程序代写代做代考 1 this is a section heading

1 this is a section heading
1.1 this is a subsection heading
1.1.1 this is a subsubsection heading

So you want to try some tex?
Inline math is like this TRUE = (λxy.x)
Or they can go on their own line like this

FALSE = (λxy.y)

You can get different sized parentheses like this:((((
()
))))

If you wanted to do the full notation (don’t) the application is ·, e.g.
(
λx.
(
λy.(y · x)

))
You can do subscripts in math x1, x2, x12, and superscripts x1, x2, x12, or both Σfoobar
Some fancy symbols: →,→β,↠β,≡,=β …
Some not so fancy symbols: {a, b, c} … (we had to escape the brace with a backslash)
Later in the course you might want some these too ∧∨ ⇒⇔⊢
In general, if you need to find a symbol go look at http://detexify.kirelabs.org/classify.html
Often you want to line up formulas:

F {a, b, c, d}
= (Y H) {a, b, c, d}
= H (Y H) {a, b, c, d} (Y Combinator)

=
(
λfa.

(
ISNIL (TAIL a)

)
(HEAD a)

(
f (TAIL a)

))
(Y H) {a, b, c, d}

=
(
λa.
(
ISNIL (TAIL a)

)
(HEAD a)

(
(Y H) (TAIL a)

))
{a, b, c, d} (β-reduction)

= …

It aligns the & characters. Don’t forget the double backslashes to end each line.
I’ll admit, manually adding all those spaces in mathmode is pretty annoying. I expect there’s a much

better way to typeset stuff.
If you don’t put a blank
line between lines with text then there isn’t a gap

• bullet

• points

1. numbered

2. points

tables are nice once
you get
the hang of

them
Here’s some truetype font for where you don’t need fancy highlighting.

1

� �
;; here’s some source code, for when you do
;; it’s verbatim — you get exactly what you write , see: $\equiv_\beta$
(defun insert (tree x)
;; inserts x to the binary search tree
)
(defun list-to-tree (mylist &optional tree)
;; note: the second argument ‘tree’ will be nil by default
;; inserts every element of the list ‘mylist ‘ into the tree
)
(defun inorder (tree)
;; list giving the inorder traversal of the tree
)� �

OK, that wasnt very fancy. You can make it prettier if you really want, e.g.
https://www.overleaf.com/latex/examples/syntax-highlighting-in-latex-with-the-listings-package/

jxnppmxxvsvk#.W4J-guj7QuV

2