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I am trying to define the function:

Fi(xi) = real

However I am finding it hard to implement subscripts into my function. The subscript i has to be a natural number, whereas x is a real number, and the output is also real.

I have tried defining the function with two arguments however I have not been successful.

How am I able to show have a function with an index in Isabelle?

A K
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  • I'm not quite sure what you mean. As I understand it, an index is typically just an additional `nat` parameter. E.g., the infinite sequence `f_0, f_2, f_3, ...` would be represented by a function `f` of type `nat => 'a` in Isabelle/HOL. Or are you talking about *subscript syntax*? – chris Feb 25 '15 at 18:46
  • @chris Thanks for the comment. Sorry for the confusion, I am referring to an index, not the subscript itself. I understand that the index is an additional nat parameter however if I try to define the above function, I end up with duplicate variables on the LHS as I have "f i v i = real". How would you represent the function above? – A K Feb 26 '15 at 11:34
  • @A K: if you have you have to times the same number `i`, then you should only use one additional parameter (unless I'm missing something else). Something like `f i v = real`, otherwise its not a function definition. But then again, assuming you have an infinite sequence `v :: nat => 'a` and a function `f :: nat => 'a => ...` you can of course write expressions like `f i (v i)`, which is maybe what you want. – chris Feb 26 '15 at 12:36
  • Thanks @chris, the last part is just what I needed. – A K Feb 26 '15 at 21:36

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