164 lines
7.2 KiB
Markdown
164 lines
7.2 KiB
Markdown
# Functional programming and type systems (2017-2018)
|
|
|
|
This page supplements
|
|
[the official page of MPRI 2-4](https://wikimpri.dptinfo.ens-cachan.fr/doku.php?id=cours:c-2-4-2).
|
|
|
|
## Location and duration
|
|
|
|
The lectures take place at University Paris 7 - Denis Diderot,
|
|
Bâtiment Sophie Germain, in room 2035.
|
|
|
|
They are scheduled on Fridays from 12:45 to 15:30.
|
|
There is a 15-minute break in the middle of each lecture.
|
|
|
|
## Teachers
|
|
|
|
* Functional Programming: Under the Hood (12h30, [François Pottier](http://gallium.inria.fr/~fpottier))
|
|
* [Metatheory of Typed Programming Languages](http://gallium.inria.fr/~remy/mpri/) (12h30, [Didier Rémy](http://gallium.inria.fr/~remy/), *head*)
|
|
* Advanced Aspects of Type Systems (12h30, [Yann Régis Gianas](http://www.pps.jussieu.fr/~yrg/))
|
|
* Dependently-typed Functional Programming (12h30, [Pierre-Evariste Dagand](https://pages.lip6.fr/Pierre-Evariste.Dagand/))
|
|
|
|
## Aims
|
|
|
|
This course presents the principles and formalisms that underlie many of
|
|
today's typed functional programming languages.
|
|
(Here are some [introductory slides](slides/fpottier-00.pdf).)
|
|
|
|
The course is made up of four parts and can be split after the first two
|
|
parts.
|
|
|
|
In the first part, we discuss the *operational semantics* of functional
|
|
programming languages, and we present several classic *program
|
|
transformations*, including closure conversion, defunctionalization, and the
|
|
transformation into continuation-passing style (CPS). These program
|
|
transformations are interesting from two points of view. First, they are
|
|
*useful programming techniques*, which can help write or understand
|
|
programs. Second, they are used in the *compilation* of functional
|
|
programming languages, so they help understand what happens when the machine
|
|
executes a program. We use operational semantics to *prove* that the meaning
|
|
of programs is preserved by these transformations. Finally, we suggest how
|
|
these definitions and theorems can be expressed in a form that a machine can
|
|
check. That is, although Coq is not a prerequisite of the course, we will at
|
|
least try to *read and understand Coq definitions and statements*.
|
|
|
|
In the second part, we focus on the meta-theoretical properties of type
|
|
systems. We study parametric polymorphism (as in System F and ML), data
|
|
types and type abstraction. We show syntactic type soundness (via progress
|
|
and subject reduction) by reasoning by induction on typing derivations. We
|
|
also show how to obtain semantic properties via logical relations by
|
|
reasoning by induction on the structure of types. Finally, we introduce
|
|
subtyping, row polymorphism, and illustrate the problems induced by
|
|
side effects (references) and the need for the value restriction.
|
|
|
|
The third part of the course describes more advanced features of type
|
|
systems: exceptions and effect handlers, including their typechecking and
|
|
static analyses: type inference, data flow and control flow analyses.
|
|
Finally, it introduces dependent types and refinement types.
|
|
|
|
The last part focuses on the use of dependent types for programming:
|
|
effectful programming with monads and algebraic effects; tagless
|
|
interpreters; programming with total functions; generic programming.
|
|
We also show the limits of dependently-typed functional programming.
|
|
|
|
## Approximate syllabus
|
|
|
|
### Functional Programming: Under the Hood
|
|
|
|
* (22/09/2017) From a small-step operational semantics...
|
|
* (29/09/2017) ... to an efficient interpreter. (2 weeks.)
|
|
* (06/10/2017) Compiling away first-class functions: closure conversion, defunctionalization.
|
|
* (13/10/2017) Compiling away the call stack: the CPS transformation.
|
|
* (20/10/2017) Equational reasoning and program optimizations.
|
|
|
|
### Metatheory of Typed Programming Languages
|
|
|
|
* (15/09/2017)
|
|
[Metatheory of System F](http://gallium.inria.fr/~remy/mpri/slides1.pdf)
|
|
(See also [intro](http://gallium.inria.fr/~remy/mpri/slides8.pdf),
|
|
and chap [1](http://gallium.inria.fr/~remy/mpri/cours1.pdf)
|
|
and [2](http://gallium.inria.fr/~remy/mpri/cours2.pdf)
|
|
of [course notes](http://gallium.inria.fr/~remy/mpri/cours.pdf))
|
|
* (27/10/2017) ADTs, existential types, GADTs.
|
|
* (03/11/2017) Logical relations.
|
|
* (10/11/2017) Subtyping. Rows.
|
|
* (17/11/2017) References, Value restriction, Side effects.
|
|
|
|
### Advanced Aspects of Type Systems
|
|
|
|
* Exceptions and effect handlers. (Compiled away via CPS.)
|
|
* Typechecking exceptions and handlers.
|
|
* Type inference. (ML. Bidirectional. Elaboration.)
|
|
* Data/control flow analysis.
|
|
* Functional correctness. Intro to dependent/refinement types.
|
|
|
|
### Dependently-typed Functional Programming
|
|
|
|
* Effectful functional programming.
|
|
* Dependent functional programming.
|
|
* Total functional programming.
|
|
* Generic functional programming.
|
|
* Open problems in dependent functional programming.
|
|
|
|
## Evaluation of the course
|
|
|
|
Two written exams (a partial and a final exam) and one programming project
|
|
or several programming exercises are used to evaluate the students that
|
|
follow the full course. Only the partial exam will count to grade students
|
|
who split the course.
|
|
|
|
Although the course has changed, you may still have a look at previous exams
|
|
available with solutions:
|
|
|
|
- mid-term exam 2016-2017:
|
|
[Record concatenation](http://gallium.inria.fr/~remy/mpri/exams/partiel-2016-2017.pdf)
|
|
- mid-term exam 2015-2016:
|
|
[Type containment](http://gallium.inria.fr/~remy/mpri/exams/partiel-2015-2016.pdf)
|
|
- final exam 2014-2015: [Copatterns](http://gallium.inria.fr/~remy/mpri/exams/final-2014-2015.pdf)
|
|
- mid-term exam 2014-2015:
|
|
[Information flow](http://gallium.inria.fr/~remy/mpri/exams/partiel-2014-2015.pdf)
|
|
- final exam 2013-2014:
|
|
[Operation on records](http://gallium.inria.fr/~remy/mpri/exams/final-2013-2014.pdf)
|
|
- mid-term exam 2013-2014:
|
|
[Typechecking Effects](http://gallium.inria.fr/~remy/mpri/exams/partiel-2013-2014.pdf)
|
|
- final exam 2012-2013:
|
|
[Refinement types](http://gallium.inria.fr/~remy/mpri/exams/final-2012-2013.pdf)
|
|
- mid-term exam 2012-2013:
|
|
[Variations on ML](http://gallium.inria.fr/~remy/mpri/exams/partiel-2012-2013.pdf)
|
|
- final exam 2011-2012:
|
|
[Intersection types](http://gallium.inria.fr/~remy/mpri/exams/final-2011-2012.pdf)
|
|
- mid-term exam 2011-2012:
|
|
[Parametricity](http://gallium.inria.fr/~remy/mpri/exams/partiel-2011-2012.pdf)
|
|
- final exam 2010-2011:
|
|
[Compiling a language with subtyping](http://gallium.inria.fr/~xleroy/mpri/2-4/exam-2010-2011.pdf)
|
|
- mid-term exam 2010-2011:
|
|
[Compilation
|
|
of polymorphic records](http://gallium.inria.fr/~remy/mpri/exams/2010/partiel-2010-2011.pdf)
|
|
|
|
## Recommended software
|
|
|
|
OCaml 4.0x and Coq **8.5**.
|
|
|
|
Once you have installed [opam](https://opam.ocaml.org/doc/Install.html), use the following commands:
|
|
```bash
|
|
opam init --comp=4.05 # for instance
|
|
opam repo add coq-released https://coq.inria.fr/opam/released
|
|
opam update
|
|
opam install -j4 -v coq.8.5.3
|
|
```
|
|
|
|
Please also install François Pottier's
|
|
[variant](https://github.com/fpottier/autosubst)
|
|
of the
|
|
[AutoSubst](https://www.ps.uni-saarland.de/autosubst/) library:
|
|
```bash
|
|
git clone git@github.com:fpottier/autosubst.git
|
|
make -C autosubst install
|
|
```
|
|
|
|
## Bibliography
|
|
|
|
[Types and Programming Languages](https://mitpress.mit.edu/books/types-and-programming-languages),
|
|
Benjamin C. Pierce, MIT Press, 2002.
|
|
|
|
[Advanced Topics in Types and Programming Languages](https://www.cis.upenn.edu/~bcpierce/attapl/),
|
|
Edited by Benjamin C. Pierce, MIT Press, 2005.
|