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4.5.1 Logical Operators and Short-circuit Control Forms

Name Resolution Rules

1
An expression consisting of two relations connected by and then or or else (a short-circuit control form) shall resolve to be of some boolean type; the expected type for both relations is that same boolean type. 
1.a
Reason: This rule is written this way so that overload resolution treats the two operands symmetrically; the resolution of overloading present in either one can benefit from the resolution of the other. Furthermore, the type expected by context can help. 

Static Semantics

2
The following logical operators are predefined for every boolean type T, for every modular type T, and for every one-dimensional array type T whose component type is a boolean type:
3
function "and"(Left, Right : T) return T
function "or" (Left, Right : T) return T
function "xor"(Left, Right : T) return T
3.a/2
This paragraph was deleted.{AI95-00145-01}
3.b/2
Ramification: {AI95-00145-01} For these operators, we are talking about the type without any (interesting) subtype, and not some subtype with a constraint or exclusion. Since it's possible that there is no name for the “uninteresting” subtype, we denote the type with an italicized T. This applies to the italicized T in many other predefined operators and attributes as well.
3.c/2
{AI95-00145-01} In many cases, there is a subtype with the correct properties available. The italicized T means: 
3.d/2
T'Base, for scalars;
3.e/2
the first subtype of T, for tagged types;
3.f/2
a subtype of the type T without any constraint or null exclusion, in other cases. 
3.g/2
Note that “without a constraint” is not the same as unconstrained. For instance, a record type with no discriminant part is considered constrained; no subtype of it has a constraint, but the subtype is still constrained.
3.h/2
Thus, the last case often is the same as the first subtype of T, but that isn't the case for constrained array types (where the correct subtype is unconstrained) and for access types with a null_exclusion (where the correct subtype does not exclude null).
3.i/2
This italicized T is used for defining operators and attributes of the language. The meaning is intended to be as described here. 
4
For boolean types, the predefined logical operators and, or, and xor perform the conventional operations of conjunction, inclusive disjunction, and exclusive disjunction, respectively.
5
For modular types, the predefined logical operators are defined on a bit-by-bit basis, using the binary representation of the value of the operands to yield a binary representation for the result, where zero represents False and one represents True. If this result is outside the base range of the type, a final subtraction by the modulus is performed to bring the result into the base range of the type.
6
The logical operators on arrays are performed on a component-by-component basis on matching components (as for equality — see 4.5.2), using the predefined logical operator for the component type. The bounds of the resulting array are those of the left operand.

Dynamic Semantics

7
The short-circuit control forms and then and or else deliver the same result as the corresponding predefined and and or operators for boolean types, except that the left operand is always evaluated first, and the right operand is not evaluated if the value of the left operand determines the result.
8
For the logical operators on arrays, a check is made that for each component of the left operand there is a matching component of the right operand, and vice versa. Also, a check is made that each component of the result belongs to the component subtype. The exception Constraint_Error is raised if either of the above checks fails.
8.a
Discussion: The check against the component subtype is per AI83-00535. 
NOTES
9
13  The conventional meaning of the logical operators is given by the following truth table:
10
       A   B (A and B) (A or B) (A xor B)

     True   True   True   True   False
     True   False  False  True   True
     False  True   False  True   True
     False  False  False  False  False

Examples

11
Examples of logical operators: 
12
Sunny or Warm
Filter(1 .. 10) and Filter(15 .. 24)   --   see 3.6.1 
13
Examples of short-circuit control forms: 
14
Next_Car.Owner /= null and then Next_Car.Owner.Age > 25   --   see 3.10.1
N = 0 or else A(N) = Hit_Value
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