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Fix some typos

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Danila Fedorin
2019-11-06 22:27:52 -08:00
parent 654239e29f
commit 2cce2859bb
3 changed files with 8 additions and 8 deletions
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content/blog/02_compiler_parsing.md
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@@ -38,7 +38,7 @@ $$
In practice, there are many ways of using a CFG to parse a programming language. Various parsing algorithms support various subsets
of context free languages. For instance, top down parsers follow nearly exactly the structure that we had. They try to parse
a nonterminal by trying to match each symbol in its body. In the rule \\(S \\rightarrow \\alpha \\beta \\gamma\\), it will
first try to match \\(alpha\\), then \\(beta\\), and so on. If one of the three contains a nonterminal, it will attempt to parse
first try to match \\(\\alpha\\), then \\(\\beta\\), and so on. If one of the three contains a nonterminal, it will attempt to parse
that nonterminal following the same strategy. However, this leaves a flaw - For instance, consider the grammar
$$
\\begin{align}
@@ -105,7 +105,7 @@ A\_{add} & \\rightarrow A\_{add}-A\_{mult} \\\\\\
A\_{add} & \\rightarrow A\_{mult}
\\end{align}
$$
The first rule matches another addition, added to the result of another addition. We use the addition in the body
The first rule matches another addition, added to the result of a multiplication. Similarly, the second rule matches another addition, from which the result of a multiplication is then subtracted. We use the \\(A\_{add}\\) on the left side of \\(+\\) and \\(-\\) in the body
because we want to be able to parse strings like `1+2+3+4`, which we want to view as `((1+2)+3)+4` (mostly because
subtraction is [left-associative](https://en.wikipedia.org/wiki/Operator_associativity)). So, we want the top level
of the tree to be the rightmost `+` or `-`, since that means it will be the "last" operation. You may be asking,
@@ -150,7 +150,7 @@ What's the last \\(C\\)? We also want a "thing" to be a case expression. Here ar
$$
\\begin{align}
C & \\rightarrow \\text{case} \\; A\_{add} \\; \\text{of} \\; \\{ L\_B\\} \\\\\\
L\_B & \\rightarrow R \\; , \\; L\_B \\\\\\
L\_B & \\rightarrow R \\; L\_B \\\\\\
L\_B & \\rightarrow R \\\\\\
R & \\rightarrow N \\; \\text{arrow} \\; \\{ A\_{add} \\} \\\\\\
N & \\rightarrow \\text{lowerVar} \\\\\\