Basic types

An 8-bit byte. A `Byte` value represents a congruence class of integers modulo 256, and may be interpreted as:

- an `unsigned` integer value in the range `0..255`, or
- a `signed` integer value in the range `-128..127`.

`Byte` is not considered a full numeric type, supporting only:

- bitwise operations, and
- addition and subtraction modulo 256.

`Byte`s with modular addition form a mathematical group. Thus, every byte `b` has an additive inverse `-b` where:

    (-b).signed == -b.signed
    (-b).unsigned == b.unsigned==0 then 0 else 256 - b.unsigned

`Byte` is a recursive enumerable type. For example, the range:

    254.byte .. 1.byte

contains the values `254.byte, 255.byte, 0.byte, 1.byte`.

`Byte` does not have a total order because any such order would:

- be inconsistent with the definition of `successor` and `predecessor` under modular addition, and
- would depend on interpretation of the `Byte` value as signed or unsigned.

Thus, to compare the magnitude of two bytes, it is necessary to first convert them to either their `signed` or `unsigned` integer values.

`Byte`s are useful mainly because they can be efficiently stored in an `Array`.

- `Anything`
  - `Object`
    - `Byte` ...and other supertypes

- `Byte`
  - `Binary`
  - `Enumerable`
    - `Ordinal`
  - `Invertible`
    - `Summable`
  - `Object`
    - `Anything`

no subtypes hierarchy

Initializer
- `Byte(Integer congruent)` Parameters: `congruent` An integer member of the congruence class of the resulting `Byte`. For any integer `x>=0`:
      x.byte.unsigned == x % 256
      x.byte.signed == x % 256
  And for an integer `x<0`:
      x.byte.unsigned == 256 + x % 256
      x.byte.signed == x % 256
  And for any integers `x` and `y` which are congruent modulo 256:
      x.byte == y.byte

Attributes
`even` | Source Code `shared Boolean even` Whether this byte is even.
`hash` | Source Code `shared actual Integer hash` The hash value of the value, which allows the value to be an element of a hash-based set or key of a hash-based map. Implementations must respect the constraint that: if `x==y` then `x.hash==y.hash`. Therefore, a class which refines `Object.equals()` must also refine `hash`. Because the `Integer` type is platform-dependent a compiler for a given platform is permitted to further manipulate the calculated hash for an object, and the resulting hash may differ between platforms. Refines `Object.hash`
`negated` | Source Code `shared actual Byte negated` The additive inverse of this byte. For any integer `x`:
    (-x.byte).signed = -x.byte.signed
Refines `Invertible.negated`
`not` | Source Code `shared actual Byte not` The binary complement of this sequence of bits. Refines `Binary.not`
`predecessor` | Source Code `shared actual Byte predecessor` The predecessor of this value. Refines `Enumerable.predecessor` ultimately refines `Ordinal.predecessor`
`signed` | Source Code `shared Integer signed` This byte interpreted as a signed integer in the range `-128..127`.
`string` | Source Code `shared actual String string` The `unsigned` interpretation of this byte as a string. Refines `Object.string`
`successor` | Source Code `shared actual Byte successor` The successor of this value. Refines `Enumerable.successor` ultimately refines `Ordinal.successor`
`unit` | Source Code `shared Boolean unit` Whether this byte is one.
`unsigned` | Source Code `shared Integer unsigned` This byte interpreted as an unsigned integer in the range `0..255`.
`zero` | Source Code `shared Boolean zero` Whether this byte is zero.

Inherited Attributes
Attributes inherited from: `Object` `hash`, `string`
Attributes inherited from: `Binary<Other>` `not`
Attributes inherited from: `Enumerable<Other>` `predecessor`, `successor`
Attributes inherited from: `Invertible<Other>` `negated`
Attributes inherited from: `Ordinal<Other>` `predecessor`, `successor`

Methods
`and` | Source Code `shared actual Byte and(Byte other)` Performs a logical AND operation. Refines `Binary.and`
`equals` | Source Code `shared actual Boolean equals(Object that)` Determine if two values are equal. Implementations should respect the constraints that: if `x===y` then `x==y` (reflexivity), if `x==y` then `y==x` (symmetry), if `x==y` and `y==z` then `x==z` (transitivity). Furthermore it is recommended that implementations ensure that if `x==y` then `x` and `y` have the same concrete class. A class which explicitly refines `equals()` is said to support value equality, and the equality operator `==` is considered much more meaningful for such classes than for a class which simply inherits the default implementation of identity equality from `Identifiable`. Refines `Object.equals`
`flip` | Source Code `shared actual Byte flip(Integer index)` Returns an instance with the given bit flipped to its opposite value if `0 <= index < size`, otherwise returns a value with the same bits as this value. Refines `Binary.flip`
`get` | Source Code `shared actual Boolean get(Integer index)` Retrieves a given bit from this bit sequence if `0 <= index < size`, otherwise returns false. Refines `Binary.get`
`leftLogicalShift` | Source Code `shared actual Byte leftLogicalShift(Integer shift)` Shift the sequence of bits to the left, by the given number of places, filling the least significant bits with zeroes. Refines `Binary.leftLogicalShift`
`neighbour` | Source Code `shared actual Byte neighbour(Integer offset)` The indirect successor or predecessor at the given `offset`, where: `x.neighbour(0) == x`, `x.neighbour(i+1) == x.neighbour(i).successor`, and `x.neighbour(i-1) == x.neighbour(i).predecessor`. Refines `Enumerable.neighbour`
`offset` | Source Code `shared actual Integer offset(Byte other)` Compute the offset from the given value, where: `x.offset(x) == 0`, and `x.successor.offset(x) == 1` if `x!=x.successor`. Refines `Enumerable.offset`
`offsetSign` | Source Code `shared actual Integer offsetSign(Byte other)` The sign of the offset from the given value. Refines `Enumerable.offsetSign`
`or` | Source Code `shared actual Byte or(Byte other)` Performs a logical inclusive OR operation. Refines `Binary.or`
`plus` | Source Code `shared actual Byte plus(Byte other)` The modulo 256 sum of this byte and the given byte. Refines `Summable.plus`
`rightArithmeticShift` | Source Code `shared actual Byte rightArithmeticShift(Integer shift)` Shift the sequence of bits to the right, by the given number of places, preserving the values of the most significant bits. If the sequence of bits represents a signed integer, the sign is preserved. Refines `Binary.rightArithmeticShift`
`rightLogicalShift` | Source Code `shared actual Byte rightLogicalShift(Integer shift)` Shift the sequence of bits to the right, by the given number of places, filling the most significant bits with zeroes. If the sequence of bits represents a signed integer, the sign is not preserved. Refines `Binary.rightLogicalShift`
`set` | Source Code `shared actual Byte set(Integer index, Boolean bit)` Returns an instance with the given bit set to the given value if `0 <= index < size`, otherwise returns a value with the same bits as this value. Refines `Binary.set`
`xor` | Source Code `shared actual Byte xor(Byte other)` Performs a logical exclusive OR operation. Refines `Binary.xor`

Inherited Methods
Methods inherited from: `Object` `equals()`
Methods inherited from: `Binary<Other>` `and()`, `clear()`, `flip()`, `get()`, `leftLogicalShift()`, `or()`, `rightArithmeticShift()`, `rightLogicalShift()`, `set()`, `xor()`
Methods inherited from: `Enumerable<Other>` `neighbour()`, `offset()`, `offsetSign()`
Methods inherited from: `Invertible<Other>` `minus()`
Methods inherited from: `Summable<Other>` `plus()`