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Date: Mon, 7 Jul 2008 06:48:26 -0700 (PDT)
From: Dario Teixeira <darioteixeira@yahoo.com>
Subject: Mapping phantom <-> non-phantom
To: caml-list@yquem.inria.fr
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X-Spam: no; 0.00; variants:01 variants:01 nodes:01 nodes:01 sig:01 node:01 node:01 val:01 val:01 struct:01 struct:01 ocamlyacc:01 parser:01 polymorphic:01 inline:01 

Hi,

Suppose you are using polymorphic variants as a phantom type to impose
certain restrictions on a data structure.  Is it possible in general to
formulate an equivalent structure that uses only regular variants, or is
the object system required for a full mapping?

As an example, consider the following structure constructed using phantom
types.  The "Text" and "Bold" nodes may appear anywhere in a document, but
the "Mref" and "See" nodes produce links, and links may not be the immediat=
e
parents of other links:


module Phantom:
sig
        type inline_t =3D node_t list
        and node_t =3D
                private
                | Text of string
                | Bold of inline_t
                | Mref of string * inline_t
                | See of string

        type 'a t

        val text: string -> [> `Nonlink] t
        val bold: [< `Link | `Nonlink] t list -> [> `Nonlink] t
        val mref: string -> [< `Nonlink] t list -> [> `Link] t
        val see: string -> [> `Link] t
end =3D
struct
        type inline_t =3D node_t list
        and node_t =3D
                | Text of string
                | Bold of inline_t
                | Mref of string * inline_t
                | See of string

        type 'a t =3D node_t

        let text txt =3D Text txt
        let bold inl =3D Bold inl
        let mref ref inl =3D Mref (ref, inl)
        let see ref =3D See ref
end


Though a bit contrived, the following structure expresses the same
restrictions using only conventional variants:


module Regular =3D
struct
        type inline_t =3D super_node_t list
        and super_node_t =3D
                | Nonlink_node of nonlink_node_t
                | Link_node of link_node_t
        and nonlink_node_t =3D
                | Text of string
                | Bold of inline_t
        and link_node_t =3D
                | Mref of string * nonlink_node_t list
                | See of string
end


The version using PV-based phantom types doesn't require all this artifical
scaffolding, and is therefore preferable in my opinion.  However, the
ocamlyacc grammar for a document parser will naturally be closer to the
non-phantom version.  My doubt is therefore if one could devise a structure
using PV-based phantom types that becomes problematic to parse.

Thanks in advance for your time!
Kind regards,
Dario Teixeira
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