Università di Torino

Rank-2 Intersection and Polymorphic Recursion for (a subset of) Caml

This page demonstrates a prototype implementation of a rank-2 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 |-0k, |-0k,ML, |-2k, |-2k,ML, and |-2k,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 ].


    • the type systems considered by the implementation are an extension of the type systems |-0k, |-0k,ML, |-2k, |-2k,ML, and |-2k,J with the rules for typing non-simple 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 top-level 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.

Use system |-0k with k =


Souce files are available: files.zip

This is free and unencumbered software released into the public domain. Anyone is free to copy, modify, publish, use, compile, sell, or distribute this software, either in source code form or as a compiled binary, for any purpose, commercial or non-commercial, and by any means. In jurisdictions that recognize copyright laws, the author or authors of this software dedicate any and all copyright interest in the software to the public domain. We make this dedication for the benefit of the public at large and to the detriment of our heirs and successors. We intend this dedication to be an overt act of relinquishment in perpetuity of all present and future rights to this software under copyright law. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. For more information, please refer to http://unlicense.org/

[On-line tools demonstrations]

Comments to: damiani[at]di[dot]unito[dot]it Last update: Feb 14, 2011