-
Notifications
You must be signed in to change notification settings - Fork 0
/
theories-ArraysEx.shtml
163 lines (136 loc) · 4.63 KB
/
theories-ArraysEx.shtml
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
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<!--
Design by http://www.bluewebtemplates.com
Released for free under a Creative Commons Attribution 3.0 License
-->
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title>SMT-LIB The Satisfiability Modulo Theories Library</title>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<link href="style.css" rel="stylesheet" type="text/css" />
<!-- CuFon: Enables smooth pretty custom font rendering. 100% SEO friendly. To disable, remove this section -->
<script type="text/javascript" src="js/cufon-yui.js"></script>
<script type="text/javascript" src="js/arial.js"></script>
<script type="text/javascript" src="js/cuf_run.js"></script>
<!-- CuFon ends -->
<link href="code-prettify/prettify.css" type="text/css" rel="stylesheet" />
<script src="code-prettify/run_prettify.js?lang=smtlib&skin=desert"></script>
</head>
<body>
<div class="main">
<div class="header">
<div class="header_resize">
<div class="menu_nav">
<ul>
<li><a href="index.shtml">Home</a></li>
<li><a href="about.shtml">About</a></li>
<li><a href="news.shtml">News</a></li>
<li class="active"><a href="standard.shtml">Standard</a></li>
<li><a href="benchmarks.shtml">Benchmarks</a></li>
<li><a href="software.shtml">Software</a></li>
<li><a href="credits.shtml">Credits</a></li>
</ul>
</div>
<div class="clr"></div>
<div class="logo">
<h1><a href="index.shtml">SMT-LIB <br/>
<small>The Satisfiability Modulo Theories Library</small></a>
</h1>
</div>
</div>
</div>
<div class="content">
<div class="content_resize">
<div class="mainbar">
<h2>ArraysEx</h2>
<pre class="prettyprint lang-smtlib">
(theory ArraysEx
:smt-lib-version 2.6
:smt-lib-release "2017-11-24"
:written-by "Cesare Tinelli"
:date "2010-04-28"
:last-updated "2015-04-25"
:update-history
"Note: history only accounts for content changes, not release changes.
2015-04-25 Updated to Version 2.5.
2010-08-15 Minor fix.
"
:sorts ((Array 2))
:funs ((par (X Y) (select (Array X Y) X Y))
(par (X Y) (store (Array X Y) X Y (Array X Y))) )
:notes "A schematic version of the theory of functional arrays with extensionality."
:definition
"For every expanded signature Sigma, the instance of ArraysEx with that signature
is the theory consisting of all Sigma-models that satisfy all axioms of the form
below, for all sorts s1, s2 in Sigma:
- (forall ((a (Array s1 s2)) (i s1) (e s2))
(= (select (store a i e) i) e))
- (forall ((a (Array s1 s2)) (i s1) (j s1) (e s2))
(=> (distinct i j)
(= (select (store a i e) j) (select a j))))
- (forall ((a (Array s1 s2)) (b (Array s1 s2)))
(=> (forall ((i s1)) (= (select a i) (select b i)))
(= a b)))
"
:values
"For all sorts s1, s2 in in the signature, the values of sort (Array s1 s2) are
abstract.
"
)
</pre>
(<a href="Theories/ArraysEx.smt2">raw file</a>)
<br>
<br>
</div>
<div class="sidebar">
<div class="gadget">
<ul class="sb_menu">
<li><a href="index.shtml">Home</a></li>
<li><a href="about.shtml">About</a></li>
<li><a href="news.shtml">News</a></li>
<li>Standard
<ul class="ex_menu">
<li><a href="language.shtml">Language</a>
<li><a href="theories.shtml">Theories</a>
<li><a href="logics.shtml">Logics</a>
<li><a href="examples.shtml">Examples</a>
</ul>
</li>
<li><a href="benchmarks.shtml">Benchmarks</a></li>
<li>Software
<ul class="ex_menu">
<li><a href="solvers.shtml">Solvers</a></li>
<li><a href="utilities.shtml">Utilities</a></li>
</ul>
</li>
<li><a href="contact.shtml">Contact</a></li>
<li><a href="related.shtml">Related</a></li>
<li><a href="credits.shtml">Credits</a></li>
</ul>
</div>
</div>
</div>
</div>
<div class="clr"></div>
<div class="footer">
<div class="footer_resize">
<p class="lf">
© Copyright The SMT-LIB Initiative <br>
Based on a design by
Blue <a href="http://www.bluewebtemplates.com">Web Templates</a>
</p>
<ul class="fmenu">
<li><a href="index.shtml">Home</a></li>
<li><a href="about.shtml">About</a></li>
<li><a href="news.shtml">News</a></li>
<li class="active"><a href="standard.shtml">Standard</a></li>
<li><a href="benchmarks.shtml">Benchmarks</a></li>
<li><a href="software.shtml">Software</a></li>
<li><a href="credits.shtml">Credits</a></li>
</ul>
<div class="clr"></div>
</div>
</div>
</div>
</body>
</html>