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
|
import utest._
import utest.ExecutionContext
import cl._
object Tests extends TestSuite {
val tests = TestSuite {
val p: Var = 'p
val q: Var = 'q
val r: Var = 'r
val s: Var = 's
'usage {
val pq = p * q
val pqr = p * q * r
val pqrs = p * q * r * s
val parens = p * (q * r) * s
val nested = p * (parens) * s
val nestedLeft = (((p * q) * r) * s)
val nestedRight = (p * (q * (r * s)))
'toString {
assert(
pq.toString == "pq",
pqr.toString == "pqr",
pqrs.toString == "pqrs",
parens.toString == "p(qr)s",
nested.toString == "p(p(qr)s)s",
nestedLeft.toString == "pqrs",
nestedRight.toString == "p(q(rs))"
)
}
'equality {
"non-commutative"-{
assert(
p * q == p * q,
p * q != q * p
)
}
"non-associative"-{
assert(p * (q*r) != (p*q) * r)
}
"left-associative"-{
assert(
p * q * r * s == (((p*q) * r) * s),
p * q * r * s != (p * (q * (r*s)))
)
}
}
"contains"-{
assert(
pq.contains(p),
pq.contains(q),
!pq.contains(r),
nestedRight.contains(s)
)
}
}
"reduction"-{
/*
"Evaluation is complete when..."-{
"...the term begins with a var"-{
val vars = s*s*s*s*s*s
assert(
eval(s) == s,
eval(s*s) == s*s,
eval(vars) == (vars),
eval(s * K * p * q) == (s * K * p * q)
)
}
"...the leading combinator has too few arguments for reduction"-{
assert(
eval(K) == K,
eval(K * p) == K * p,
eval(K * p * p) == p
)
}
}
"basic combinators"-{
assert(
eval(I * p) == p,
eval(K * p * q) == p,
eval(S * p * q * r) == p * r * (q * r)
)
}
"head reduction"-{
// NOTE: Implementing head reduction separately is optional,
// but could be a helpful first step.
assert(
//evalHead(K * p * q * r * s) == p * r * s,
//evalHead(K * p * q * K * p * q) == p * K * p * q,
//evalHead(K * I * p * q) == I * q
)
}
"step by step reduction"-{
/*assert(
evalHead(S * (K * S) * K * p * q * r) == (S * (K * S) * K * p * q * r),
evalHead(K * S * p * (K * p) * q * r) == (S * (K * p) * q * r),
evalHead(S * (K * p) * q * r) == (K * p * r * (q * r)),
evalHead(K * p * r * (q * r)) == (p * (q * r))
)*/
}
"complete reduction"-{
assert(
eval(S * (K * S) * K * p * q * r) == p * (q * r),
eval(Sp * K * I * I * s) == s,
eval(B * (B * S) * B * K * I * I * s) == s,
eval(S*(K*S)*K * (S*(K*S)*K * S) * (S*(K*S)*K) * K * (S*K*K) * I * s) == s
)
}
*/
}
"bracket abstraction"-{
/*
val TRUE = K
val FALSE = K*I
def evalBool(bool: Term): Boolean = {
val p: Var = 'P
val q: Var = 'Q
// if bool then p else q
eval(bool * p * q) match {
case x if x == p => true
case x if x == q => false
}
}
"Booleans evaluating properly"-{
assert(
evalBool(TRUE),
!evalBool(FALSE)
)
}
def not = (p: Term) => p * FALSE * TRUE
def and = (p: Term, q: Term) => p * q * FALSE
def or = (p: Term, q: Term) => p * TRUE * q
"basic boolean functions"-{
assert(
evalBool(not(FALSE)),
!evalBool(not(TRUE)),
evalBool(and(TRUE, TRUE)),
!evalBool(and(TRUE, FALSE)),
!evalBool(and(FALSE, TRUE)),
!evalBool(and(FALSE, FALSE)),
evalBool(or(TRUE, TRUE)),
evalBool(or(TRUE, FALSE)),
evalBool(or(FALSE, TRUE)),
!evalBool(or(FALSE, FALSE))
)
}
"variable extraction"-{
val x: Var = 'x
val term = not(x).extract(x)
assert(
not(x).contains(x),
!term.contains(x),
evalBool(term * TRUE) == evalBool(not(TRUE)),
evalBool(term * FALSE) == evalBool(not(FALSE))
)
}
"boolean functions abstracted"-{
val NOT: Term = bracketAbstraction(not)
val AND: Term = bracketAbstraction(and)
val OR: Term = bracketAbstraction(or)
assert(
evalBool(NOT * FALSE),
!evalBool(NOT * TRUE),
evalBool(AND * TRUE * TRUE),
!evalBool(AND * TRUE * FALSE),
!evalBool(AND * FALSE * TRUE),
!evalBool(AND * FALSE * FALSE),
evalBool(OR * TRUE * TRUE),
evalBool(OR * TRUE * FALSE),
evalBool(OR * FALSE * TRUE),
!evalBool(OR * FALSE * FALSE)
)
}
*/
}
}
}
|
