1. 4TC00 Model-based systems engineering 2.2 Types and values
Bert van Beek (dr.ir. D.A. van Beek)
Gem-Z 0.120

2. Answers of first guided self study are online
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Specific link to go directly to the answers on the exercises website.

3. Examples of type, values and expressions
disc int x = 1;
disc int y = 2 * x;
int is a type
1 is a value (of type int)
2 * x is an expression, but x and 1 are also expressions

4. CIF definition of Type

5. Types and values
Type of a variable is the set of all allowed values of the variable.
Type also defines the allowed operations on variables and expressions of the type.
Type
Allowed values
Default initial value
bool
true, false
false
int[1..3]
1, 2, 3 1
int
integer values
real
1.35, -25e5, etc
string
“true”, “hello world”, etc “”

6. Expressions A simple expression is a:
literal value
variable
function call
Expressions can be composed of other expressions by means of operators
Expressions can be evaluated, resulting in a value

7. Integers and operators
// 9
// 9
// 13
// 5
9 * // 36
9 / // 2.25 (result is a real number, not an integer number)
9 div // 2 (9 / 4 = 2.25, so 4 fits at two whole times in 9)
9 mod // 1 (the remainder of 9 div 4)
pow(2, 4) // 16 (2 to the power of 4, or 2 * 2 * 2 * 2)
abs(-9) // 9 (absolute value)
min(9, 4) // 4 (minimum value)
max(9, 4) // 9 (maximum value)

8. Reals and operators +1.23 // 1.23 --1.2 // 1.2 1.5 + 0.5 // 2.0
// 1.23
// 1.2
// 2.0
// 1.0
1.5 * // 0.75
1.5 / // 3.0
pow(3.5, 2.0) // (3.5 to the power of 2, or 3.5 * 3.5)
abs(-1.5) // (absolute value)
min(1.5, 0.5) // (minimum value)
max(1.5, 0.5) // (maximum value)
sqrt(16.0) // (square root)
cbrt(16.0) // (cube root)
sin(1.0) // (sine)
cos(1.0) // (cosine)
tan(1.0) // (tangent)
log(100.0) // (logarithm to base 10)
ln(100.0) // (natural logarithm)

9. Operators on reals and integers
x < y // less than
x <= y // less than or equal to
x = y // equal to
x != y // not equal to
x >= y // larger than or equal to
x > y // larger than
round(1.6) // 2 (round real to closest integer, half up)
ceil(0.7) // 1 (round real up to integer)
floor(0.7) // 0 (round real down to integer)

10. Boolean operators not x // inverse
x and y // conjunction (both x and y must hold)
x or y // disjunction (either x, y, or both must hold)
x => y // implication (if x holds, y must hold)

11. "hello" + " " + "world" = "hello world"
String concatenation
"hello" + " " + "world" = "hello world"

12. Enumerations
enum TrafficColor = RED, ORANGE, GREEN; // enum declaration
automaton A:
event change_color;
disc TrafficColor light = RED;
location:
initial;
edge change_color when light = RED do light := GREEN;
end