2017-09-11 10:40:02 +02:00
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# Functional programming and type systems (2017-2018)
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2017-09-11 10:29:22 +02:00
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2017-09-11 10:40:02 +02:00
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## Teachers
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2017-09-11 10:29:22 +02:00
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2017-09-11 10:32:58 +02:00
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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 (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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2017-09-11 10:40:02 +02:00
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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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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. We also introduce
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subtyping and row polymorphism and illustrate typing 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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2017-09-11 10:41:47 +02:00
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* (22/09/2017) From a small-step operational semantics...
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* (29/09/2017) ... to an efficient interpreter. (2 weeks.)
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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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First lesson on Sep 15, other lessons on Oct 27, Nov 02, 17, 24.
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2017-09-11 10:41:47 +02:00
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* Metatheory of System F. (Type soundness. Erasure.)
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* ADTs, existential types, GADTs. (Typed program transformations.)
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* Logical relations.
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* Subtyping. Rows. (Covariant arrays and covariant functions!)
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* References. (Value restriction.)
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### Advanced Aspects of Type Systems
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2017-09-11 10:41:47 +02:00
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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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2017-09-11 10:41:47 +02:00
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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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