B Langage Keywords and Operators version 1.8.6
ASCII
Math.
Pri.
!
∀
250
As.
"
#
&
ASCII
<
String or definition file
<+
There exists
Math.
Pri.
50
+
90
<->
1
125
130
∃
250
Value of data before substitution
<-
j
λ
250
Lambda expression
<--
c
∧
40
G
Conjunction (logical AND)
<:
⊆
250
G
$0
%
Description
For any
As.
Description
ASCII
G
Strictly less than
DEFINITIONS
DEFINITIONS clause
G
Overload a relation
DO
WHILE substitution
G
Set of relations
EITHER
CASE substitution
G
Insert at end of sequence
ELSE
IF or CASE substitution
ELSIF
IF substitution
END
Terminator of clauses or of
substitutions BEGIN, PRE,
ASSERT, CHOICE, IF, SELECT,
ANY, LET, VAR, CASE and
WHILE
EXTENDS
clause EXTENDS
G
Operation output parameters
60
G
Inclusion
Strict inclusion
Access to a record field
<<:
⊂
60
G
(
Open bracket
<<|
a
130
G
Substraction to the domain
)
Close bracket
<=
≤
50
G
Less than or equal
G
Multiplication or Cartesian product
<=>
⇔
30
G
Equivalence
<|
r
130
G
Restriction to the domain
G
Equals
'
*
×
190
x ** y
xy
200
+
D
Power of
180
=
G
Addition
+->
2
125
G
Partial function
==
+->>
6
125
G
Partial surjection
=>
>
50
Definition
⇒
30
G
Implies
50
G
Strictly greater than
G
Partial injection
,
115
G
Comma
-
180
G
Subtraction
>+>
4
125
-
210
Unary minus
>->
5
125
G
Total injection
>->>
9
125
G
Total bijection
G
Direct product of relations
G
Greater than or equal
-->
3
125
G
Total function
-->>
7
125
G
Surjection
><
⊗
100
->
k
130
G
Insert at the start of a sequence
>=
≥
50
.
220
D
Renaming or data separator used
in the operators ∀, ∃, ∪, ∩, Σ, Π, λ
ABSTRACT_CONSTANTS
ABSTRACT_CONSTANTS clause
..
170
ABSTRACT_VARIABLES
ABSTRACT_VARIABLES clause
G
Interval
/
190
ANY
ANY substitution
G
Integer division
60
G
Non-belonging
ASSERT
/:
∉
Math.
FIN1
As.
Description
Literal Boolean constant “false”
FALSE
FIN
Pri.
F
F1
Set of finite sub-sets
Set of finite non empty sub-sets
IF
Substitution IF
IMPLEMENTATION
IMPLEMENTATION clause
IMPORTS
IMPORTS clause
IN
BE or VAR substitution
INCLUDES
INCLUDES clause
INITIALISATION
INITIALISATION clause
INT
Set of implementable relative
integers
INTEGER
INTER
Z
Set of relative integers
I
Quantified intersection
INVARIANT
INVARIANT clause or WHILE
substitution
ASSERT substitution
LET
LET substitution
ASSERTIONS clause
LOCAL_OPERATIONS
LOCAL_OPERATIONS clause
/<:
-
60
G
Non-inclusion
ASSERTIONS
/<<:
⊄
60
Strict non-inclusion
LET substitution
MACHINE
G
BE
MACHINE clause
BEGIN
MAXINT
Largest implementable integer
G
Not equal
BEGIN substitution
MININT
Smallest implementable integer
NAT
Set of implementable natural
integers
/=
≠
50
/\
∩
140
G
Intersection
BOOL
Conversion of a predicate into a
Boolean value
/|\
q
150
G
Restriction of a sequence to the
head
CASE
CASE substitution
:
60
CHOICE
CHOICE substitution
G
Belonging
NAT1
∈
80
G
Record field
CONCRETE_CONSTANTS
CONCRETE_CONSTANTS
clause
NATURAL
:
::
:∈
:=
;
80
NAT1
Set of non-empty implementable
natural integers
N
Set of natural integers
N1
Set of non-empty natural integers
G
Becomes part of (belonging)
CONCRETE_VARIABLES
CONCRETE_VARIABLES clause
NATURAL1
Becomes equal to
CONSTANTS
CONSTANTS clause
OF
CASE substitution
G
Sequencing for substitution or
composition of relations
CONSTRAINTS
CONSTRAINTS clause
OPERATIONS
OPERATIONS clause
G
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B Langage Keywords and Operators version 1.8.6
ASCII
Math.
Pri.
As.
Description
ASCII
CHOICE or CASE substitution
card
Π
Quantified integer product
closure(R)
P
Set of sub-sets
closure1(R)
Set of non-empty sub-sets
OR
PI
POW
POW1
P1
Math.
Pri.
As.
Description
ASCII
Cardinal
rev
Math.
Pri.
As.
Reverse of a sequence
Description
R*
Reflexive closure of a relation
right
Right tree
R+
Closure of a relation
seq
Set of sequences
conc
Concatenation of a succession
seq1
Set of non-empty sequences
PRE
Precondition substitution
const
Tree constructor
size
Size of a sequence
PROMOTES
PROMOTES clause
dom
Domain of a function
sizet
Size of a tree
PROPERTIES
PROPERTIES clause
father
Father of a tree node
skip
Null substitution
REFINES
REFINES clause
first
First element in a sequence
son
i son of a tree
REFINEMENT
REFINEMENT clause
fnc
Transformed into a function
sons
Sons of a tree node
SEES
SEES clause
front
Front of a sequence
struct
Set of records
SELECT
SELECT clause
id
Function identity
subtree
Subtree of a tree
SETS
SETS clause
infix
Infix formulae of a tree
succ
Successor
Quantified product
inter
General intersection
tail
Tail of a sequence
iseq
Set of injective sequences
top
Top of a tree
Set of injective non-empty
sequences
tree
Trees
Iteration of a relation
union
Generalized union
{
Start of set
SIGMA
Σ
STRING
Set of character strings
THEN
Precondition substitution,
ASSERT, IF or CASE
iseq1
iseq1
TRUE
Literal Boolean constant “true”
iterate(R, n)
R
U
n
th
Quantified union
last
Last element in a sequence
USES
USES clause
left
Left tree
VALUES
VALUES clause
max
Maximum in a set of integers
VAR
VAR substitution
min
Minimum in a set of integers
|->
VARIANT
WHILE substitution
mirror
Mirror of a tree
VARIABLES
VARIABLES clause
mod
Modulo
WHEN
SELECT substitution
Logical no
||
WHERE
ANY substitution
or
WHILE
WHILE substitution
perm
[
Start of sequence
Set of permutations (bijective
sequences)
[]
Empty sequence
postfix
Postfix formulae of a tree
pred
Predecessor of an integer
UNION
\/
u
140
G
Union
\|/
w
150
G
Restrict a sequence to the end
]
^
End of sequence
)
110
G
Concatenate sequences
arity
Tree node arity
bin
Binary tree in extension
bool
Predicate boolean cast
btree
Binary trees
not
190
G
¬
∨
40
G
Disjunction (logical OR)
Prefix formulae of a tree
prefix
prj1
prj1
prj2
prj2
First projection of a relation
Second projection of a relation
ran
Range of a relation
rank
Rank of a tree node
rec
Record in extension
rel
Set of relations
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{}
Empty set
Ø
|
10
G
Vertical bar used in ∀, ∃, ∪, ∩, Σ,
Π, λ
α
160
G
Maplet
|>
R
130
G
Restriction to the range
|>>
A
130
G
Substraction to the range
100
G
Simultaneous substitutions
parallel product of relations
}
r~
End of set
r -1
230
G
Reverse relation