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    Lab 2: Nested Function Call Exercises
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# Lab 2: Nested Function Call Exercises

**Do these exercises on the whiteboard with your partner(s).**

## Exercise Nested 1

```py
@php
include DOC_ROOT . '/content/labs/lab02/starter/funs1.py';
@endphp
```

Answer the following questions for the functions `h` and `q` defined above:

* **Nested 1a:**: What are the values of each of the following expressions?
  + `h(q('d'))`
  + `q(h('e'))`
  + `h(q(h('F')))`

* **Nested 1b:** Using `h`, `q`, and `'F'`, what is a different expression than `h(q(h('F')))`
that returns the same value? 

* **Nested 1c:** Using `h`, `q`, and `'g'`, write three different expressions that evaluate
to the string `'##G???'`

## Exercise Nested 2

```py
@php
include DOC_ROOT . '/content/labs/lab02/starter/funs2.py';
@endphp
```

Answer the following questions for the functions `z`, `d`, and `i` defined above:

* **Nested 2a:**  What are the values of each of the following expressions?
  + `i(d(i(z())))`
  + `d(i(i(z())))`

* **Nested 2b:** Using only calls to `d`, `i`, and `z`,
write expressions that evaluate to the following integers:
  + 7
  + 10
  + 13
  + 15
  + 16

* **Nested 2c:** For any nonnegative integer _n_, is it possible to express
  _n_ with an expression involving calls to only `d`, `i`, and `z`?
  Explain your answer. 

* **Nested 2d:** For any integer _n_ expressible involving calls to only
    `d`, `i`, and `z`, can there be more than one expression involving calls
    to only `d`, `i`, and `z` that evaluates to _n_?

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