1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
|
#
# Copyright Applied Language Solutions 2012
#
# This file is part of Pypeline.
#
# Pypeline is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Pypeline is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with Pypeline. If not, see <http://www.gnu.org/licenses/>.
#
import types
from pypeline.core.arrows.arrow import Arrow
#
# Kleisli arrows of a monad
#
# See:
# Publications:
# http://www.cse.chalmers.se/~rjmh/Papers/arrows.pdf
#
class KleisliArrow(Arrow):
#
# patcher :: Monad m => a -> m a
# function :: Monad m => a -> m b
#
def __init__(self, patcher, f):
if not isinstance(patcher, types.FunctionType) and not isinstance(patcher, types.MethodType):
raise ValueError("Patcher must be a function")
if f and (not isinstance(f, types.FunctionType) and
not isinstance(f, types.MethodType)):
raise ValueError("Function must be a function")
self._patcher = patcher
self._func = f
# arr f = K(\b ->return(f b))
def arr(self, f):
return KleisliArrow(self._patcher, lambda b: self._patcher(f(b)))
# K f >>> K g = K(\b -> f b >>= g)
def __rshift__(self, other):
if not isinstance(other, KleisliArrow):
raise ValueError("Must be an KleisliArrow")
return KleisliArrow(other._patcher, lambda b: self._func(b) >= other._func)
# K f (***) K g = first K f >>> second K g
def __pow__(self, other):
if not isinstance(other, KleisliArrow):
raise ValueError("Must be an KleisliArrow")
return self.first() >> other.second()
# K f &&& K g = K $ \a -> do
# b <- f a
# c <- g a
# return (b,c)
def __and__(self, other):
if not isinstance(other, KleisliArrow):
raise ValueError("Must be an KleisliArrow")
func = lambda a: self._func(a) >= (lambda b: other._func(a) >= (lambda c: other._patcher((b, c))))
return KleisliArrow(other._patcher, func)
# first (K f) = K(\(b, d) -> f b >>= \c -> return (c, d))
def first(self):
func = lambda t: self._func(t[0]) >= (lambda c: self._patcher((c, t[1])))
return KleisliArrow(self._patcher, func)
# second (K f) = K(\(d, b) -> f b >>= \c -> return (d, c))
def second(self):
func = lambda t: self._func(t[1]) >= (lambda c: self._patcher((t[0], c)))
return KleisliArrow(self._patcher, func)
@staticmethod
def runKleisli(k, a):
if not isinstance(k, KleisliArrow):
raise ValueError("Arrow must be a Kleisli arrow")
return k._func(a)
#
# Split
#
def split(patcher):
return KleisliArrow(patcher, lambda b: patcher((b, b)))
#
# Unsplit
#
def unsplit(patcher, op_func):
return KleisliArrow(patcher, lambda t: patcher(op_func(t[0], t[1])))
|
