In this lab, we'll be getting some practice working with Strings. We won't do this much in this course, but it's important to know how to do. I would recommend pair programming for this lab. Since there's nothing to turn in, it would be a good way to talk through how to approach each problem.
Run the following command to create a dune project in a directory called lab03:
dune init project lab03lib/lab03.ml and put your solutions there.Implement a function drop_leading of type char -> string -> string so that drop_leading c s is the result of removing all instances of c from the front of s. Also implement a function drop_trailing of type char -> string -> string so that drop_trailing c s is the result of removing all instances of c from the back of s. You should use the function String.get and String.sub in your solution. See the stdlib320 documentation for more details.
let _ = assert (drop_leading 'a' "aaabbbaaa" = "bbbaaa")
let _ = assert (drop_trailing 'a' "aaabbbaaa" = "aaabbb")\def\code#1{\textcolor{purple}{\texttt{#1}}}
\{ \code{x} : \code{int} \} \vdash \code{let y = 2 in x + y} : \code{int}
Write a typing derivation for the above typing judgment using the following rules. Make sure to label each instance of a rule with its name, and to exclude side conditions from your derivation.
\def\code#1{\textcolor{purple}{\texttt{#1}}}
\def\side#1{\textcolor{green}{#1}}
\frac
{\side{\code{n} \text{ is an \code{int} literal}}}
{\Gamma \vdash \code{n} : \code{int}}
\text{(int)}
\qquad
\frac{\side{(x : \tau) \in \Gamma}}{\Gamma \vdash x : \tau} \text{(var)}
\qquad
\frac{\Gamma \vdash e_1 : \code{int} \qquad \Gamma \vdash e_2 : \code{int}}{\Gamma \vdash e_1 \code{ + } e_2 : \code{int}} \text{(add)}
\qquad
\frac
{\Gamma \vdash e_1 : \tau_1 \qquad \Gamma, \code x : \tau_1 \vdash e_2 : \tau_2}
{\Gamma \vdash \code{let x = } e_1 \code{ in } e_2 : \tau_2} \text{(let)}
\def\code#1{\textcolor{purple}{\texttt{#1}}}
\code{let y = 2 in 3 + y} \Downarrow 5
Write an evaluation derivation for the above evaluation judgment using the following rules. Make sure to label each instance of a rule with its name, and to exclude side conditions from your derivation.
\def\code#1{\textcolor{purple}{\texttt{#1}}}
\def\side#1{\textcolor{green}{#1}}
\frac
{\side{\code{n} \text{ is an \code{int} literal for } n}}
{\code{n} \Downarrow n}
\text{(int-eval)}
\qquad
\frac{e_1 \Downarrow v_1 \qquad e_2 \Downarrow v_2 \qquad \side{v_1 + v_2 = v}}
{e_1 \code{ + } e_2 \Downarrow v} \text{(add-eval)}
\qquad
\frac
{e_1 \Downarrow v_1 \qquad
\side{e = [v_1 / x] e_2} \qquad
e \Downarrow v}
{\code{let x = } e_1 \code{ in } e_2 \Downarrow v} \text{(let-eval)}