[isabelle] Problem with pretty printing rationals



Dear all,

I just encountered the following problem. When writing a pretty printer for rational numbers the standard function I would like to write is:

show_rat (Fract a b) = (if b = 1 then show_int a else show_int a @ ''/'' @ show_int b)"

However, since Fract is a only a code_datatype and not a datatype, Isabelle refused this function definition. (And it must refuse, since Fract 1 2 = Fract 2 4, but show_rat .. = 1/2 != 2/4 = show_rat .. Hence, show_rat is not a function.)

Instead, I now added an axiom

consts show_rat
axioms show_rat_def[code]: "show_rat (Fract a b) = (if b = 1 then show_int a else show_int a @ ''/'' @ show_int b)"

Now, the code-generator is working. However, I do not like to add axioms to my theory, so is there a better way around? Are there for example functions like "get_numerator" and "get_denominator" which return unique results independent of whether using (Fract 1 2) or (Fract 2 4) which I overlooked in Rational.thy?

Thanks a lot,
René



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