GeezerVison

so that the new concepts can be seen ``in action'' as soon as

possible.

TODO: update with actual learning outcomes

The course has two major learning outcomes.

First, the students should be able to design and implement a DSL in a

new domain.

Second, they should be able to handle new mathematical areas using the

computer science perspective.

(For the detailed learning outcomes, see figure~\ref{fig:LearningOutcomes}.)

\begin{wrapfigure}{R}{0.5\textwidth}

\begin{itemize}

\item Knowledge and understanding

\begin{itemize}

\item design and implement a DSL (Domain Specific Language) for a new domain

\item organize areas of mathematics in DSL terms

\item explain main concepts of elementary real and complex analysis,

algebra, and linear algebra

\end{itemize}

\item Skills and abilities

\begin{itemize}

\item develop adequate notation for mathematical concepts

\item perform calculational proofs

\item use power series for solving differential equations

\item use Laplace transforms for solving differential equations

\end{itemize}

\item Judgement and approach

\begin{itemize}

\item discuss and compare different software implementations of

mathematical concepts

\end{itemize}

\end{itemize}

\caption{Learning outcomes for DSLsofMath}

\label{fig:LearningOutcomes}

\end{wrapfigure}

To achieve these objectives, the course consists of a sequence of case

studies in which a mathematical area is first presented (for example,

quickly, and in any case we aim to keep to a restricted subset of

Haskell (no ``advanced'' features are required).

TODO: rewrite when the evaluation results are available

To assess the impact in terms of increased quality of education, we

plan to measure how well the students do in ulterior courses that

The work that lead up to the current course is as follows:

\begin{itemize}

\item 2014: in interaction with our colleagues from the various study

programmes, we performed an assessment of the current status of

potential students for the course in terms of their training (what

prerequisites we can reasonably assume) and future path (what

mathematical fields they are likely to encounter in later studies),

and we worked out a course plan (which we submitted in February

2015, so that the first instance of the course could start in

January 2016).

We also make a survey of similar courses being offered at other

universities, but did not find any close matches.

\item 2015: we developed course materials for use within the first

instance, wrote a paper \citep{TFPIE15_DSLsofMath_IonescuJansson}

about the course and pressented the pedagogical ideas at several

events (TODO: perhaps fill in TFPIE'15, DSLDI'15, IFIP WG 2.1 \#73

in Göteborg, LiVe4CS in Glasgow).

\item 2016: we ran the first instance of DSLM (partly paid by the

regular course budget, partly by this project) with Cezar Ionescu as

main lecturer.

\item 2017: we ran the second instance of DSLM (paid fully by the

regular course budget), now with Patrik Jansson as main lecturer.

\item 2016 and 2017: we used the feedback from students following the

standard Chalmers course evaluation in order to improve and further

develop the course material.

\end{itemize}

\paragraph{2014:} in interaction with our colleagues from the various

study programmes, we performed an assessment of the current status of

potential students for the course in terms of their training (what

prerequisites we can reasonably assume) and future path (what

mathematical fields they are likely to encounter in later studies),

and we worked out a course plan (which we submitted in February 2015,

so that the first instance of the course could start in January 2016).

We also make a survey of similar courses being offered at other

universities, but did not find any close matches.

Future work includes involving faculty from CSE and mathematics in the

development of other mathematics courses (prel.\ Linear Algebra,

Analysis) with the aim to incorporate these ideas also there.

\paragraph{2015:} we developed course materials for use within the

first instance, wrote a paper

\citep{TFPIE15_DSLsofMath_IonescuJansson} about the course and

pressented the pedagogical ideas at several events (TFPIE'15,

DSLDI'15, IFIP WG 2.1 \#73 in Göteborg, LiVe4CS in Glasgow).

\paragraph{2016:} we ran the first instance of DSLM (partly paid by

the regular course budget, partly by this project) with Cezar Ionescu

as main lecturer.

\paragraph{2017:} we ran the second instance of DSLM (paid fully by

the regular course budget), now with Patrik Jansson as main lecturer.

\paragraph{2016 and 2017:} we used the feedback from students

following the standard Chalmers course evaluation in order to improve

and further develop the course material.

\paragraph{Future work} includes involving faculty from CSE and

mathematics in the development of other mathematics courses (prel.\

Linear Algebra, Analysis) with the aim to incorporate these ideas also

there.

A major concern will be to work together with our colleagues in the

mathematics department in order to distill the essential principles

\subsection{Who should read these lecture notes?}

TODO: Convert formal prerequisites to ``what is expected of the reader''

The prerequisites of the underlying course may give a hint about what

is expected of the reader.

But feel free to keep going and fill in missing concepts as you go

along.

The student should have successfully completed

\begin{itemize}

\item a course in discrete mathematics as for example Introductory Discrete Mathematics.

\item 15 hec in mathematics, for example Linear Algebra and Calculus

Informally: One full time year (60 hec) of university level study

consisting of a mix of mathematics and computer science.

Working knowledge of functional programming is helpful, but it should

be possible to pick up quite a bit of Haskell along the way.

\subsection{Roadmap}

TODO: write about the lecture plan and internal dependencies

and implementing mathematical text.

TODO: fill in more about notation

\subsection*{Acknowledgments}

\end{code}

\paragraph{Lifting operations to a parameterised type}

|r| which supports addition.

\begin{code}

\end{exercise}

\begin{exercise}

\label{exc:embedeval}

When is |embed (eval e) == e|?

Step 0: type the quantification: what is the type of |e|?

Step 1: what equality is suitable for this type?

Step 2: if you use ``equality up to eval'' --- how is the resulting

property related to the first round-trip property?

\end{exercise}

TODO: Add an exercise to implement some property as a boolean functions (for example some from the semiring properties.

\begin{exercise} \label{exc:e1_semiring}