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Minor clarifications on exercises in Naturals and Induction.

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Wen Kokke 2020-01-21 17:03:56 +00:00
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12
src/plfa/part1/Induction.lagda.md
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@ -75,13 +75,11 @@ that a newly introduced operator is associative but not commutative.
Give another example of a pair of operators that have an identity
and are associative, commutative, and distribute over one another.
(You do not have to prove these properties.)
Give an example of an operator that has an identity and is
associative but is not commutative.
```
-- Your code goes here
```
(You do not have to prove these properties.)
## Associativity
@ -944,9 +942,9 @@ for all naturals `m`, `n`, and `p`.
Show the following three laws
m ^ (n + p) ≡ (m ^ n) * (m ^ p)
(m * n) ^ p ≡ (m ^ p) * (n ^ p)
m ^ (n * p) ≡ (m ^ n) ^ p
m ^ (n + p) ≡ (m ^ n) * (m ^ p) (^-distribˡ-+-*)
(m * n) ^ p ≡ (m ^ p) * (n ^ p) (^-distribʳ-*)
(m ^ n) ^ p ≡ m ^ (n * p) (^-*-assoc)
for all `m`, `n`, and `p`.

7
src/plfa/part1/Naturals.lagda.md
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@ -428,7 +428,7 @@ other word for evidence, which we will use interchangeably, is _proof_.
#### Exercise `+-example` (practice) {#plus-example}
Compute `3 + 4`, writing out your reasoning as a chain of equations.
Compute `3 + 4`, writing out your reasoning as a chain of equations, using the equations for `+`.
```
-- Your code goes here
@ -489,7 +489,8 @@ it can easily be inferred from the corresponding term.
#### Exercise `*-example` (practice) {#times-example}
Compute `3 * 4`, writing out your reasoning as a chain of equations.
Compute `3 * 4`, writing out your reasoning as a chain of equations, using the equations for `*`.
(You do not need to step through the evaluation of `+`.)
```
-- Your code goes here
@ -566,7 +567,7 @@ _ =
∎
```
#### Exercise `∸-examples` (recommended) {#monus-examples}
#### Exercise `∸-example₁` and `∸-example₂` (recommended) {#monus-examples}
Compute `5 ∸ 3` and `3 ∸ 5`, writing out your reasoning as a chain of equations.