Rank2 Intersection
and
Polymorphic Recursion
for (a subset of) Caml
This page demonstrates a prototype implementation
of a
rank2 intersection type system for higher order functional languages.
The current version of the prototype (1.0), released (as Unlicensed Free Software  http://unlicense.org/) in December 2010:

Implements the type systems
_{0}^{k},
_{0}^{k,ML},
_{2}^{k},
_{2}^{k,ML}, and
_{2}^{k,J}
described in
[
Damiani, 2007]
(revised and extended version of
[
Damiani, 2005
),
which proposes
new rules for
typing recursive definitions.
Let  be an intersection type system.
We say that a term is simple
(or just simple when the systen  is clear from the context)
if system  can prove that it has a simple type.
At the best of our knowledge, previous proposals for typing recursive
definitions in presence of intersection types
[Jim, 1995; Jim, 1996;
van Bakel, 2003
;
Damiani, 2003
]
allow only
simple recursive definitions to be typed.
The proposed rules are
also able to type interesting examples of polymorphic
recursion (i.e., recursive definitions rec{x=e} where
different occurrences of x in e are used with different
types)
[Meertens, 1983;
Mycroft, 1984;
Henglein, 1993
;
Kfoury, Tiuryn, Urzyczyn, 1993
].
Indeed:

the type systems considered by the implementation are
an extension of the type systems
_{0}^{k},
_{0}^{k,ML},
_{2}^{k},
_{2}^{k,ML}, and
_{2}^{k,J}
with the rules for typing nonsimple local definitions and
conditional expressions
described in
[
Damiani, 2003
], and

the programming language considered by the implementation
is richer than the one considered in the report
(in particular
it includes toplevel definitions and datatype declarations).

Is written in
OCaml
.

Accepts as input
a subset of (O')Caml itself.
Type a program in the form below, select the type system to be used,
and press the button.

Parsing is not particularly smart
(for instance, all the infix operators have the same precedence 
to avoid problems, it is better to use a lot of parentheses)
and the error messages are quite poor.
Here you can find
a description of the accepted
SYNTAX
and
some
EXAMPLES
that you can copy and paste.
BIBLIOGRAPHY

[van Bakel, 2003]
Rank 2 types for term graph rewriting.
In:
Proceedings of TIP'02,
volume 75 of ENTCS. Elsevier, 2003.

[Damiani, 2003]
Rank 2 intersection types for local definitions and conditional expressions.
ACM Transactions On Programming Languages and Systems, 25(4):401451, 2003.

[Damiani, 2005]
Rank 2 Intersection Types and Polymorphic Recursion.
In:
Proceedings of International Symposium on
Typed Lambda Calculi and Applications,
LNCS 3461, Springer, 2005.

[Damiani, 2007]
Rank 2 Intersection for Recursive Definitions.
Fundamenta Informaticae, 77, 2007.

[Henglein, 1993]
Type inference with polymorphic recursion.
ACM Transactions On Programming Languages and Systems, 15(2):253289, 1993.

[Jim, 1995]
Rank 2 type systems and recursive definitions.
Technical Report MITT/LCS/TM531, LCS, Massachusetts Institute of
Technology, 1995.

[Jim, 1996]
What are principal typings and what are good for?
In:
Proceedings of ACM SIGPLAN/SIGTACT Symposium on
Principles of Programming Languages 1996 (POPL'96),
pp. 4253.

[Kfoury, Tiuryn, Urzyczyn, 1993]
Type reconstruction in the presence of polymorphic recursion.
ACM Transactions On Programming Languages and Systems, 15(2):290311, 1993.

[Meertens, 1983]
Incremental type checking in B.
In:
Proceedings of ACM SIGPLAN/SIGTACT Symposium on
Principles of Programming Languages 1983 (POPL'83),
pp. 265275.

[Mycroft, 1984]
Polymorphic Type Schemes and Recursive Definitions.
In:
Proceedings of International Symposium on
Programming 1984, LNCS 167, pp. 217228. Springer, 1984.
Souce files are available:
files.zip
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