-
Notifications
You must be signed in to change notification settings - Fork 154
/
boolean.scala
304 lines (236 loc) · 10.4 KB
/
boolean.scala
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
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
package eu.timepit.refined
import eu.timepit.refined.api._
import eu.timepit.refined.api.Inference.==>
import eu.timepit.refined.boolean._
import eu.timepit.refined.internal.Resources
import shapeless.{::, HList, HNil}
import shapeless.ops.hlist.ToList
/** Module for logical predicates. */
object boolean extends BooleanValidate with BooleanInference0 {
/** Constant predicate that is always `true`. */
final case class True()
/** Constant predicate that is always `false`. */
final case class False()
/** Negation of the predicate `P`. */
final case class Not[P](p: P)
/** Conjunction of the predicates `A` and `B`. */
final case class And[A, B](a: A, b: B)
/** Disjunction of the predicates `A` and `B`. */
final case class Or[A, B](a: A, b: B)
/** Exclusive disjunction of the predicates `A` and `B`. */
final case class Xor[A, B](a: A, b: B)
/** Conjunction of all predicates in `PS`. */
final case class AllOf[PS](ps: PS)
/** Disjunction of all predicates in `PS`. */
final case class AnyOf[PS](ps: PS)
/** Exclusive disjunction of all predicates in `PS`. */
final case class OneOf[PS](ps: PS)
/** Negated conjunction of the predicates `A` and `B`. */
type Nand[A, B] = Not[A And B]
/** Negated disjunction of the predicates `A` and `B`. */
type Nor[A, B] = Not[A Or B]
}
private[refined] trait BooleanValidate {
implicit def trueValidate[T]: Validate.Plain[T, True] =
Validate.alwaysPassed(True())
implicit def falseValidate[T]: Validate.Plain[T, False] =
Validate.alwaysFailed(False())
implicit def notValidate[T, P, R](
implicit v: Validate.Aux[T, P, R]): Validate.Aux[T, Not[P], Not[v.Res]] =
new Validate[T, Not[P]] {
override type R = Not[v.Res]
override def validate(t: T): Res = {
val r = v.validate(t)
Result.fromBoolean(r.isFailed, Not(r))
}
override def showExpr(t: T): String =
s"!${v.showExpr(t)}"
override def showResult(t: T, r: Res): String = {
val expr = v.showExpr(t)
val rp = r.detail.p
rp match {
case Passed(_) => Resources.showResultNotInnerPassed(expr)
case Failed(_) => Resources.showResultNotInnerFailed(expr)
}
}
}
implicit def andValidate[T, A, RA, B, RB](
implicit va: Validate.Aux[T, A, RA],
vb: Validate.Aux[T, B, RB]
): Validate.Aux[T, A And B, va.Res And vb.Res] =
new Validate[T, A And B] {
override type R = va.Res And vb.Res
override def validate(t: T): Res = {
val (ra, rb) = (va.validate(t), vb.validate(t))
Result.fromBoolean(ra.isPassed && rb.isPassed, And(ra, rb))
}
override def showExpr(t: T): String =
s"(${va.showExpr(t)} && ${vb.showExpr(t)})"
override def showResult(t: T, r: Res): String = {
val expr = showExpr(t)
val (ra, rb) = (r.detail.a, r.detail.b)
(ra, rb) match {
case (Passed(_), Passed(_)) =>
Resources.showResultAndBothPassed(expr)
case (Passed(_), Failed(_)) =>
Resources.showResultAndRightFailed(expr, vb.showResult(t, rb))
case (Failed(_), Passed(_)) =>
Resources.showResultAndLeftFailed(expr, va.showResult(t, ra))
case (Failed(_), Failed(_)) =>
Resources.showResultAndBothFailed(expr, va.showResult(t, ra), vb.showResult(t, rb))
}
}
}
implicit def orValidate[T, A, RA, B, RB](
implicit va: Validate.Aux[T, A, RA],
vb: Validate.Aux[T, B, RB]
): Validate.Aux[T, A Or B, va.Res Or vb.Res] =
new Validate[T, A Or B] {
override type R = va.Res Or vb.Res
override def validate(t: T): Res = {
val (ra, rb) = (va.validate(t), vb.validate(t))
Result.fromBoolean(ra.isPassed || rb.isPassed, Or(ra, rb))
}
override def showExpr(t: T): String =
s"(${va.showExpr(t)} || ${vb.showExpr(t)})"
override def showResult(t: T, r: Res): String = {
val expr = showExpr(t)
val (ra, rb) = (r.detail.a, r.detail.b)
(ra, rb) match {
case (Passed(_), Passed(_)) =>
Resources.showResultOrBothPassed(expr)
case (Passed(_), Failed(_)) =>
Resources.showResultOrLeftPassed(expr)
case (Failed(_), Passed(_)) =>
Resources.showResultOrRightPassed(expr)
case (Failed(_), Failed(_)) =>
Resources.showResultOrBothFailed(expr, va.showResult(t, ra), vb.showResult(t, rb))
}
}
}
implicit def xorValidate[T, A, RA, B, RB](
implicit va: Validate.Aux[T, A, RA],
vb: Validate.Aux[T, B, RB]
): Validate.Aux[T, A Xor B, va.Res Xor vb.Res] =
new Validate[T, A Xor B] {
override type R = va.Res Xor vb.Res
override def validate(t: T): Res = {
val (ra, rb) = (va.validate(t), vb.validate(t))
Result.fromBoolean(ra.isPassed ^ rb.isPassed, Xor(ra, rb))
}
override def showExpr(t: T): String =
s"(${va.showExpr(t)} ^ ${vb.showExpr(t)})"
override def showResult(t: T, r: Res): String = {
val expr = showExpr(t)
val (ra, rb) = (r.detail.a, r.detail.b)
(ra, rb) match {
case (Passed(_), Passed(_)) =>
Resources.showResultOrBothPassed(expr)
case (Passed(_), Failed(_)) =>
Resources.showResultOrLeftPassed(expr)
case (Failed(_), Passed(_)) =>
Resources.showResultOrRightPassed(expr)
case (Failed(_), Failed(_)) =>
Resources.showResultOrBothFailed(expr, va.showResult(t, ra), vb.showResult(t, rb))
}
}
}
implicit def allOfHNilValidate[T]: Validate.Plain[T, AllOf[HNil]] =
Validate.alwaysPassed(AllOf(HList()))
implicit def allOfHConsValidate[T, PH, RH, PT <: HList, RT <: HList](
implicit vh: Validate.Aux[T, PH, RH],
vt: Validate.Aux[T, AllOf[PT], AllOf[RT]]
): Validate.Aux[T, AllOf[PH :: PT], AllOf[vh.Res :: RT]] =
new Validate[T, AllOf[PH :: PT]] {
override type R = AllOf[vh.Res :: RT]
override def validate(t: T): Res = {
val rh = vh.validate(t)
val rt = vt.validate(t)
Result.fromBoolean(rh.isPassed && rt.isPassed, AllOf(rh :: rt.detail.ps))
}
override def showExpr(t: T): String =
accumulateShowExpr(t).mkString("(", " && ", ")")
override def accumulateShowExpr(t: T): List[String] =
vh.showExpr(t) :: vt.accumulateShowExpr(t)
}
implicit def anyOfHNilValidate[T]: Validate.Plain[T, AnyOf[HNil]] =
Validate.alwaysFailed(AnyOf(HList()))
implicit def anyOfHConsValidate[T, PH, RH, PT <: HList, RT <: HList](
implicit vh: Validate.Aux[T, PH, RH],
vt: Validate.Aux[T, AnyOf[PT], AnyOf[RT]]
): Validate.Aux[T, AnyOf[PH :: PT], AnyOf[vh.Res :: RT]] =
new Validate[T, AnyOf[PH :: PT]] {
override type R = AnyOf[vh.Res :: RT]
override def validate(t: T): Res = {
val rh = vh.validate(t)
val rt = vt.validate(t)
Result.fromBoolean(rh.isPassed || rt.isPassed, AnyOf(rh :: rt.detail.ps))
}
override def showExpr(t: T): String =
accumulateShowExpr(t).mkString("(", " || ", ")")
override def accumulateShowExpr(t: T): List[String] =
vh.showExpr(t) :: vt.accumulateShowExpr(t)
}
implicit def oneOfHNilValidate[T]: Validate.Plain[T, OneOf[HNil]] =
Validate.alwaysFailed(OneOf(HList()))
implicit def oneOfHConsValidate[T, PH, RH, PT <: HList, RT <: HList](
implicit vh: Validate.Aux[T, PH, RH],
vt: Validate.Aux[T, OneOf[PT], OneOf[RT]],
toList: ToList[RT, Result[_]]
): Validate.Aux[T, OneOf[PH :: PT], OneOf[vh.Res :: RT]] =
new Validate[T, OneOf[PH :: PT]] {
override type R = OneOf[vh.Res :: RT]
override def validate(t: T): Res = {
val rh = vh.validate(t)
val rt = vt.validate(t).detail.ps
val passed = (rh :: toList(rt)).count(_.isPassed) == 1
Result.fromBoolean(passed, OneOf(rh :: rt))
}
override def showExpr(t: T): String =
accumulateShowExpr(t).mkString("oneOf(", ", ", ")")
override def accumulateShowExpr(t: T): List[String] =
vh.showExpr(t) :: vt.accumulateShowExpr(t)
}
}
private[refined] trait BooleanInference0 extends BooleanInference1 {
implicit def minimalTautology[A]: A ==> A =
Inference.alwaysValid("minimalTautology")
implicit def doubleNegationElimination[A, B](implicit p1: A ==> B): Not[Not[A]] ==> B =
p1.adapt("doubleNegationElimination(%s)")
implicit def doubleNegationIntroduction[A, B](implicit p1: A ==> B): A ==> Not[Not[B]] =
p1.adapt("doubleNegationIntroduction(%s)")
implicit def conjunctionAssociativity[A, B, C]: ((A And B) And C) ==> (A And (B And C)) =
Inference.alwaysValid("conjunctionAssociativity")
implicit def conjunctionCommutativity[A, B]: (A And B) ==> (B And A) =
Inference.alwaysValid("conjunctionCommutativity")
implicit def conjunctionEliminationR[A, B, C](implicit p1: B ==> C): (A And B) ==> C =
p1.adapt("conjunctionEliminationR(%s)")
implicit def disjunctionAssociativity[A, B, C]: ((A Or B) Or C) ==> (A Or (B Or C)) =
Inference.alwaysValid("disjunctionAssociativity")
implicit def disjunctionCommutativity[A, B]: (A Or B) ==> (B Or A) =
Inference.alwaysValid("disjunctionCommutativity")
implicit def disjunctionIntroductionL[A, B]: A ==> (A Or B) =
Inference.alwaysValid("disjunctionIntroductionL")
implicit def disjunctionIntroductionR[A, B]: B ==> (A Or B) =
Inference.alwaysValid("disjunctionIntroductionR")
implicit def deMorgansLaw1[A, B]: Not[A And B] ==> (Not[A] Or Not[B]) =
Inference.alwaysValid("deMorgansLaw1")
implicit def deMorgansLaw2[A, B]: Not[A Or B] ==> (Not[A] And Not[B]) =
Inference.alwaysValid("deMorgansLaw2")
implicit def xorCommutativity[A, B]: (A Xor B) ==> (B Xor A) =
Inference.alwaysValid("xorCommutativity")
implicit def nandCommutativity[A, B]: (A Nand B) ==> (B Nand A) =
Inference.alwaysValid("nandCommutativity")
implicit def norCommutativity[A, B]: (A Nor B) ==> (B Nor A) =
Inference.alwaysValid("norCommutativity")
}
private[refined] trait BooleanInference1 extends BooleanInference2 {
implicit def modusTollens[A, B](implicit p1: A ==> B): Not[B] ==> Not[A] =
p1.adapt("modusTollens(%s)")
}
private[refined] trait BooleanInference2 {
implicit def conjunctionEliminationL[A, B, C](implicit p1: A ==> C): (A And B) ==> C =
p1.adapt("conjunctionEliminationL(%s)")
implicit def hypotheticalSyllogism[A, B, C](implicit p1: A ==> B, p2: B ==> C): A ==> C =
Inference.combine(p1, p2, "hypotheticalSyllogism(%s, %s)")
}