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John Gatward committed 2026-10-04 15:24:17 +01:00
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docs/lectures/compilers/02_arithmetic.md
+7 -9
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@@ -28,7 +28,7 @@ exp -> exp + exp
-> 7 + (10 / 3) * (-2)
```
This grammar is **ambiguous**, this means one input expression could be generated in several different ways.
This grammar is **ambiguous**: this means one input expression could be generated in several different ways.
$$
5 - 4 \times 7
@@ -43,7 +43,7 @@ exp -> exp - exp
-> 5 - 4 * 7
```
However there is another way to derive this expression starting with `*`
However, there is another way to derive this expression starting with `*`
```haskell
exp -> exp * exp
@@ -52,7 +52,7 @@ exp -> exp * exp
-> 5 - 4 * 7
```
These give us two different ASTs, which gives us two different numeric answers. We must use more terminal symbols to follow BIDMAS.
These give us two different ASTs, which give us two different numeric answers. We must use more terminal symbols to follow BIDMAS.
![](img/e.png)
@@ -74,7 +74,7 @@ This grammar is unique (non-ambiguous)
## Semantics of Expressions
On the left hand side the $+$ is just a symbol, however on the right hand side it is an arithmetic sum operation.
On the left-hand side, the $+$ is just a symbol; however, on the right-hand side it is an arithmetic sum operation.
$[\![ exp + exp ]\!] = [\![exp ]\!] + [\![exp ]\!]$ | $[\![ exp - exp ]\!] = [\![exp ]\!] - [\![exp ]\!]$ ... same for all binary operations
@@ -99,14 +99,12 @@ $[\![d_0 ]\!] = value(d_0)$
$[\![d_s d_0]\!] = [\![d_s ]\!]\times10 + value(d_0)$
## Scanners and Parsers
![img](img/f.png)
Scanners take the source language as input and outputs a stream of tokens.
Scanners take the source language as input and output a stream of tokens.
A **token** is a chunk of input; "words" of the language eg. integers, operator symbols, identifiers (function & variable names etc), parenthesis.
A **token** is a chunk of input; "words" of the language, e.g. integers, operator symbols, identifiers (function & variable names etc.), parentheses.
The **grammar of tokens is always regular**, this means it can be generated and recognised by a DFA (deterministic finite automata).
The **grammar of tokens is always regular**: this means it can be generated and recognised by a DFA (deterministic finite automaton).