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(* Copyright (c) 2008, Adam Chlipala
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* - The names of contributors may not be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*)
structure Disjoint :> DISJOINT = struct
open Elab
open ElabOps
datatype piece =
NameC of string
| NameR of int
| NameN of int
| NameM of int * string list * string
| RowR of int
| RowN of int
| RowM of int * string list * string
fun p2s p =
case p of
NameC s => "NameC(" ^ s ^ ")"
| NameR n => "NameR(" ^ Int.toString n ^ ")"
| NameN n => "NameN(" ^ Int.toString n ^ ")"
| NameM (n, _, s) => "NameR(" ^ Int.toString n ^ ", " ^ s ^ ")"
| RowR n => "RowR(" ^ Int.toString n ^ ")"
| RowN n => "RowN(" ^ Int.toString n ^ ")"
| RowM (n, _, s) => "RowR(" ^ Int.toString n ^ ", " ^ s ^ ")"
fun pp p = print (p2s p ^ "\n")
structure PK = struct
type ord_key = piece
fun join (o1, o2) =
case o1 of
EQUAL => o2 ()
| v => v
fun joinL f (os1, os2) =
case (os1, os2) of
(nil, nil) => EQUAL
| (nil, _) => LESS
| (h1 :: t1, h2 :: t2) =>
join (f (h1, h2), fn () => joinL f (t1, t2))
| (_ :: _, nil) => GREATER
fun compare (p1, p2) =
case (p1, p2) of
(NameC s1, NameC s2) => String.compare (s1, s2)
| (NameR n1, NameR n2) => Int.compare (n1, n2)
| (NameN n1, NameN n2) => Int.compare (n1, n2)
| (NameM (n1, ss1, s1), NameM (n2, ss2, s2)) =>
join (Int.compare (n1, n2),
fn () => join (String.compare (s1, s2), fn () =>
joinL String.compare (ss1, ss2)))
| (RowR n1, RowR n2) => Int.compare (n1, n2)
| (RowN n1, RowN n2) => Int.compare (n1, n2)
| (RowM (n1, ss1, s1), RowM (n2, ss2, s2)) =>
join (Int.compare (n1, n2),
fn () => join (String.compare (s1, s2), fn () =>
joinL String.compare (ss1, ss2)))
| (NameC _, _) => LESS
| (_, NameC _) => GREATER
| (NameR _, _) => LESS
| (_, NameR _) => GREATER
| (NameN _, _) => LESS
| (_, NameN _) => GREATER
| (NameM _, _) => LESS
| (_, NameM _) => GREATER
| (RowR _, _) => LESS
| (_, RowR _) => GREATER
| (RowN _, _) => LESS
| (_, RowN _) => GREATER
end
structure PS = BinarySetFn(PK)
structure PM = BinaryMapFn(PK)
type env = PS.set PM.map
type goal = ErrorMsg.span * ElabEnv.env * env * Elab.con * Elab.con
val empty = PM.empty
fun nameToRow (c, loc) =
(CRecord ((KUnit, loc), [((c, loc), (CUnit, loc))]), loc)
fun pieceToRow (p, loc) =
case p of
NameC s => nameToRow (CName s, loc)
| NameR n => nameToRow (CRel n, loc)
| NameN n => nameToRow (CNamed n, loc)
| NameM (n, xs, x) => nameToRow (CModProj (n, xs, x), loc)
| RowR n => (CRel n, loc)
| RowN n => (CNamed n, loc)
| RowM (n, xs, x) => (CModProj (n, xs, x), loc)
datatype piece' =
Piece of piece
| Unknown of con
fun pieceEnter p =
case p of
NameR n => NameR (n + 1)
| RowR n => RowR (n + 1)
| _ => p
fun enter denv =
PM.foldli (fn (p, pset, denv') =>
PM.insert (denv', pieceEnter p, PS.map pieceEnter pset))
PM.empty denv
fun prove1 denv (p1, p2) =
case (p1, p2) of
(NameC s1, NameC s2) => s1 <> s2
| _ =>
case PM.find (denv, p1) of
NONE => false
| SOME pset => PS.member (pset, p2)
fun decomposeRow (env, denv) c =
let
fun decomposeName (c, (acc, gs)) =
let
val (cAll as (c, _), gs') = hnormCon (env, denv) c
val acc = case c of
CName s => Piece (NameC s) :: acc
| CRel n => Piece (NameR n) :: acc
| CNamed n => Piece (NameN n) :: acc
| CModProj (m1, ms, x) => Piece (NameM (m1, ms, x)) :: acc
| _ => Unknown cAll :: acc
in
(acc, gs' @ gs)
end
fun decomposeRow (c, (acc, gs)) =
let
val (cAll as (c, _), gs') = hnormCon (env, denv) c
val gs = gs' @ gs
in
case c of
CRecord (_, xcs) => foldl (fn ((x, _), acc_gs) => decomposeName (x, acc_gs)) (acc, gs) xcs
| CConcat (c1, c2) => decomposeRow (c1, decomposeRow (c2, (acc, gs)))
| CRel n => (Piece (RowR n) :: acc, gs)
| CNamed n => (Piece (RowN n) :: acc, gs)
| CModProj (m1, ms, x) => (Piece (RowM (m1, ms, x)) :: acc, gs)
| _ => (Unknown cAll :: acc, gs)
end
in
decomposeRow (c, ([], []))
end
and assert env denv (c1, c2) =
let
val (ps1, gs1) = decomposeRow (env, denv) c1
val (ps2, gs2) = decomposeRow (env, denv) c2
val unUnknown = List.mapPartial (fn Unknown _ => NONE | Piece p => SOME p)
val ps1 = unUnknown ps1
val ps2 = unUnknown ps2
(*val () = print "APieces1:\n"
val () = app pp ps1
val () = print "APieces2:\n"
val () = app pp ps2*)
fun assertPiece ps (p, denv) =
let
val pset = Option.getOpt (PM.find (denv, p), PS.empty)
val ps = case p of
NameC _ => List.filter (fn NameC _ => false | _ => true) ps
| _ => ps
val pset = PS.addList (pset, ps)
in
PM.insert (denv, p, pset)
end
val denv = foldl (assertPiece ps2) denv ps1
in
(foldl (assertPiece ps1) denv ps2, gs1 @ gs2)
end
and prove env denv (c1, c2, loc) =
let
val (ps1, gs1) = decomposeRow (env, denv) c1
val (ps2, gs2) = decomposeRow (env, denv) c2
val hasUnknown = List.exists (fn Unknown _ => true | _ => false)
val unUnknown = List.mapPartial (fn Unknown _ => NONE | Piece p => SOME p)
in
if hasUnknown ps1 orelse hasUnknown ps2 then
[(loc, env, denv, c1, c2)]
else
let
val ps1 = unUnknown ps1
val ps2 = unUnknown ps2
in
(*print "Pieces1:\n";
app pp ps1;
print "Pieces2:\n";
app pp ps2;*)
foldl (fn (p1, rem) =>
foldl (fn (p2, rem) =>
if prove1 denv (p1, p2) then
rem
else
(loc, env, denv, pieceToRow (p1, loc), pieceToRow (p2, loc)) :: rem) rem ps2)
(gs1 @ gs2) ps1
end
end
and hnormCon (env, denv) c =
let
val cAll as (c, loc) = ElabOps.hnormCon env c
fun doDisj (c1, c2, c) =
let
val (c, gs) = hnormCon (env, denv) c
in
(c, prove env denv (c1, c2, loc) @ gs)
end
in
case c of
CDisjoint cs => doDisj cs
| TDisjoint cs => doDisj cs
| _ => (cAll, [])
end
end
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