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
|
set show timing off .
set show advisories off .
***
*** Test continue and debug options with various commands.
***
***
*** rewriting search
***
mod COLLATZ is
pr RAT .
sort Foo .
op f : Nat -> Foo .
var N : Nat .
crl f(N) => f(N / 2) if N rem 2 = 0 .
crl f(N) => f(3 * N + 1) if N rem 2 = 1 .
endm
debug search [10] f(27) =>+ f(N) .
step .
step .
resume .
debug cont 10 .
step .
resume .
cont .
***
*** variant generation
***
fmod XOR is
sort XOR .
sort Elem .
ops cst1 cst2 cst3 cst4 : -> Elem .
subsort Elem < XOR .
op _+_ : XOR XOR -> XOR [ctor assoc comm] .
op 0 : -> XOR .
op a : -> XOR .
vars X Y : XOR .
eq Y + 0 = Y [variant] .
eq X + X = 0 [variant] .
eq X + X + Y = Y [variant] .
endfm
get variants [1] in XOR : X:XOR + cst1 .
debug cont 1 .
step .
resume .
cont .
***
*** variant unification
***
variant unify [2] X:XOR + cst1 =? Y:XOR + cst2 .
debug cont 3 .
step .
step .
resume .
cont .
variant unify [1] X:XOR + cst1 =? Y:XOR + cst2 such that X:XOR + cst1 irreducible .
cont 1 .
cont 1 .
cont 1 .
***
*** regular narrowing
***
mod FOO is
sort Foo .
op f : Foo Foo -> Foo [assoc] .
var X Y Z W A B C D : Foo .
rl f(X, Y, Y, Z) => f(X, Y, Z) [narrowing] .
endm
debug narrow [5, 1] f(A, A) =>+ C .
step .
resume .
debug cont 5 .
resume .
cont 5 .
***
*** narrowing with variant unification.
***
mod BAZ is
sort Foo .
ops f g h : Foo -> Foo .
ops i j k : Foo Foo -> Foo .
vars X Y Z W A B C D : Foo .
eq j(f(X), Y) = i(f(Y), X) [variant] .
rl g(i(X, k(Y, Z))) => f(k(Z, X)) [narrowing] .
rl f(k(X, X)) => h(X) [narrowing] .
endm
debug vu-narrow [2] in BAZ : g(j(A, B)) =>* C .
resume .
debug cont 1 .
step .
resume .
cont 2 .
cont .
***
*** rewriting with strategies
***
mod FOO3 is
sort Foo .
ops a b c d e : -> Foo .
ops f g : Foo Foo -> Foo [comm].
ops h i : Foo -> Bool .
vars X Y Z : Foo .
crl f(X, Y) => g(X, Z) if h(X) => i(Z) [label 1] .
eq h(a) = i(d) .
eq h(b) = i(e) .
endm
debug srew [1] f(a, b) using 1{all *} .
step .
resume .
debug cont 1 .
step .
cont .
***
*** variant matching.
***
fmod XOR is
sort XOR .
sort Elem .
ops a b c d w x y z : -> Elem .
subsort Elem < XOR .
op _+_ : XOR XOR -> XOR [ctor assoc comm] .
op 0 : -> XOR .
vars X Y : XOR .
eq Y + 0 = Y [variant] .
eq X + X = 0 [variant] .
eq X + X + Y = Y [variant] .
endfm
debug variant match [1] in XOR : X + Y <=? c + d .
step .
resume .
*** No point in trying "debug cont" because all rewriting/narrowing
*** has be done at this stage.
cont 2 .
cont .
|
