I'm going to read the matrix.

There's no quiz today.

It's postponed to Thursday morning.

They changed latex overnight

and that uncovered a very deep bug in our backend pipeline.

Even though Dennis fixed that half an hour ago

it's based on Rust

and Rust has a very

optimizing compiler

so it takes about one and a half hours to compile the whole thing

which means there's no quiz today.

Are there any questions?

So we were talking about Prolog as a programming language

and we kind of started getting into

the programming features.

Right in the beginning

I tried to sell you on this story that is sometimes called declarative

programming

or in other words

we only have to say what the program is supposed to do

and backtracking search actually does it for you.

And that is correct.

For instance

for addition

multiplication

and exponentiation

we just need to say what

the operations of addition

multiplication

and exponentiation do on zeros and successors

and the rest is being done.

If you look at these things here and kind of switch before your inner eye

the functional

and the relational kind of versions

these are exactly the same defining equations we

had on the slides in the beginning.

Those are the things you learn typically.

Those are the inductive definitions of plus.

Here they become recursive predicates.

But other than that, this is just specification.

It can work so well that we can do it for other things as well.

The Fibonacci numbers

we just write the defining equations.

The zero Fibonacci number is one

the second one is also one

and then you get the next

Fibonacci number by adding up the last two.

Just the specification.

You don't have to say for i equals something to something

do this and that and so on.