What makes these initial functions so special?

In summary, if a function can be broken down into the three basic functions (constant, successor, projection) using certain operators, then it is considered primitive recursive. These functions are not inherently special, but are chosen for their simplicity and ability to give enough power without becoming too complex.
  • #1
japplepie
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People say that if you could break a function down into these three functions (constant, successor, projection or sometimes called initial/basic functions) using some operators, then it is primitive recursive.

What makes these three functions so special?
 
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  • #2
japplepie said:
People say that if you could break a function down into these three functions (constant, successor, projection or sometimes called initial/basic functions) using some operators, then it is primitive recursive.

What makes these three functions so special?
I don't know what you are talking about but I advise you that "people say ... " is just about the absolute worst reference you can use for this site and I suggest you get more specific.
 
  • #3
phinds said:
I don't know what you are talking about but I advise you that "people say ... " is just about the absolute worst reference you can use for this site and I suggest you get more specific.
Kleene said; http://plato.stanford.edu/entries/recursive-functions/#1.1
 
  • #4
Again, I don't know anything about what you are talking about but I was struck by the fact that in your second post it became clear that you are talking about recursive functions whereas in your initial post there was not a hint of that. Perhaps people who are familiar w/ the characteristics of functions are automatically flagged by terms like "initial function" to know you are talking about recursive functions but I never would have guessed it.

My point is simply that the more clarity you can bring to your questions, the more likely you are to get helpful answers.
 
  • #5
I am having trouble understanding the thrust of the question. The definition for primitive recursive function is cast in terms of the constant function, the successor function and the projection function. That does not make those functions "special". They are simply the functions that happened to be used in the definition.

Perhaps a better phrasing is: "Why is the definition the way it is -- why choose those functions as building blocks?"

One answer to that is easy: Because they are about as simple a set of building blocks as it is possible to imagine. And, because, in conjunction with composition and recursion, they give about as much power as it is possible to have without being so powerful that undecidability becomes an issue.

Like phinds, I have no particular expertise in this area. Just muttering stuff that seems blatantly obvious.
 

1. What are initial functions?

Initial functions, also known as initializers, are a type of function used in programming languages to initialize objects or variables with a specific value or state. They are typically used at the beginning of a program or when creating new objects.

2. How are initial functions different from regular functions?

Initial functions are different from regular functions in that they are only executed once, at the beginning of a program or when creating a new object, whereas regular functions can be called multiple times throughout a program. Additionally, initial functions are often used for initialization purposes, while regular functions can perform a variety of tasks.

3. Why are initial functions important?

Initial functions are important because they allow for the proper initialization of objects and variables, which is crucial for the correct functioning of a program. They also help to improve the efficiency and readability of code by separating the initialization process from other tasks.

4. What makes initial functions special?

Initial functions are special because they are executed automatically without the need for any explicit calls. They also have a specific syntax and are typically used for a specific purpose, making them stand out from regular functions in a program.

5. Can initial functions be used in all programming languages?

While the concept of initial functions exists in most programming languages, the syntax and implementation may vary. Some languages may not have a specific keyword for initial functions, but they can still achieve the same functionality through other means. It is important to consult the documentation of the specific programming language to understand how to use initial functions in that language.

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