# Lecture - Functional Programming, MT22, VIII

> Source: https://ollybritton.com/notes/uni/prelims/mt22/functional-programming/lectures/8/ · Updated: 2022-11-24 · Tags: uni, lecture

- [Course - Functional Programming MT22](https://ollybritton.com/notes/uni/prelims/mt22/functional-programming/)

### Flashcards
When all the conditions hold, what does fold fusion say about $\text{f} \cdot \text{fold g a}$?::
$$
\text{f} \cdot \text{fold g a} = \text{fold h b}
$$

The fold fusion law is
$$
\text{f} \cdot \text{fold g a} = \text{fold h b}
$$
How many conditions are there for this to hold?::
3

The fold fusion law is
$$
\text{f} \cdot \text{fold g a} = \text{fold h b}
$$
What, broadly, are the three conditions for this to hold?::
- Strictness
- Zero value
- Moving $f$ through

The fold fusion law is
$$
\text{f} \cdot \text{fold g a} = \text{fold h b}
$$
What is the condition about stritcness?::
$f$ is strict, i.e. $f \bot = \bot$.

The fold fusion law is
$$
\text{f} \cdot \text{fold g a} = \text{fold h b}
$$
What is the condition about the zero value $b$?
$$
\text{f a = b}
$$

The fold fusion law is
$$
\text{f} \cdot \text{fold g a} = \text{fold h b}
$$
What is the tricky condition about “moving $f$ through”?::
$$
\text{f (g x y)} = \text{h x (f y)} 
$$

What is the identity $\text{id}$ function as a fold?::
$$
\text{fold (:) []}
$$

How do you determine if a function $f$ can be written as a fold?::
Use fold fusion with the identity fold,
$$
\text{f}\cdot \text{fold (:) []} 
$$

When determining if a function $f$ is a fold on lists by composing it with the identity fold, i.e.
$$
\text{f}\cdot \text{fold (:) []}
$$
What does the tricky condition about “moving $f$ through” become?::
$$
\text{f (x : xs)} = \text{h x (f xs)}
$$

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