The other day, an article titled [Mathematics] The Party to Protect the People from NHK to the Party to Protect the People from NHK was posted on Qiita. I did.
In this article, ** the party grammar that protects the people from NHK ** is defined. After reading this, I thought:
The grammar that protects the people from NHK can unambiguously describe a binary tree with two types of leaves, ** NHK ** and ** people **.
I focused on Lazy K as a programming language with such a simple syntax.
Lazy K is [Combinatory Logic](https://ja.wikipedia.org/wiki/%E3%82%B3%E3%83%B3%E3%83%93%E3%83%8D%E3%83%BC It is a programming language based on% E3% 82% BF% E8% AB% 96% E7% 90% 86), and you can write programs with only three combinators, S`` K
ʻI. Of these, ʻI
is known to be extensionally equal to S K K
, so the only practical combinators needed are S
and K
. [^ 1]
[^ 1]: If you say ι = (λf. (F S) K)
, you don't even need S
and K
. Reference
Therefore, you can make a Turing complete language just by reading the following [^ 2].
[^ 2]: In other words, "the language that protects the people from NHK" like Ook! For Brainfuck is just a change of the reserved word of Lazy K.
Grammar to protect the people from NHK | Combinator |
---|---|
NHK | S |
People | K |
Party that protects B from A | (A B) |
Please refer to Lazy K's introductory site for input / output and handling of numerical values.
I used Python to implement the processing system.
nhk.py
#!/usr/bin/env python3
import sys
class Combinator :
'''X-Y is synonym of Apply(X,Y)'''
def __sub__(self, arg) :
return Apply(self, arg)
def evaluate(self) :
return self
def get_left(self, xs) :
xs.append(self)
class _SIN(Combinator) :
'''Do not call _SIN() . Use SIN instead'''
sinlist = None
def evaluate(self) :
if _SIN.sinlist is None :
_SIN.sinlist = str_to_sk(sys.stdin.read())
return _SIN.sinlist
class _S(Combinator) :
'''Do not call _S() . Use S instead'''
class _K(Combinator) :
'''Do not call _K() . Use K instead'''
class Foreign(Combinator) :
'''Non-combinator class. ((Foreign f)-(Foreign x)).evaluate() == f(x)'''
def __init__(self, val) :
self.val = val
class Apply(Combinator) :
'''Application of combinators. Apply(X,Y) represents (X Y)'''
def __init__(self, fun, arg) :
self.fun = fun
self.arg = arg
def get_left(self, xs) :
xs.append(self.arg)
self.fun.get_left(xs)
def evaluate(self) :
left_evaled = self.fun.evaluate() - self.arg
left = []
left_evaled.get_left(left)
n = len(left)
if(n == 4 and left[3] == S) :
return (left[2] - left[0] - (left[1] - left[0])).evaluate()
if(n == 3 and left[2] == K) :
return (left[1]).evaluate()
if(n == 2 and isinstance(left[1], Foreign)) :
return Foreign(left[1].val(left[0].evaluate().val))
return left_evaled
S = _S()
K = _K()
SIN = _SIN()
I = S-K-K
true = K
false = K-I
# cons = \ x y c . c x y
cons = S-(S-(K-S)-(S-(K-K)-(S-(K-S)-(S-(K-(S-I))-K))))-(K-K)
succ = S-(S-(K-S)-K)
zero = K-I
one = I
two = succ-one
mul = S-(K-S)-K
def str_to_sk(string) :
ret = cons - int_to_church(256) - false
for c in reversed(string) :
ret = cons - int_to_church(ord(c)) - ret
return ret
def church_to_int(c) :
return (c-(Foreign(lambda n: n+1))-(Foreign(0))).evaluate().val
def int_to_church(n) :
if(n == 0) :
return zero
if(n == 1) :
return one
if(n == 2) :
return two
else :
ret = one
for c in bin(n)[3:]:
ret = mul - two - ret
if c == '1' :
ret = succ - ret
return ret
def get_car(c) :
return (c-true).evaluate()
def get_cdr(c) :
return (c-false).evaluate()
def evalAsLazyK(arg) :
sk = arg - SIN
while True :
n = church_to_int(get_car(sk))
if n > 255 :
break
print(chr(n), end='')
sk = get_cdr(sk)
def parseNHK(code) :
len_NHK = len('NHK')
len_people = len('People')
len_from = len('From')
len_save = len('Party to protect')
stk = []
code = code.replace('\n', '')
while code :
if code.startswith('NHK') :
stk.append(S)
code = code[len_NHK:]
elif code.startswith('People') :
stk.append(K)
code = code[len_people:]
elif code.startswith('From') :
code = code[len_from:]
elif code.startswith('Party to protect') :
try :
arg = stk.pop()
fun = stk.pop()
except IndexError as e :
raise Exception('parseNHK failed. Too much "Party to protect"')
stk.append(fun-arg)
code = code[len_save:]
elif code.startswith(' ') or code.startswith('\t') or code.startswith(' ') :
code = code[1:]
else :
raise Exception('parseNHK failed at ' + code[:10])
if len(stk) == 1 :
return stk.pop()
else :
raise Exception('parseNHK failed. Too few "Party to protect"')
if __name__ == '__main__' :
with open(sys.argv[1]) as f:
src = f.read()
ast = parseNHK(src)
evalAsLazyK(ast)
Actually, I wanted to read one character from the standard input each time I needed it, but because my kung fu wasn't enough, it was designed to read all the standard input when I first needed it [^ 3] ].
[^ 3]: I'll fix it when I feel like it
echo Let's write a program that just outputs the standard input to the standard output. The code looks like this:
sample.nhk
The party that protects the people from the NHK
I will try it.
python
echo "foo bar baz" |./nhk.py sample.nhk
output
foo bar baz
It's working well.
If you use the people (K combinator), you can write a program that ignores standard input and gives a fixed output.
Below is the sample code.
sample2.nhk
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From the party that protects the party From the party that protects the NHK From the people From the party that protects the party that protects the party From the party that protects the people From NHK From NHK From the people NH
From the party that protects K From the party that protects the people From the party that protects the people From the party that protects the people from NHK From the party that protects the people
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From the party that protects the party that protects the people From the party that protects the people From NHK From NHK From the party that protects NHK From the party that protects the party that protects the people
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From the party to the people From the NHK Protect the people From the party Protect the people Protect the party Protect the party Protect the party Protect the party Protect the party Protect the party
The party that protects the party that protects the party that protects the party that protects the party that protects the party that protects the party that protects the party that protects the party that protects the party
I will try it.
python
./nhk.py sample2.nhk
output
Down with NHK!
Looks good.
How was it?
It is wonderful.
Pioneer is here.
After all, there seems to be a great demand for programming with a grammar that protects the people from NHK.
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