-
-
Notifications
You must be signed in to change notification settings - Fork 1.2k
Expand file tree
/
Copy pathSemilattice.scala
More file actions
89 lines (80 loc) · 3.16 KB
/
Copy pathSemilattice.scala
File metadata and controls
89 lines (80 loc) · 3.16 KB
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
/*
* Copyright (c) 2015 Typelevel
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
package cats.kernel
import scala.{specialized => sp}
/**
* Semilattices are commutative semigroups whose operation
* (i.e. combine) is also idempotent.
*/
trait Semilattice[@sp(Int, Long, Float, Double) A] extends Any with Band[A] with CommutativeSemigroup[A] { self =>
/**
* Given Eq[A], return a PartialOrder[A] using the `combine`
* operator to determine the partial ordering. This method assumes
* `combine` functions as `meet` (that is, as a lower bound).
*
* This method returns:
*
* 0.0 if x = y
* -1.0 if x = combine(x, y)
* 1.0 if y = combine(x, y)
* NaN otherwise
*/
def asMeetPartialOrder(implicit ev: Eq[A]): PartialOrder[A] = (x, y) =>
if (ev.eqv(x, y)) 0.0
else {
val z = self.combine(x, y)
if (ev.eqv(x, z)) -1.0 else if (ev.eqv(y, z)) 1.0 else Double.NaN
}
/**
* Given Eq[A], return a PartialOrder[A] using the `combine`
* operator to determine the partial ordering. This method assumes
* `combine` functions as `join` (that is, as an upper bound).
*
* This method returns:
*
* 0.0 if x = y
* -1.0 if y = combine(x, y)
* 1.0 if x = combine(x, y)
* NaN otherwise
*/
def asJoinPartialOrder(implicit ev: Eq[A]): PartialOrder[A] = (x, y) =>
if (ev.eqv(x, y)) 0.0
else {
val z = self.combine(x, y)
if (ev.eqv(y, z)) -1.0 else if (ev.eqv(x, z)) 1.0 else Double.NaN
}
}
abstract class SemilatticeFunctions[S[T] <: Semilattice[T]] extends SemigroupFunctions[S] {
def asMeetPartialOrder[A](implicit s: S[A], ev: Eq[A]): PartialOrder[A] =
s.asMeetPartialOrder(using ev)
def asJoinPartialOrder[A](implicit s: S[A], ev: Eq[A]): PartialOrder[A] =
s.asJoinPartialOrder(using ev)
}
object Semilattice extends SemilatticeFunctions[Semilattice] {
/**
* Access an implicit `Semilattice[A]`.
*/
@inline final def apply[@sp(Int, Long, Float, Double) A](implicit ev: Semilattice[A]): Semilattice[A] = ev
/**
* Create a `Semilattice` instance from the given function.
*/
@inline def instance[A](cmb: (A, A) => A): Semilattice[A] = cmb(_, _)
}