Isabelle Real Datatype - Malformed definition: Non-constructor pattern not allowed in sequential mode

问题

I am creating a function of the form

y(t+h) = y(t) + h/y(t)

where y(0) = 1

fun y :: "real ⇒ real" where "y 0 = Suc(0)"| "y(t+h) = y(t) + h*(1/y(t))"

Unfortunately, I am getting an error

Malformed definition: Non-constructor pattern not allowed in sequential mode.

y 0 = real (Suc 0)

Googling showed me that I am not adhering to some constructor pattern of real datatype but I am not able to find what the pattern is and how I should change my function.

回答1:

Real numbers are not an algebraic datatype, so you can't pattern match on them with fun. You have to use either ‘normal’ equational definitions or some of the more advanced features of the function package, but that also makes things more difficult since you have to prove some well-definedness properties yourself.

Also, the Suc 0 on the right-hand side is a natural number, not a real number. (just write 1 instead)

However, the biggest problem with your definition is that the way you have written it down is too informal. I don't understand what it means even informally.

• What assumptions do you have about h?
• For what t should that second equation be valid?
• What happens when you put in a negative value for t? (the way you've written it: non-termination)
• What happens when 0 < t < h?

Once you have a mathematically precise specification for the function you want to define, you can probably write it down without too much of a headache with the function command

来源：https://stackoverflow.com/questions/44238481/isabelle-real-datatype-malformed-definition-non-constructor-pattern-not-allow