What Is Output?

Definition

Output is the result a system makes available after applying a rule to input, state, or both.

Output can be:

• a returned value
• a changed state
• an external effect
• a signal to another system
• an intermediate result used by a later step

Output = result made available by computation

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Output vs State

State is the system's current condition.

Output is what the system exposes, returns, changes, or makes available from that condition.

Example:

State: x = 5
Rule: return x + 1
Output: 6

The state contains x = 5.

The output is 6.

State is what the system currently has. Output is what the system makes available.

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Output As Final Result

In many cases, the final state contains the information used as output.

Example:

Input: 3
Rule: add 2 three times

States:
3 -> 5 -> 7 -> 9

Output: 9

The final state is 9.

The output is the value exposed from that final state.

A final state can determine the final output.

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Output As Extracted Information

Output can also be derived from the state.

Example:

State: (x = 5, y = 10)
Rule: return x + y
Output: 15

The output is not the whole state.

It is extracted from part of the state.

Output may be a value derived from the current state.

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Output As Effect

Output is not always a returned value.

It can also be an effect.

Examples:

print("hello") -> text appears on screen
delete file -> file no longer exists
send signal -> another system receives it

In these cases, the output is what the computation causes or exposes.

Output can be a value, a state change, or an observable effect.

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Output Does Not Always Change State

Output may leave the internal state unchanged while still creating an external effect.

Example:

Internal state: x = 5
Rule: print x
External output: 5
Internal state after output: x = 5

The internal state did not change.

But something was still produced outside the internal state.

Output can expose information without changing the internal state.

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Output Over Time

Output is not always a single result.

Single output

input -> computation -> final output

Continuous output

Output may be produced during computation.

Example:

State: 3 -> output: 3
State: 5 -> output: 5
State: 7 -> output: 7
State: 9 -> output: 9

Each output is produced before the full sequence is finished.

Output can be generated at intermediate steps.

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Output Must Be Available

Output must be available to some observer, system, or later step.

Examples:

• displayed value
• returned result
• saved file
• signal to another system
• value passed into the next step

If nothing can access or use the result, then it does not function as output for that system.

Output must be representable and accessible.

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No Final Output

Some computations may never produce a final output.

Example:

while true:
  keep running

The system may keep changing state.

It may even produce intermediate outputs.

But if it never stops, it does not produce a final result.

A computation can have no final output if it never reaches a final result.

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Output As Input

Output can feed into further computation.

Example:

First computation:
Input: 3
Rule: add 2
Output: 5

Next computation:
Input: 5
Rule: add 2
Output: 7

What counts as output in one step may become input for another step.

Output of one computation can become input to another.

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Raw Output vs Interpreted Output

The same output can be interpreted differently by different systems.

Example:

Output: "7"

One system may treat it as text:

"7" -> count characters -> 1

Another system may treat it as a number:

"7" -> convert to number -> 7
7 -> add 1 -> 8

The raw output is the same.

The interpretation depends on the system that receives it.

Output becomes useful only relative to a system that can handle it.

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Output vs Meaning

Output does not require meaning.

Example:

Output: "xk3#9!"

This may have no human meaning.

But it can still be output if it is produced by the system and made available.

Output is a structured result, not necessarily meaningful interpretation.

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Final Summary

• Output is a result made available by computation.
• Output may come from input, state, or both.
• State is what the system currently has; output is what it exposes, returns, changes, or makes available.
• A final state can determine the final output.
• Output can be extracted from part of the state.
• Output can be a returned value, state change, signal, or external effect.
• Output can expose information without changing internal state.
• Output may be produced once, continuously, or at intermediate steps.
• Some computations may never produce a final output.
• Output of one computation can become input to another.
• Output does not require human meaning.