Functional programming and type systems (2017-2018)

Teachers

• Functional Programming: Under the Hood (12h30, François Pottier)
• Metatheory of Typed Programming Languages (12h30, Didier Rémy, head)
• Advanced Aspects of Type Systems (12h30, Yann Régis Gianas)
• Dependently-typed Functional Programming (12h30, Pierre-Evariste Dagand)

Aims

This course presents the principles and formalisms that underlie many of today's typed functional programming languages.

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. We also introduce subtyping and row polymorphism and illustrate typing 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. (Type soundness. Erasure.)
• (27/10/2017) ADTs, existential types, GADTs. (Typed program transformations.)
• (03/11/2017) Logical relations.
• (17/11/2017) Subtyping. Rows. (Covariant arrays and covariant functions!)
• (24/11/2017) References. (Value restriction.)

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.

Recommended software

OCaml 4.0x and Coq 8.5.

Once you have installed opam, use the following commands:

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

Bibliography

Types and Programming Languages, Benjamin C. Pierce, MIT Press, 2002.