$$ \begin{eqnarray} & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Expressions in Haskell are similar to those in other languages.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ But there are only expressions, no statements in Haskell.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Assignments are not updates of values but equations.}}}} \
\end{eqnarray} $$
$$ \begin{eqnarray} & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Haskell programs compute by } \mathit{reduction} \hbox{.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ i.e. gradually replacing expressions by their values.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ A function takes one or more } \mathit{arguments} \hbox{ }}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ and computes a } \mathit{result} \hbox{.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ Given the same arguments, the result will always be the same.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ In Haskell there are no side-effects.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ The list is the key datastructure.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ It is quite similar to lists in other languages but immutable.}}}} \
\end{eqnarray} $$
$$ \begin{eqnarray} & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ The basic mechanism for computing on}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ any datastructure in Haskell is recursion.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ Recursion always has a } \mathit{base} \hbox{ case and an } \mathit{induction} \hbox{ case.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ For lists, the base case is the empty list [],}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ the induction case is adding an element to the list } \mathit{x:xs} \hbox{.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ For list operations, it is usually easier}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ to use higher-order functions}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ like map (performing an operation on every element of a list)}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ and foldl/foldr (reducing a list to a single value).}}}} \
\end{eqnarray} $$
$$ \begin{eqnarray} & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Parsing text is a very common and important operation.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Monadic parser combinators are a convenient mechanism}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ to build parsers by combining building blocks,}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ and a good illustration of the practical use of a monad.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Each parser is a higher-order function}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ that returns a function.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ The parser combinators combine these functions into the final parser.}}}} \
\end{eqnarray} $$
$$ \begin{eqnarray} & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Function types describe the types of}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ arguments and return value of a function.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ The type of an argument can be a type variable,}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ in which case we call the function polymorphic.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Currying means rewriting a function}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ of more than one argument to a}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ sequence of functions of a single argument.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Type classes allow to impose restrictions}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ on polymorphic type variables.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ Type classes express that e.g. a type represents}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ a number, or something that can be ordered.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Type inference is the analysis of code}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ in order to infer its type.}}}} \ & & \Large{\color{navy}{\mathsf{; ; \hbox{ It works using type inference rules that}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ generate typings based on the program text.}}}} \
\end{eqnarray} $$
$$ \begin{eqnarray} & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Type classes provide a set of function type signatures}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Haskell provides special keywords to create type classes}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ To create an instance, we create functions}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ for a given type that match the signature of the type class}}}} \
\end{eqnarray} $$
$$ \begin{eqnarray} & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ The lambda calculus is a formal model}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ for computation using only lambda functions.}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ Haskell, as other functional languages,}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ is based on the lambda calculus}}}} \ & & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ The reduction rules from the lambda calculus}}}} \ & & \LARGE{\color{navy}{\mathsf{; ; \hbox{ are use to reduce expressions in Haskell.}}}} \
\end{eqnarray} $$
$$
\begin{eqnarray}
& & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ A monad is a mechanism for combining computations}}}} \
& & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ It is a typeclass providing the } \mathit{bind} \hbox{ and } \mathit{return} \hbox{ operations}}}} \
& & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ To be an actual monadic type, the implementations of}}}} \
& & \LARGE{\color{navy}{\mathsf{; ; \hbox{ bind and return must conform to the three monad laws}}}} \
& & \LARGE{\color{navy}{\mathsf{\bullet ;\hbox{ The Maybe monad illustrates how to create}}}} \
& & \LARGE{\color{navy}{\mathsf{; ; \hbox{ a simple monad and its benefits.}}}} \
\end{eqnarray} $$