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Monads for normal people!

Dustin Getz https://github.com/dustingetz/monadic-interpreter
@dustingetz https://github.com/dustingetz/pymonads

intended audience
• coders
• who are comfortable with lambdas
• who learn by example

goals
• how do monads work
• how do monads help
• are monads useful IRL?
• especially in enterprise?
• where do they fall short and what's next

large codebases are complex
• Spring, EJB, AspectJ, DI, AOP
• Common goal: make code look like business
logic
• (to varying degrees of success)

Aspect Oriented Programming
From Wikipedia, the free encyclopedia

In computing, aspect-oriented programming (AOP) is a
programming paradigm which aims to increase modularity by allowing the
separation of cross-cutting concerns.
Typically, an aspect is scattered or tangled as code, making it harder to
understand and maintain. It is scattered by virtue of the function (such as
logging) being spread over a number of unrelated functions that might use
its function, possibly in entirely unrelated systems, different source
languages, etc. That means to change logging can require modifying all
affected modules. Aspects become tangled not only with the mainline
function of the systems in which they are expressed but also with each
other. That means changing one concern entails understanding all the
tangled concerns or having some means by which the effect of changes can
be inferred.

Lots of code to follow
• Pay attention to how the functions compose

a bank API
def get_account(person):
if person.name == "Alice": return 1
elif person.name == "Bob": return 2
else: return None

def get_balance(account):
if account.id == 1: return 1000000
elif account.id == 2: return 75000
else: return None

def get_qualified_amount(balance):
if balance.cash > 200000: return balance.cash
else: return None
(shoutout to Tumult on hackernews for the 'bank' example)

what we want to write
def get_loan(name):
account = get_account(name)
balance = get_balance(account)
loan = get_qualified_amount(balance)
return loan

My boss could write this code
get_qualified_amount( get_balance( get_account( alice )))

alice | get_account | get_balance | get_qualified_amount

(-> get_account get_balance get_qualified_amount)(alice)

alice.get_account().get_balance().get_qualified_amount()

i love NullPointerExceptions
if person.name == "Alice": return 1
elif person.name == "Bob": return 2
else: return None

>>> get_account(None)
AttributeError: 'NoneType' object has no attribute 'id'

what the prod code looks like :(
def get_loan(person):
account = get_account(person)
if not account:
return None
balance = get_balance(account)
if not balance:
return None
loan = get_qualified_amount(balance)
return loan

factor! abstract! happy!
def bind(v, f):
if (v):
return f(v)
else:
return None

def bind(v, f):
if (v): # v == alice
return f(v) # get_account(alice)
else:
return None

>>> alice = Person(...)
>>> bind(alice, get_account)
1

def bind(v, f):
if (v):
return f(v)
else: # v == None
return None # don't call f

>>> bind(None, get_account)
None

the code we really want to write
def bind(v,f): return f(v) if v else None

def get_loan(name):
m_account = get_account(name)
m_balance = bind(m_account, get_balance)
m_loan = bind(m_balance, get_qualified_amount)
return m_loan

>>> alice = Person(...)
>>> get_loan(alice)
100000
>>> get_loan(None)
None

or more succinctly
def bind(v,f): return f(v) if v else None

def m_pipe(val, fns):
m_val = val
for f in fns:
m_val = bind(m_val, f)
return m_val

>>> fns = [get_account, get_balance, get_qualified_amount]
>>> m_pipe(alice, fns)
1000000
>>> m_pipe(dustin, fns)
None

big picture goal
• make the code look like the business logic
• "good clojure programmers write a language to write
their program in" -- DSLs
• build a language to build your business logic
• add features without changing your business logic

add a feature to our API
if person.name == "Alice": return (1, None)
elif person.name == "Bob": return (2, None)
else: return (None, "No acct for '%s'" % person.name)

>>> get_account(alice)
(1, None)

>>> get_account(dustin)
(None, "No acct for 'Dustin'")

def get_balance(account):
if account.id == 1: return (1000000, None)
elif account.id == 2: return (75000, None)
else: return (None, "No balance, acct %s" %
account.id)

def get_qualified_amount(balance):
if balance.cash > 200000: return (balance, None)
else: return (None, "Insufficient funds: %s" %
balance.cash)

def bind(mval, mf):
value = mval[0]
error = mval[1]
if not error:
return mf(value)
else:
return mval

def bind(mval, mf): # mval == (1, None)
value = mval[0] # value == 1
error = mval[1] # error == None
if not error:
return mf(value) # mf(1)
else:
return mval

>>> mval = (1, None)
>>> bind(mval, get_balance)
(100000, None)

def bind(mval, mf): # mval == (None, "insuf funds")
value = mval[0] # value == None
error = mval[1 # error == "insuf funds"
if not error:
return mf(value)
else:
return mval # short circuit

>>> mval = (None, "insuf funds")
>>> bind(mval, get_balance)
(None, "insuf funds")

Business logic didn't change
# error monad
def bind(mv, mf): mf(mv[0]) if mv[0] else mv
def unit(v): return (v, None)

def m_pipe(val, *fns):
m_val = unit(val)
for f in fns:
m_val = bind(m_val, f)
return m_val

>>> m_pipe(alice, get_account, get_balance,
get_qualified_amount)
(1000000, None)

# error monad

def m_chain(*fns): ...

>>> get_loan = m_chain(get_account, get_balance,
<fn that composes the fns in order>

>>> get_loan(alice)
(1000000, None)
>>> get_loan(dustin)

get_loan = m_chain(get_account, get_balance,

>>> map(get_loan, [alice, dustin, bob])
[(1000000, None), (None, "insuf funds"), (75000, None)]

>>> mmap(get_loan, [alice, bob])
([1000000, 75000], None)

>>> mmap(get_loan, [alice, bob, dustin])

here be monads
# maybe monad
def bind(mv, mf): return mf(mv) if mv else None
def unit(v): return v

# error monad

monad comprehensions
# error monad

>>> mv1 = (7, None)
>>> mv2 = bind( mv1,
lambda x: unit(x))
(7, None)

lambda x: unit(x+1))
(8, None)

monad comprehensions
# error monad

>>> mv1 = (7, None); mv2 = (3, None)
lambda x: bind( mv2,
lambda y: unit(x + y)))
(10, None)

>>> mv4 = (None, “error”)
>>> bind( mv3,
lambda x: bind( mv4,
(None, “error”)

the simplest monad
# identity monad
def bind(mv,mf): return mf(mv)

>>> bind( 7,
lambda x: bind( 3,
10

the simplest monad
# identity monad
def bind(mv,mf): return mf(mv)

>>> bind( 7, lambda x:
bind( 3, lambda y:
unit(x + y)))
10

repl> (let [x 7
y 3]
x + y)
10

Lists are a monad!
>>> [(x,y) for x in ranks for y in files]

# list monad
def unit(v): return [v]
def bind(mv,mf): return flatten(map(mf, mv))

>>> ranks = list("abcdefgh")
>>> files = list("12345678")
>>> bind( ranks, lambda rank:
bind( files, lambda file:
unit((rank, file))))
repl> (for [rank (seq “abcdefgh”)
file (seq “12345678”)]
[rank, file])

monads are...
• a design pattern for composing functions
that have incompatible types, but can still
logically define composition
• by overriding function application
• to increase modularity and manage
accidental complexity

here comes the fun stuff
• introduce a few harder monads
• combine monads to build...
o a Clojure parsing DSL
o a Python lisp interpreter

writer monad
def unit(v): return (v, [])
def bind(mv, mf): …

def addOne(x):
val = x+1
logmsg = "x+1==%s" % val
return (val, [logmsg])

>>> mv = addOne(7)
(8, ['x+1==8'])
>>> m_chain(addOne, addOne, addOne)(mv)
(11, ['x+1==9', 'x+1==10', 'x+1==11'])

writer monad

def addOne(x):
val = x+1

>>> addThreeLogged = m_chain(addOne, addOne, addOne)
>>> map(addThreeLogged, [10,20,30])
[(13, ['x+1==11', 'x+1==12', 'x+1==13']),
(23, ['x+1==21', 'x+1==22', 'x+1==23']),
(33, ['x+1==31', 'x+1==32', 'x+1==33'])]

writer monad

def addOne(x):
val = x+1

>>> mmap(addOne, [1,2,3])
([2, 3, 4], ['x+1==2', 'x+1==3', 'x+1==4'])

reader monad
def unit(v): return lambda env: v

def read(key):
def _(env):
return env[key]
return _

>>> mv = read('a')
<a function of env>
>>> mv({'a': 7})
7
>>> mv({'a': 10, 'b': 3})
10

reader monad

def read(key):
def _(env):
return env[key]
return _

>>> computation = bind( read('a'), lambda a:
bind( read('b'), lambda b:
unit( a+b ))
<a function of env>
>>> computation({'a': 7, 'b': 3})
10

reader monad

def read(key):
def _(env):
return env[key]
return _

unit( a+b ))
<a function of env>
>>> computation({'a': 42, 'b': 1})
43

environment = reader + writer
def unit(v): …

def read(key): lambda env: (env[key], env)
def write(key, val): lambda env: … (None, newEnv)

>>> write('a', 2)
<a function of env>
>>> myenv = {'a': 999, 'b': 999}
>>> write('a', 2)(myenv)
(None, {'a': 2, 'b': 999})
>>> read('a')(myenv)
(999, {'a': 999, 'b': 999})

environment = reader + writer
bind( write('c', a+b), lambda _:
unit(c+1) )))
<a function of env>

>>> computation({'a': 7, 'b': 3})
(11, {'a': 7, 'b': 3, 'c': 10})

interpreter = environment + error
def read(key): lambda env: ... # can fail
def write(key, val): lambda env: ... # can fail

bind( write('c', a+b), lambda _:
unit(c+1) )))

>>> computation({'a': 7, 'b': 3})
( (11, {'a': 7, 'b': 3, 'c': 10}), None)

>>> computation({'b': 3})
( (None, {'b': 3}), "unbound symbol 'a'")

lis.py> 1
((1, {}), None)
lis.py> x
((None, {}), 'referenced unbound symbol x')
lis.py> (define x 1)
((None, {'x': 1}), None)
lis.py> x
((1, {'x': 1}), None)
lis.py> (+ x 2)
((3, {'x': 1}), None)
lis.py> (set! x (+ x 2))
((None, {'x': 5}), None)
lis.py> x
((5, {'x': 5}), None)

lis.py> +
((<function <lambda> at 0x10047f320>,
{
'+': <function <lambda> at 0x10047f320>
'*': <function <lambda> at 0x10047f398>,
'dumpenv': <function <lambda> at 0x10047ecf8>,
'assert': <function <lambda> at 0x10047ec80>,
'symbol?': <function <lambda> at 0x10047eed8>,
'eq?': <function <lambda> at 0x10047f1b8>,
'car': <function <lambda> at 0x10047f2a8>,
... snip ...
}), None)

interpreter = monad heaven
• identity -> values
• reader -> read-only globals (builtins)
• environment -> def, set!, lambda (lexical
scope)
• error -> assert, throw
• continuation -> call/cc, try/catch/finally

"monads are how you implement special forms"

parser = environment + maybe
• env where you are in the input, not a map
• `nil` indicates failed parse branch, discard
current env, restore env to last successful
parse point and try another branch

So who cares?
• Monads are a tool to manage complexity
• Write code with maximally separated
concerns
• trust that you won't break existing code,
allow you to maintain with minimal changes
• write a language to talk about business state
transitions, write your business logic in that
language

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