Fixed left inverse in Isomorphism

This commit is contained in:
Philip Wadler 2019-01-22 11:59:00 +00:00
commit 324b974461
4 changed files with 22 additions and 6 deletions

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@ -8,6 +8,21 @@ permalink: /Notes/
<https://analytics.google.com/analytics/web/>
## Git commands
Git commands to create a branch and pull request
git help <command> -- get help on <command>
git branch -- list all branches
git branch <name> -- create new local branch <name>
git checkout <name> -- make <name> the current branch
git merge <name> -- merge branch <name> into current branch
git push origin <name> -- make local branch <name> into remote
git rebase <base> -- merge branch <base> into current branch
On website, use pulldown menu to swith branch and then
click "new pull request" button.
## Suggestion from Conor for Inference
Conor McBride <conor.mcbride@strath.ac.uk>

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@ -171,7 +171,8 @@ configuration file at `~/.emacs`, if you have the mentioned fonts available:
## Markdown
The book is written in [Kramdown Markdown](https://kramdown.gettalong.org/syntax.html).
The book is written in
[Kramdown Markdown](https://kramdown.gettalong.org/syntax.html).
## Travis Continuous Integration

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@ -348,7 +348,7 @@ an order that will make sense to the reader.
The proof of monotonicity from
Chapter [Relations][plfa.Relations]
can be written in a more readable form by using an anologue of our
can be written in a more readable form by using an analogue of our
notation for `≡-reasoning`. Define `≤-reasoning` analogously, and use
it to write out an alternative proof that addition is monotonic with
regard to inequality. Rewrite both `+-monoˡ-≤` and `+-mono-≤`.
@ -399,7 +399,7 @@ even-comm : ∀ (m n : )
even-comm m n ev rewrite +-comm n m = ev
\end{code}
Here `ev` ranges over evidence that `even (m + n)` holds, and we show
that it is also provides evidence that `even (n + m)` holds. In
that it also provides evidence that `even (n + m)` holds. In
general, the keyword `rewrite` is followed by evidence of an
equality, and that equality is used to rewrite the type of the
goal and of any variable in scope.
@ -452,8 +452,8 @@ here is a second proof that addition is commutative, relying on rewrites rather
than chains of equalities:
\begin{code}
+-comm : ∀ (m n : ) → m + n ≡ n + m
+-comm zero n rewrite +-identity n = refl
+-comm (suc m) n rewrite +-suc n m | +-comm m n = refl
+-comm zero n rewrite +-identity n = refl
+-comm (suc m) n rewrite +-suc n m | +-comm m n = refl
\end{code}
This is far more compact. Among other things, whereas the previous
proof required `cong suc (+-comm m n)` as the justification to invoke

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@ -778,7 +778,7 @@ operations associate to the left rather than the right. For example:
#### Exercise `foldr-monoid-foldl`
Show that if `__` and `e` form a monoid, then `foldr _⊗_ e` and
Show that if `__` and `e` form a monoid, then `foldr _⊗_ e` and
`foldl _⊗_ e` always compute the same result.