def check(suite):
tests = [
attr
for attr in (getattr(suite, name) for name in dir(suite))
if callable(attr) and hasattr(attr, 'is_test')]
for to_test in tests:
try:
to_test(suite())
except:
print('Failed: ' + to_test.__name__ + '()')

Express intention
Naming
Grouping and nesting
of code usage
Realisation of intent
with respect to data
One exemplar or many
Explicit or generated

class LeapYearSpec:
@test
@test
@test
@test

class LeapYearSpec:
@test
@test
@test
@test
for year in range(400, 2401, 400):
assert is_leap_year(year)

class LeapYearSpec:
@test
@test
@test
if year % 400 != 0:
assert not is_leap_year(year)
@test

def test(function):
function.is_test = True
return function
def data(*values):
def prepender(function):
function.data = values + getattr(function, 'data', ())
return function
return prepender
def check(suite):
tests = [
attr
for attr in (getattr(suite, name) for name in dir(suite))
if callable(attr) and hasattr(attr, 'is_test')]
for to_test in tests:
try:
if hasattr(to_test, 'data'):
for value in to_test.data:
call = '(' + str(value) + ')'
to_test(suite(), value)
else:
call = '()'
to_test(suite())
except:
print('Failed: ' + to_test.__name__ + call)

class LeapYearSpec:
@test
@data(2015)
@data(1999)
@data(1)
def years_not_divisible_by_4_are_not_leap_years(self, year):
@test
@test
@test

class LeapYearSpec:
@test
@data(2015)
@data(1999)
@data(1)
@test
@data(2016, 1984, 4)
def years_divisible_by_4_but_not_by_100_are_leap_years(self, year):
@test
@test

class LeapYearSpec:
@test
@data(2015)
@data(1999)
@data(1)
@test
@data(2016, 1984, 4)
@test
@test
@data(*range(400, 2401, 400))
def years_divisible_by_400_are_leap_years(self, year):

class LeapYearSpec:
@test
@data(2015)
@data(1999)
@data(1)
@test
@data(2016, 1984, 4)
@test
@data(*(year for year in range(100, 2101, 100) if year % 400 != 0))
def years_divisible_by_100_but_not_by_400_are_not_leap_years(self, year):
@test
@data(*range(400, 2401, 400))

class LeapYearSpec:
@test
@data(2015)
@data(1999)
@data(1)
@test
@data(2016, 1984, 4)
@test
@data(*range(100, 2101, 400))
@data(*range(200, 2101, 400))
@data(*range(300, 2101, 400))
def years_divisible_by_100_but_not_by_400_are_not_leap_years(self, year):
@test
@data(*range(400, 2401, 400))

Our task is not to find the
maximum amount of
content in a work of art.
Our task is to cut back
content so that we can see
the thing at all.
Susan Sontag

Declarative Thinking, Declarative Practice

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