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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 Termination :> TERMINATION = struct
open Elab
structure E = ElabEnv
structure IM = IntBinaryMap
structure IS = IntBinarySet
datatype pedigree =
Func of int
| Arg of int * int * con
| Subarg of int * int * con
| Rabble
fun p2s p =
case p of
Func i => "Func" ^ Int.toString i
| Arg (i, j, _) => "Arg" ^ Int.toString i ^ "," ^ Int.toString j
| Subarg (i, j, _) => "Subarg" ^ Int.toString i ^ "," ^ Int.toString j
| Rabble => "Rabble"
fun declOk' env (d, loc) =
case d of
DValRec vis =>
let
val nfns = length vis
val fenv = ListUtil.foldli (fn (i, (_, j, _, _), fenv) => IM.insert (fenv, j, i)) IM.empty vis
fun namesEq ((c1, _), (c2, _)) =
case (c1, c2) of
(CName s1, CName s2) => s1 = s2
| (CRel n1, CRel n2) => n1 = n2
| (CNamed n1, CNamed n2) => n1 = n2
| (CModProj n1, CModProj n2) => n1 = n2
| _ => false
fun patCon pc =
let
fun unravel (t, _) =
case t of
TCFun (_, _, _, t) => unravel t
| TFun (dom, _) => dom
| _ => raise Fail "Termination: Unexpected constructor type"
in
case pc of
PConVar i =>
let
val (_, t) = E.lookupENamed env i
in
unravel t
end
| PConProj (m1, ms, x) =>
let
val (str, sgn) = E.chaseMpath env (m1, ms)
in
case E.projectVal env {str = str, sgn = sgn, field = x} of
NONE => raise Fail "Termination: Bad constructor projection"
| SOME t => unravel t
end
end
fun pat penv (p, (pt, _)) =
let
fun con (i, j, pc, pt') = pat penv (Subarg (i, j, patCon pc), pt')
fun record (i, j, t, xps) =
case t of
(TRecord (CRecord (_, xts), _), _) =>
foldl (fn ((x, pt', _), penv) =>
let
val p' =
case List.find (fn (x', _) =>
namesEq ((CName x, ErrorMsg.dummySpan), x')) xts of
NONE => Rabble
| SOME (_, t) => Subarg (i, j, t)
in
pat penv (p', pt')
end) penv xps
| _ => foldl (fn ((_, pt', _), penv) => pat penv (Rabble, pt')) penv xps
in
case (p, pt) of
(_, PWild) => penv
| (_, PVar _) => p :: penv
| (_, PPrim _) => penv
| (_, PCon (_, _, _, NONE)) => penv
| (Arg (i, j, _), PCon (_, pc, _, SOME pt')) => con (i, j, pc, pt')
| (Subarg (i, j, _), PCon (_, pc, _, SOME pt')) => con (i, j, pc, pt')
| (_, PCon (_, _, _, SOME pt')) => pat penv (Rabble, pt')
| (Arg (i, j, t), PRecord xps) => record (i, j, t, xps)
| (Subarg (i, j, t), PRecord xps) => record (i, j, t, xps)
| (_, PRecord xps) => foldl (fn ((_, pt', _), penv) => pat penv (Rabble, pt')) penv xps
end
fun exp parent (penv, calls) e =
let
val default = (Rabble, calls)
fun apps () =
let
fun combiner calls e =
case #1 e of
EApp ((ECApp (
(ECApp (
(ECApp (
(ECApp (
(ECApp (
(ECApp (
(ECApp (
(ECApp (
(EModProj (m, [], "tag"), _),
_), _),
_), _),
_), _),
_), _),
_), _),
_), _),
_), _),
_), _),
(ERecord xets, _)) =>
let
val checkName =
case E.lookupStrNamed env m of
("Basis", _) => (fn x : con => case #1 x of
CName s => s = "Link"
orelse s = "Action"
| _ => false)
| _ => (fn _ => false)
val calls = foldl (fn ((x, e, _), calls) =>
if checkName x then
calls
else
#2 (exp parent (penv, calls) e)) calls xets
in
(Rabble, [Rabble], calls)
end
| EApp (e1, e2) =>
let
val (p1, ps, calls) = combiner calls e1
val (p2, calls) = exp parent (penv, calls) e2
val p = case p1 of
Rabble => Rabble
| Arg _ => Rabble
| Subarg (i, j, (TFun (_, ran), _)) => Subarg (i, j, ran)
| Subarg _ => Rabble
| Func _ => Rabble
in
(p, ps @ [p2], calls)
end
| ECApp (e, _) =>
let
val (p, ps, calls) = combiner calls e
val p = case p of
Rabble => Rabble
| Arg _ => Rabble
| Subarg (i, j, (TCFun (_, _, _, ran), _)) => Subarg (i, j, ran)
| Subarg _ => Rabble
| Func _ => Rabble
in
(p, ps, calls)
end
| EKApp (e, _) => combiner calls e
| _ =>
let
val (p, calls) = exp parent (penv, calls) e
in
(*Print.prefaces "Head" [("e", ElabPrint.p_exp env e)];
print (p2s p ^ "\n");*)
(p, [p], calls)
end
val (p, ps, calls) = combiner calls e
val calls =
case ps of
[] => raise Fail "Termination: Empty ps"
| f :: ps =>
case f of
Func i => (parent, i, ps) :: calls
| _ => calls
in
(p, calls)
end
in
case #1 e of
EPrim _ => default
| ERel n => (List.nth (penv, n), calls)
| ENamed n =>
let
val p = case IM.find (fenv, n) of
NONE => Rabble
| SOME n' => Func n'
in
(p, calls)
end
| EModProj _ => default
| EApp _ => apps ()
| EAbs (_, _, _, e) =>
let
val (_, calls) = exp parent (Rabble :: penv, calls) e
in
(Rabble, calls)
end
| ECApp _ => apps ()
| ECAbs (_, _, _, e) =>
let
val (_, calls) = exp parent (penv, calls) e
in
(Rabble, calls)
end
| EKApp _ => apps ()
| EKAbs (_, e) =>
let
val (_, calls) = exp parent (penv, calls) e
in
(Rabble, calls)
end
| ERecord xets =>
let
val calls = foldl (fn ((_, e, _), calls) => #2 (exp parent (penv, calls) e)) calls xets
in
(Rabble, calls)
end
| EField (e, x, _) =>
let
val (p, calls) = exp parent (penv, calls) e
val p =
case p of
Subarg (i, j, (TRecord (CRecord (_, xts), _), _)) =>
(case List.find (fn (x', _) => namesEq (x, x')) xts of
NONE => Rabble
| SOME (_, t) => Subarg (i, j, t))
| _ => Rabble
in
(p, calls)
end
| ECut (e, _, _) =>
let
val (_, calls) = exp parent (penv, calls) e
in
(Rabble, calls)
end
| ECutMulti (e, _, _) =>
let
val (_, calls) = exp parent (penv, calls) e
in
(Rabble, calls)
end
| EConcat (e1, _, e2, _) =>
let
val (_, calls) = exp parent (penv, calls) e1
val (_, calls) = exp parent (penv, calls) e2
in
(Rabble, calls)
end
| ECase (e, pes, _) =>
let
val (p, calls) = exp parent (penv, calls) e
val calls = foldl (fn ((pt, e), calls) =>
let
val penv = pat penv (p, pt)
val (_, calls) = exp parent (penv, calls) e
in
calls
end) calls pes
in
(Rabble, calls)
end
| EError => (Rabble, calls)
| EUnif (ref (SOME e)) => exp parent (penv, calls) e
| EUnif (ref NONE) => (Rabble, calls)
| ELet (eds, e, _) =>
let
fun extPenv ((ed, _), penv) =
case ed of
EDVal _ => Rabble :: penv
| EDValRec vis => foldl (fn (_, penv) => Rabble :: penv) penv vis
in
exp parent (foldl extPenv penv eds, calls) e
end
end
fun doVali (i, (_, f, _, e), calls) =
let
fun unravel (e, j, penv) =
case #1 e of
EAbs (_, t, _, e) =>
unravel (e, j + 1, Arg (i, j, t) :: penv)
| ECAbs (_, _, _, e) =>
unravel (e, j, penv)
| _ => (j, #2 (exp f (penv, calls) e))
in
unravel (e, 0, [])
end
val (ns, calls) = ListUtil.foldliMap doVali [] vis
fun isRecursive (from, to, _) =
let
fun search (at, soFar) =
at = from
orelse List.exists (fn (from', to', _) =>
from' = at
andalso not (IS.member (soFar, to'))
andalso search (to', IS.add (soFar, to')))
calls
in
search (to, IS.empty)
end
val calls = List.filter isRecursive calls
fun search (ns, choices) =
case ns of
[] =>
let
val choices = rev choices
in
List.all (fn (_, f, args) =>
let
val recArg = List.nth (choices, f)
fun isDatatype (t, _) =
case t of
CNamed _ => true
| CModProj _ => true
| CApp (t, _) => isDatatype t
| _ => false
in
length args > recArg andalso
case List.nth (args, recArg) of
Subarg (i, j, t) => isDatatype t andalso j = List.nth (choices, i)
| _ => false
end) calls
end
| n :: ns' =>
let
fun search' i =
i < n andalso (search (ns', i :: choices) orelse search' (i + 1))
in
search' 0
end
in
if search (ns, []) then
()
else
ErrorMsg.errorAt loc "Can't prove termination of recursive function(s)"
end
| DStr (_, _, _, (StrConst ds, _)) => ignore (foldl declOk env ds)
| _ => ()
and declOk (d, env) =
(declOk' env d;
E.declBinds env d)
fun check ds = ignore (foldl declOk E.empty ds)
end
|