Chapter 13, Monadic parsing Video Solutions, Programming in Haskell

Problem 1

Define a parser comment :: Parser () for ordinary Haskell comments that begin with the symbol - and extend to the end of the current line, which is represented by the control character ' $\backslash n^{\prime}$.

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09:48

Problem 2

Using our second grammar for arithmetic expressions, draw the two possible parse trees for the expression $2+3+4$.

Chris Trentman

Numerade Educator

09:48

Problem 3

Using our third grammar for arithmetic expressions, draw the parse trees for the expressions $2+3,2 \star 3 \star 4$ and $(2+3)+4$.

Chris Trentman

Numerade Educator

00:53

Problem 4

Explain why the final simplification of the grammar for arithmetic expressions has a dramatic effect on the efficiency of the resulting parser. Hint: begin by considering how an expression comprising a single number would be parsed if this simplification step had not been made.

Karly Williams

Numerade Educator

06:18

Problem 5

Define a suitable type Expr for arithmetic expressions and modify the parser for expressions to have type expr :: Parser Expr.

Chris Trentman

Numerade Educator

06:18

Problem 6

Extend the parser expr :: Parser Int to support subtraction and division, and to use integer values rather than natural numbers, based upon the following revisions to the grammar:
$$
\begin{array}{ll}
\operatorname{expr} & :=\operatorname{term}(+\exp r|-\operatorname{expr}| \epsilon) \\
\text { term } & :=\operatorname{factor}(* \operatorname{term}|/ \operatorname{term}| \epsilon) \\
\text { factor }::=(\text { expr }) \mid \text { int } \\
\text { int } & ::=\cdots|-1| 0|1| \cdots
\end{array}
$$

Chris Trentman

Numerade Educator

01:47

Problem 7

Further extend the grammar and parser for arithmetic assumed to associate to the right and have higher priority than multiplication and division, but lower priority than parentheses and numbers. For example, $2^{\wedge} 3^* 4$ means $\left(2^{\wedge} 3\right) * 4$. Hint: the new level of priority requires a new rule in the grammar.

James Kiss

Numerade Educator

Problem 8

Consider expressions built up from natural numbers using a subtraction operator that is assumed to associate to the left.
a. Translate this description directly into a grammar.
b. Implement this grammar as a parser expr :: Parser Int.
c. What is the problem with this parser?
d. Show how it can be fixed. Hint: rewrite the parser using the repetition primitive many and the library function foldl.

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00:40

Problem 9

Modify the calculator program to indicate the approximate position of an error rather than just sounding a beep, by using the fact that the parser returns the unconsumed part of the input string.
Solutions to exercises 1-4 are given in appendix A.

Vanna Tran

Numerade Educator