203 lines
8.5 KiB
Markdown
203 lines
8.5 KiB
Markdown
# Functional programming and type systems (2017-2018)
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This page supplements
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[the official page of MPRI 2-4](https://wikimpri.dptinfo.ens-cachan.fr/doku.php?id=cours:c-2-4-2).
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## Location and duration
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The lectures take place at University Paris 7 - Denis Diderot,
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Bâtiment Sophie Germain, in room 2035.
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They are scheduled on Fridays from 12:45 to 15:30.
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There is a 15-minute break in the middle of each lecture.
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## Teachers
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* Functional Programming: Under the Hood (12h30, [François Pottier](http://gallium.inria.fr/~fpottier))
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* [Metatheory of Typed Programming Languages](http://gallium.inria.fr/~remy/mpri/) (12h30, [Didier Rémy](http://gallium.inria.fr/~remy/), *head*)
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* Advanced Aspects of Type Systems (12h30, [Yann Régis Gianas](http://www.pps.jussieu.fr/~yrg/))
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* Dependently-typed Functional Programming (12h30, [Pierre-Evariste Dagand](https://pages.lip6.fr/Pierre-Evariste.Dagand/))
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## Aims
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This course presents the principles and formalisms that underlie many of
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today's typed functional programming languages.
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(Here are some [introductory slides](slides/fpottier-00.pdf).)
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The course is made up of four parts and can be split after the first two
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parts.
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In the first part, we discuss the *operational semantics* of functional
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programming languages, and we present several classic *program
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transformations*, including closure conversion, defunctionalization, and the
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transformation into continuation-passing style (CPS). These program
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transformations are interesting from two points of view. First, they are
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*useful programming techniques*, which can help write or understand
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programs. Second, they are used in the *compilation* of functional
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programming languages, so they help understand what happens when the machine
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executes a program. We use operational semantics to *prove* that the meaning
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of programs is preserved by these transformations. Finally, we suggest how
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these definitions and theorems can be expressed in a form that a machine can
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check. That is, although Coq is not a prerequisite of the course, we will at
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least try to *read and understand Coq definitions and statements*.
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In the second part, we focus on the meta-theoretical properties of type
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systems. We study parametric polymorphism (as in System F and ML), data
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types and type abstraction. We show syntactic type soundness (via progress
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and subject reduction) by reasoning by induction on typing derivations. We
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also show how to obtain semantic properties via logical relations by
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reasoning by induction on the structure of types. Finally, we introduce
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subtyping, row polymorphism, and illustrate the problems induced by
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side effects (references) and the need for the value restriction.
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The third part of the course describes more advanced features of type
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systems: exceptions and effect handlers, including their typechecking and
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static analyses: type inference, data flow and control flow analyses.
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Finally, it introduces dependent types and refinement types.
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The last part focuses on the use of dependent types for programming:
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effectful programming with monads and algebraic effects; tagless
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interpreters; programming with total functions; generic programming.
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We also show the limits of dependently-typed functional programming.
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## Approximate syllabus
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### Functional Programming: Under the Hood
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* (22/09/2017)
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Introduction ([slides 00](slides/fpottier-00.pdf)).
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Syntax and operational semantics, on paper and on a machine
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([slides 01a](slides/fpottier-01a.pdf))
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([slides 01b](slides/fpottier-01b.pdf))
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([OCaml solution to Newton-Raphson exercise](ocaml/NewtonRaphson.ml))
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([Even.v](coq/Even.v)).
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* (29/09/2017)
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From a small-step semantics down to an efficient interpreter,
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in several stages
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([Coq demo](coq/DemoSyntaxReduction.v)).
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* (06/10/2017) Compiling away first-class functions: closure conversion, defunctionalization.
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* (13/10/2017) Compiling away the call stack: the CPS transformation.
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* (20/10/2017) Equational reasoning and program optimizations.
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### Metatheory of Typed Programming Languages
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* (15/09/2017)
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[Metatheory of System F](http://gallium.inria.fr/~remy/mpri/slides1.pdf)
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(See also [intro](http://gallium.inria.fr/~remy/mpri/slides8.pdf),
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and chap [1](http://gallium.inria.fr/~remy/mpri/cours1.pdf)
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and [2](http://gallium.inria.fr/~remy/mpri/cours2.pdf)
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of [course notes](http://gallium.inria.fr/~remy/mpri/cours.pdf))
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* (27/10/2017) ADTs, existential types, GADTs.
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* (03/11/2017) Logical relations.
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* (10/11/2017) Subtyping. Rows.
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* (17/11/2017) References, Value restriction, Side effects.
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### Advanced Aspects of Type Systems
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* Exceptions and effect handlers. (Compiled away via CPS.)
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* Typechecking exceptions and handlers.
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* Type inference. (ML. Bidirectional. Elaboration.)
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* Data/control flow analysis.
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* Functional correctness. Intro to dependent/refinement types.
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### Dependently-typed Functional Programming
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* Effectful functional programming.
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* Dependent functional programming.
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* Total functional programming.
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* Generic functional programming.
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* Open problems in dependent functional programming.
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## Evaluation of the course
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Two written exams (a partial and a final exam) and one programming project
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or several programming exercises are used to evaluate the students that
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follow the full course. Only the partial exam will count to grade students
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who split the course.
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Although the course has changed, you may still have a look at previous exams
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available with solutions:
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- mid-term exam 2016-2017:
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[Record concatenation](http://gallium.inria.fr/~remy/mpri/exams/partiel-2016-2017.pdf)
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- mid-term exam 2015-2016:
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[Type containment](http://gallium.inria.fr/~remy/mpri/exams/partiel-2015-2016.pdf)
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- final exam 2014-2015: [Copatterns](http://gallium.inria.fr/~remy/mpri/exams/final-2014-2015.pdf)
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- mid-term exam 2014-2015:
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[Information flow](http://gallium.inria.fr/~remy/mpri/exams/partiel-2014-2015.pdf)
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- final exam 2013-2014:
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[Operation on records](http://gallium.inria.fr/~remy/mpri/exams/final-2013-2014.pdf)
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- mid-term exam 2013-2014:
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[Typechecking Effects](http://gallium.inria.fr/~remy/mpri/exams/partiel-2013-2014.pdf)
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- final exam 2012-2013:
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[Refinement types](http://gallium.inria.fr/~remy/mpri/exams/final-2012-2013.pdf)
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- mid-term exam 2012-2013:
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[Variations on ML](http://gallium.inria.fr/~remy/mpri/exams/partiel-2012-2013.pdf)
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- final exam 2011-2012:
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[Intersection types](http://gallium.inria.fr/~remy/mpri/exams/final-2011-2012.pdf)
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- mid-term exam 2011-2012:
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[Parametricity](http://gallium.inria.fr/~remy/mpri/exams/partiel-2011-2012.pdf)
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- final exam 2010-2011:
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[Compiling a language with subtyping](http://gallium.inria.fr/~xleroy/mpri/2-4/exam-2010-2011.pdf)
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- mid-term exam 2010-2011:
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[Compilation
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of polymorphic records](http://gallium.inria.fr/~remy/mpri/exams/2010/partiel-2010-2011.pdf)
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## Recommended software
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Please install [opam](https://opam.ocaml.org/doc/Install.html) first.
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Then, install OCaml 4.0x and Coq **8.5** via the following commands:
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```bash
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opam init --comp=4.05 # for instance
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opam repo add coq-released https://coq.inria.fr/opam/released
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opam update
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opam install -j4 -v coq.8.5.3
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```
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(Do *not* install Coq 8.6. The version of AutoSubst that I am using is
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not compatible with it. If for some reason you need Coq 8.6, or have
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already installed Coq 8.6, note that `opam switch` can be used to let
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multiple versions of Coq coexist.)
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Please also install François Pottier's
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[variant](https://github.com/fpottier/autosubst)
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of the
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[AutoSubst](https://www.ps.uni-saarland.de/autosubst/) library:
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```bash
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git clone git@github.com:fpottier/autosubst.git
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make -C autosubst install
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```
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In order to use Coq inside `emacs`,
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[ProofGeneral](https://proofgeneral.github.io/)
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is highly recommended.
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Here is a suggested installation script:
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```bash
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rm -rf /tmp/PG
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cd /tmp
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git clone git@github.com:ProofGeneral/PG.git
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cd PG
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EMACS=/Applications/Aquamacs.app/Contents/MacOS/Aquamacs
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if [ ! -x $EMACS ]; then
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EMACS=emacs
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fi
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make EMACS=$EMACS compile
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TARGET=/usr/local/share/emacs/site-lisp/ProofGeneral
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sudo rm -rf $TARGET
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sudo mv /tmp/PG $TARGET
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```
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Enable ProofGeneral by adding the following line to your `.emacs` file:
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```elisp
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(load-file "/usr/local/share/emacs/site-lisp/ProofGeneral/generic/proof-site.el")
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```
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If desired, ProofGeneral can be further
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[customized](https://proofgeneral.github.io/doc/userman/ProofGeneral_9/).
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## Bibliography
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[Types and Programming Languages](https://mitpress.mit.edu/books/types-and-programming-languages),
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Benjamin C. Pierce, MIT Press, 2002.
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[Advanced Topics in Types and Programming Languages](https://www.cis.upenn.edu/~bcpierce/attapl/),
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Edited by Benjamin C. Pierce, MIT Press, 2005.
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