blob: 3a651455628b3fa526ec2b54f3c87341ea2dda51 (
plain) (
blame)
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
|
% Universals over infinite domains are proven or refuted
% symbolically, never enumerated.
% The specification's true example: every natural is at least zero.
Query expression:
[ForAll variable: X
quantifier: [Natural value: X]
body: [GreaterEqual left: X right: 0]]
% The specification's false example: not every integer is.
Query expression:
[ForAll variable: X
quantifier: [Integer value: X]
body: [GreaterEqual left: X right: 0]]
% Subtype inclusion, decided symbolically: every integer is a
% rational, literally.
Query expression:
[ForAll variable: X
quantifier: [Integer value: X]
body: [Rational value: X]]
% The algebra of Plus: adding zero is the identity, over all
% integers, stated flat as membership.
Query expression:
[ForAll variable: X
quantifier: [Integer value: X]
body: [Plus left: X right: 0 result: X]]
% Universals over finite quantifiers just run.
Query expression:
[ForAll variable: X
quantifier: [Between value: X lower: 1 upper: 5]
body: [GreaterThan left: X right: 0]]
% Existence, over a finite quantifier.
Query expression:
[Exists variable: X
quantifier: [Between value: X lower: 1 upper: 10]
body: [Times left: X right: X result: 49]]
|
