data abstraction

Complete

Summary

Pairs

js
const x = pair(1, 2);

Box and pointer diagrams

x12

Concept

Primitive form of data abstraction using pairs to store 2 values
Second value can be used to store another pair, into a chain of pairs
First value can also be a pair, to form a tree of pairs

js
const p = pair(a, b) // -> [a, b]

head(p) // -> a
tail(p) // -> b

Further abstracted to lists, trees(cs) and arrays

Equality vs Identity
=== -> Equal by identity
equal() -> Equal by value

js
const a = pair(1, 2);
const b = a;
const c = pair(1, 2);

a === b; // -> true
a === c; // -> false

equal(a, b); // -> true
equal(a, c); // -> true
12abc12

Extra

Tikz template for box and pointer diagrams

latex
\usepackage{tikz}
\usetikzlibrary{positioning,arrows.meta}
% definitions for box and pointer diagrams
\def\boxsize{6mm}
\tikzset{cell/.style={inner sep=0pt,minimum size=\boxsize, node distance=2em and 3.5em}}
\newcommand\ptr[2]%
  {
      \draw[arrows={-Latex}] (#1.center)--(#2);
  }
\newcommand\pnull[1]%
  {
      \draw (#1.south west)--(#1.north east);
  }
\newcommand\pair[4][]%
  {
	\node[draw,cell,#1] (#2) {#3};
	\node[draw,cell,anchor=west] (#2tail) at (#2.east) {#4};
  }
\begin{document}
\begin{tikzpicture}
% draw diagram here
  \node (start) {list};
  \pair[right=of start]{p1}{10}{}
  \pair[right=of p1]{p2}{}{}
  \pair[below=of p2]{p3}{40}{}
  \ptr{p1tail}{p2}
  \ptr{p2}{p3}
  \ptr{p2tail}{p3}
  \draw[arrows={-Latex}] (start.east)--(p1);
  \pnull{p3tail}
\end{tikzpicture}
\end{document}