how to create conditionals in a Fixpoint definition Coq

Question

I am working through the book "Software Foundations", and am on the last problem in Chapter two. The problem asks to convert a natural number into a binary number, where a binary number is defined in the following ways:

  - [is] zero,
  - [is] twice a binary number, or
  - [is] one more than twice a binary number.

My thought process is that if a natural number is even, then it can be expressed as

double(nat_to_bin n)

However, in my Fixpoint definition, when I tried to write

(evenb n' = true) => double(nat_to_bin)

I got an error because evenb n' is not a constructor of nat. Is there any way for me to create a conditional such that the above line would be a valid function definition, without changing the definition of nat?

Roquentin · Answer 1 · 2018-12-23T05:49:35.887

2

Nevermind, I figured out a solution. I can just write the term

match (evenb n') with
| true => ....

Took me a while, though.

edited Dec 23 '18 at 05:49

answered Dec 23 '18 at 05:30

Roquentin

177
2
12

2

or `if evenb n' then ... else ...` – Li-yao Xia Dec 23 '18 at 13:14

how to create conditionals in a Fixpoint definition Coq

1 Answers1