(* Copyright (c) 2010, 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 Iflow :> IFLOW = struct open Mono structure IS = IntBinarySet structure IM = IntBinaryMap structure SK = struct type ord_key = string val compare = String.compare end structure SS = BinarySetFn(SK) structure SM = BinaryMapFn(SK) val writers = ["htmlifyInt_w", "htmlifyFloat_w", "htmlifyString_w", "htmlifyBool_w", "htmlifyTime_w", "attrifyInt_w", "attrifyFloat_w", "attrifyString_w", "attrifyChar_w", "urlifyInt_w", "urlifyFloat_w", "urlifyString_w", "urlifyBool_w", "set_cookie"] val writers = SS.addList (SS.empty, writers) type lvar = int datatype func = DtCon0 of string | DtCon1 of string | UnCon of string | Other of string datatype exp = Const of Prim.t | Var of int | Lvar of lvar | Func of func * exp list | Recd of (string * exp) list | Proj of exp * string | Finish datatype reln = Known | Sql of string | PCon0 of string | PCon1 of string | Eq | Ne | Lt | Le | Gt | Ge datatype prop = True | False | Unknown | And of prop * prop | Or of prop * prop | Reln of reln * exp list | Cond of exp * prop val unif = ref (IM.empty : exp IM.map) fun reset () = unif := IM.empty fun save () = !unif fun restore x = unif := x local open Print val string = PD.string in fun p_func f = string (case f of DtCon0 s => s | DtCon1 s => s | UnCon s => "un" ^ s | Other s => s) fun p_exp e = case e of Const p => Prim.p_t p | Var n => string ("x" ^ Int.toString n) | Lvar n => (case IM.find (!unif, n) of NONE => string ("X" ^ Int.toString n) | SOME e => p_exp e) | Func (f, es) => box [p_func f, string "(", p_list p_exp es, string ")"] | Recd xes => box [string "{", p_list (fn (x, e) => box [string x, space, string "=", space, p_exp e]) xes, string "}"] | Proj (e, x) => box [p_exp e, string ("." ^ x)] | Finish => string "FINISH" fun p_bop s es = case es of [e1, e2] => box [p_exp e1, space, string s, space, p_exp e2] | _ => raise Fail "Iflow.p_bop" fun p_reln r es = case r of Known => (case es of [e] => box [string "known(", p_exp e, string ")"] | _ => raise Fail "Iflow.p_reln: Known") | Sql s => box [string (s ^ "("), p_list p_exp es, string ")"] | PCon0 s => box [string (s ^ "("), p_list p_exp es, string ")"] | PCon1 s => box [string (s ^ "("), p_list p_exp es, string ")"] | Eq => p_bop "=" es | Ne => p_bop "<>" es | Lt => p_bop "<" es | Le => p_bop "<=" es | Gt => p_bop ">" es | Ge => p_bop ">=" es fun p_prop p = case p of True => string "True" | False => string "False" | Unknown => string "??" | And (p1, p2) => box [string "(", p_prop p1, string ")", space, string "&&", space, string "(", p_prop p2, string ")"] | Or (p1, p2) => box [string "(", p_prop p1, string ")", space, string "||", space, string "(", p_prop p2, string ")"] | Reln (r, es) => p_reln r es | Cond (e, p) => box [string "(", p_exp e, space, string "==", space, p_prop p, string ")"] end local val count = ref 1 in fun newLvar () = let val n = !count in count := n + 1; n end end fun isKnown e = case e of Const _ => true | Func (_, es) => List.all isKnown es | Recd xes => List.all (isKnown o #2) xes | Proj (e, _) => isKnown e | _ => false fun isFinish e = case e of Finish => true | _ => false fun simplify e = case e of Const _ => e | Var _ => e | Lvar n => (case IM.find (!unif, n) of NONE => e | SOME e => simplify e) | Func (f, es) => Func (f, map simplify es) | Recd xes => Recd (map (fn (x, e) => (x, simplify e)) xes) | Proj (e, s) => Proj (simplify e, s) | Finish => Finish datatype atom = AReln of reln * exp list | ACond of exp * prop fun p_atom a = p_prop (case a of AReln x => Reln x | ACond x => Cond x) fun lvarIn lv = let fun lvi e = case e of Const _ => false | Var _ => false | Lvar lv' => lv' = lv | Func (_, es) => List.exists lvi es | Recd xes => List.exists (lvi o #2) xes | Proj (e, _) => lvi e | Finish => false in lvi end fun lvarInP lv = let fun lvi p = case p of True => false | False => false | Unknown => true | And (p1, p2) => lvi p1 orelse lvi p2 | Or (p1, p2) => lvi p1 orelse lvi p2 | Reln (_, es) => List.exists (lvarIn lv) es | Cond (e, p) => lvarIn lv e orelse lvi p in lvi end fun varIn lv = let fun lvi e = case e of Const _ => false | Lvar _ => false | Var lv' => lv' = lv | Func (_, es) => List.exists lvi es | Recd xes => List.exists (lvi o #2) xes | Proj (e, _) => lvi e | Finish => false in lvi end fun varInP lv = let fun lvi p = case p of True => false | False => false | Unknown => false | And (p1, p2) => lvi p1 orelse lvi p2 | Or (p1, p2) => lvi p1 orelse lvi p2 | Reln (_, es) => List.exists (varIn lv) es | Cond (e, p) => varIn lv e orelse lvi p in lvi end fun eq' (e1, e2) = case (e1, e2) of (Const p1, Const p2) => Prim.equal (p1, p2) | (Var n1, Var n2) => n1 = n2 | (Lvar n1, _) => (case IM.find (!unif, n1) of SOME e1 => eq' (e1, e2) | NONE => case e2 of Lvar n2 => (case IM.find (!unif, n2) of SOME e2 => eq' (e1, e2) | NONE => n1 = n2 orelse (unif := IM.insert (!unif, n2, e1); true)) | _ => if lvarIn n1 e2 then false else (unif := IM.insert (!unif, n1, e2); true)) | (_, Lvar n2) => (case IM.find (!unif, n2) of SOME e2 => eq' (e1, e2) | NONE => if lvarIn n2 e1 then false else ((*Print.prefaces "unif" [("n2", Print.PD.string (Int.toString n2)), ("e1", p_exp e1)];*) unif := IM.insert (!unif, n2, e1); true)) | (Func (f1, es1), Func (f2, es2)) => f1 = f2 andalso ListPair.allEq eq' (es1, es2) | (Recd xes1, Recd xes2) => ListPair.allEq (fn ((x1, e1), (x2, e2)) => x1 = x2 andalso eq' (e1, e2)) (xes1, xes2) | (Proj (e1, s1), Proj (e2, s2)) => eq' (e1, e2) andalso s1 = s2 | (Finish, Finish) => true | _ => false fun eq (e1, e2) = let val saved = save () in if eq' (simplify e1, simplify e2) then true else (restore saved; false) end val debug = ref false fun eeq (e1, e2) = case (e1, e2) of (Const p1, Const p2) => Prim.equal (p1, p2) | (Var n1, Var n2) => n1 = n2 | (Lvar n1, Lvar n2) => n1 = n2 | (Func (f1, es1), Func (f2, es2)) => f1 = f2 andalso ListPair.allEq eeq (es1, es2) | (Recd xes1, Recd xes2) => length xes1 = length xes2 andalso List.all (fn (x2, e2) => List.exists (fn (x1, e1) => x1 = x2 andalso eeq (e1, e2)) xes2) xes1 | (Proj (e1, x1), Proj (e2, x2)) => eeq (e1, e2) andalso x1 = x2 | (Finish, Finish) => true | _ => false (* Congruence closure *) structure Cc :> sig type database exception Contradiction exception Undetermined val database : unit -> database val assert : database * atom -> unit val check : database * atom -> bool val p_database : database Print.printer val builtFrom : database * {Base : exp list, Derived : exp} -> bool end = struct exception Contradiction exception Undetermined structure CM = BinaryMapFn(struct type ord_key = Prim.t val compare = Prim.compare end) datatype node = Node of {Rep : node ref option ref, Cons : node ref SM.map ref, Variety : variety, Known : bool ref} and variety = Dt0 of string | Dt1 of string * node ref | Prim of Prim.t | Recrd of node ref SM.map ref * bool | VFinish | Nothing type representative = node ref val finish = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = VFinish, Known = ref true}) type database = {Vars : representative IM.map ref, Consts : representative CM.map ref, Con0s : representative SM.map ref, Records : (representative SM.map * representative) list ref, Funcs : ((string * representative list) * representative) list ref } fun database () = {Vars = ref IM.empty, Consts = ref CM.empty, Con0s = ref SM.empty, Records = ref [], Funcs = ref []} fun unNode n = case !n of Node r => r open Print val string = PD.string val newline = PD.newline fun p_rep n = case !(#Rep (unNode n)) of SOME n => p_rep n | NONE => box [string (Int.toString (Unsafe.cast n) ^ ":"), space, case #Variety (unNode n) of Nothing => string "?" | Dt0 s => string ("Dt0(" ^ s ^ ")") | Dt1 (s, n) => box[string ("Dt1(" ^ s ^ ","), space, p_rep n, string ")"] | Prim p => Prim.p_t p | Recrd (ref m, b) => box [string "{", p_list (fn (x, n) => box [string x, space, string "=", space, p_rep n]) (SM.listItemsi m), string "}", if b then box [space, string "(complete)"] else box []] | VFinish => string "FINISH"] fun p_database (db : database) = box [string "Vars:", newline, p_list_sep newline (fn (i, n) => box [string ("x" ^ Int.toString i), space, string "=", space, p_rep n, if !(#Known (unNode n)) then box [space, string "(known)"] else box []]) (IM.listItemsi (!(#Vars db)))] fun repOf (n : representative) : representative = case !(#Rep (unNode n)) of NONE => n | SOME r => let val r = repOf r in #Rep (unNode n) := SOME r; r end fun markKnown r = let val r = repOf r in (*Print.preface ("markKnown", p_rep r);*) if !(#Known (unNode r)) then ()(*TextIO.print "Already known\n"*) else (#Known (unNode r) := true; SM.app markKnown (!(#Cons (unNode r))); case #Variety (unNode r) of Dt1 (_, r) => markKnown r | Recrd (xes, _) => SM.app markKnown (!xes) | _ => ()) end fun representative (db : database, e) = let fun rep e = case e of Const p => (case CM.find (!(#Consts db), p) of SOME r => repOf r | NONE => let val r = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Prim p, Known = ref true}) in #Consts db := CM.insert (!(#Consts db), p, r); r end) | Var n => (case IM.find (!(#Vars db), n) of SOME r => repOf r | NONE => let val r = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Nothing, Known = ref false}) in #Vars db := IM.insert (!(#Vars db), n, r); r end) | Lvar n => (case IM.find (!unif, n) of NONE => raise Undetermined | SOME e => rep e) | Func (DtCon0 f, []) => (case SM.find (!(#Con0s db), f) of SOME r => repOf r | NONE => let val r = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Dt0 f, Known = ref true}) in #Con0s db := SM.insert (!(#Con0s db), f, r); r end) | Func (DtCon0 _, _) => raise Fail "Iflow.rep: DtCon0" | Func (DtCon1 f, [e]) => let val r = rep e in case SM.find (!(#Cons (unNode r)), f) of SOME r => repOf r | NONE => let val r' = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Dt1 (f, r), Known = ref (!(#Known (unNode r)))}) in #Cons (unNode r) := SM.insert (!(#Cons (unNode r)), f, r'); r' end end | Func (DtCon1 _, _) => raise Fail "Iflow.rep: DtCon1" | Func (UnCon f, [e]) => let val r = rep e in case #Variety (unNode r) of Dt1 (f', n) => if f' = f then repOf n else raise Contradiction | Nothing => let val cons = ref SM.empty val r' = ref (Node {Rep = ref NONE, Cons = cons, Variety = Nothing, Known = ref (!(#Known (unNode r)))}) val r'' = ref (Node {Rep = ref NONE, Cons = #Cons (unNode r), Variety = Dt1 (f, r'), Known = #Known (unNode r)}) in cons := SM.insert (!cons, f, r''); #Rep (unNode r) := SOME r''; r' end | VFinish => r | _ => raise Contradiction end | Func (UnCon _, _) => raise Fail "Iflow.rep: UnCon" | Func (Other f, es) => let val rs = map rep es in case List.find (fn (x : string * representative list, _) => x = (f, rs)) (!(#Funcs db)) of NONE => let val r = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Nothing, Known = ref false}) in #Funcs db := ((f, rs), r) :: (!(#Funcs db)); r end | SOME (_, r) => repOf r end | Recd xes => let val xes = map (fn (x, e) => (x, rep e)) xes val len = length xes in case List.find (fn (xes', _) => SM.numItems xes' = len andalso List.all (fn (x, n) => case SM.find (xes', x) of NONE => false | SOME n' => n = repOf n') xes) (!(#Records db)) of SOME (_, r) => repOf r | NONE => let val xes = foldl SM.insert' SM.empty xes val r' = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Recrd (ref xes, true), Known = ref false}) in #Records db := (xes, r') :: (!(#Records db)); r' end end | Proj (e, f) => let val r = rep e in case #Variety (unNode r) of Recrd (xes, _) => (case SM.find (!xes, f) of SOME r => repOf r | NONE => let val r = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Nothing, Known = ref (!(#Known (unNode r)))}) in xes := SM.insert (!xes, f, r); r end) | Nothing => let val r' = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Nothing, Known = ref (!(#Known (unNode r)))}) val r'' = ref (Node {Rep = ref NONE, Cons = #Cons (unNode r), Variety = Recrd (ref (SM.insert (SM.empty, f, r')), false), Known = #Known (unNode r)}) in #Rep (unNode r) := SOME r''; r' end | VFinish => r | _ => raise Contradiction end | Finish => finish in rep e end fun assert (db, a) = case a of ACond _ => () | AReln x => case x of (Known, [e]) => ((*Print.prefaces "Before" [("e", p_exp e), ("db", p_database db)];*) markKnown (representative (db, e))(*; Print.prefaces "After" [("e", p_exp e), ("db", p_database db)]*)) | (PCon0 f, [e]) => let val r = representative (db, e) in case #Variety (unNode r) of Dt0 f' => if f = f' then () else raise Contradiction | Nothing => let val r' = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Dt0 f, Known = ref false}) in #Rep (unNode r) := SOME r' end | _ => raise Contradiction end | (PCon1 f, [e]) => let val r = representative (db, e) in case #Variety (unNode r) of Dt1 (f', e') => if f = f' then () else raise Contradiction | Nothing => let val r'' = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Nothing, Known = ref false}) val r' = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = Dt1 (f, r''), Known = ref false}) in #Rep (unNode r) := SOME r' end | _ => raise Contradiction end | (Eq, [e1, e2]) => let fun markEq (r1, r2) = if r1 = r2 then () else case (#Variety (unNode r1), #Variety (unNode r2)) of (Prim p1, Prim p2) => if Prim.equal (p1, p2) then () else raise Contradiction | (Dt0 f1, Dt0 f2) => if f1 = f2 then () else raise Contradiction | (Dt1 (f1, r1), Dt1 (f2, r2)) => if f1 = f2 then markEq (r1, r2) else raise Contradiction | (Recrd (xes1, _), Recrd (xes2, _)) => let fun unif (xes1, xes2) = SM.appi (fn (x, r1) => case SM.find (xes2, x) of NONE => () | SOME r2 => markEq (r1, r2)) xes1 in unif (!xes1, !xes2); unif (!xes2, !xes1) end | (VFinish, VFinish) => () | (Nothing, _) => mergeNodes (r1, r2) | (_, Nothing) => mergeNodes (r2, r1) | _ => raise Contradiction and mergeNodes (r1, r2) = (#Rep (unNode r1) := SOME r2; if !(#Known (unNode r1)) then markKnown r2 else (); if !(#Known (unNode r2)) then markKnown r1 else (); #Cons (unNode r2) := SM.unionWith #1 (!(#Cons (unNode r2)), !(#Cons (unNode r1))); compactFuncs ()) and compactFuncs () = let fun loop funcs = case funcs of [] => [] | (fr as ((f, rs), r)) :: rest => let val rest = List.filter (fn ((f' : string, rs'), r') => if f' = f andalso ListPair.allEq (fn (r1, r2) => repOf r1 = repOf r2) (rs, rs') then (markEq (r, r'); false) else true) rest in fr :: loop rest end in #Funcs db := loop (!(#Funcs db)) end in markEq (representative (db, e1), representative (db, e2)) end | _ => () fun check (db, a) = case a of ACond _ => false | AReln x => case x of (Known, [e]) => let fun isKnown r = let val r = repOf r in !(#Known (unNode r)) orelse case #Variety (unNode r) of Dt1 (_, r) => isKnown r | Recrd (xes, true) => List.all isKnown (SM.listItems (!xes)) | _ => false end val r = representative (db, e) in isKnown r end | (PCon0 f, [e]) => (case #Variety (unNode (representative (db, e))) of Dt0 f' => f' = f | _ => false) | (PCon1 f, [e]) => (case #Variety (unNode (representative (db, e))) of Dt1 (f', _) => f' = f | _ => false) | (Eq, [e1, e2]) => let val r1 = representative (db, e1) val r2 = representative (db, e2) in repOf r1 = repOf r2 end | _ => false fun builtFrom (db, {Base = bs, Derived = d}) = let val bs = map (fn b => representative (db, b)) bs fun loop d = let val d = repOf d in List.exists (fn b => repOf b = d) bs orelse case #Variety (unNode d) of Dt0 _ => true | Dt1 (_, d) => loop d | Prim _ => true | Recrd (xes, _) => List.all loop (SM.listItems (!xes)) | VFinish => true | Nothing => false end in loop (representative (db, d)) end end fun decomp fals or = let fun decomp p k = case p of True => k [] | False => fals | Unknown => k [] | And (p1, p2) => decomp p1 (fn ps1 => decomp p2 (fn ps2 => k (ps1 @ ps2))) | Or (p1, p2) => or (decomp p1 k, fn () => decomp p2 k) | Reln x => k [AReln x] | Cond x => k [ACond x] in decomp end fun imply (hyps, goals, outs) = let fun gls goals onFail acc = case goals of [] => (let val cc = Cc.database () val () = app (fn a => Cc.assert (cc, a)) hyps in (*Print.preface ("db", Cc.p_database cc);*) (List.all (fn a => if Cc.check (cc, a) then true else ((*Print.prefaces "Can't prove" [("a", p_atom a), ("hyps", Print.p_list p_atom hyps), ("db", Cc.p_database cc)];*) false)) acc (*andalso (Print.preface ("Finding", Cc.p_database cc); true)*) andalso (case outs of NONE => true | SOME outs => Cc.builtFrom (cc, {Derived = Var 0, Base = outs}))) handle Cc.Contradiction => false end handle Cc.Undetermined => false) orelse onFail () | (g as AReln (Sql gf, [ge])) :: goals => let fun hps hyps = case hyps of [] => gls goals onFail (g :: acc) | (h as AReln (Sql hf, [he])) :: hyps => if gf = hf then let val saved = save () in if eq (ge, he) then let val changed = IM.numItems (!unif) <> IM.numItems saved in gls goals (fn () => (restore saved; changed andalso hps hyps)) acc end else hps hyps end else hps hyps | _ :: hyps => hps hyps in hps hyps end | g :: goals => gls goals onFail (g :: acc) in reset (); (*Print.prefaces "Big go" [("hyps", Print.p_list p_atom hyps), ("goals", Print.p_list p_atom goals)];*) gls goals (fn () => false) [] end handle Cc.Contradiction => true fun patCon pc = case pc of PConVar n => "C" ^ Int.toString n | PConFfi {mod = m, datatyp = d, con = c, ...} => m ^ "." ^ d ^ "." ^ c datatype chunk = String of string | Exp of Mono.exp fun chunkify e = case #1 e of EPrim (Prim.String s) => [String s] | EStrcat (e1, e2) => let val chs1 = chunkify e1 val chs2 = chunkify e2 in case chs2 of String s2 :: chs2' => (case List.last chs1 of String s1 => List.take (chs1, length chs1 - 1) @ String (s1 ^ s2) :: chs2' | _ => chs1 @ chs2) | _ => chs1 @ chs2 end | _ => [Exp e] type 'a parser = chunk list -> ('a * chunk list) option fun always v chs = SOME (v, chs) fun parse p s = case p (chunkify s) of SOME (v, []) => SOME v | _ => NONE fun const s chs = case chs of String s' :: chs => if String.isPrefix s s' then SOME ((), if size s = size s' then chs else String (String.extract (s', size s, NONE)) :: chs) else NONE | _ => NONE fun follow p1 p2 chs = case p1 chs of NONE => NONE | SOME (v1, chs) => case p2 chs of NONE => NONE | SOME (v2, chs) => SOME ((v1, v2), chs) fun wrap p f chs = case p chs of NONE => NONE | SOME (v, chs) => SOME (f v, chs) fun wrapP p f chs = case p chs of NONE => NONE | SOME (v, chs) => case f v of NONE => NONE | SOME r => SOME (r, chs) fun alt p1 p2 chs = case p1 chs of NONE => p2 chs | v => v fun altL ps = case rev ps of [] => (fn _ => NONE) | p :: ps => foldl (fn (p1, p2) => alt p1 p2) p ps fun opt p chs = case p chs of NONE => SOME (NONE, chs) | SOME (v, chs) => SOME (SOME v, chs) fun skip cp chs = case chs of String "" :: chs => skip cp chs | String s :: chs' => if cp (String.sub (s, 0)) then skip cp (String (String.extract (s, 1, NONE)) :: chs') else SOME ((), chs) | _ => SOME ((), chs) fun keep cp chs = case chs of String "" :: chs => keep cp chs | String s :: chs' => let val (befor, after) = Substring.splitl cp (Substring.full s) in if Substring.isEmpty befor then NONE else SOME (Substring.string befor, if Substring.isEmpty after then chs' else String (Substring.string after) :: chs') end | _ => NONE fun ws p = wrap (follow (skip (fn ch => ch = #" ")) (follow p (skip (fn ch => ch = #" ")))) (#1 o #2) fun log name p chs = (if !debug then case chs of String s :: _ => print (name ^ ": " ^ s ^ "\n") | _ => print (name ^ ": blocked!\n") else (); p chs) fun list p chs = altL [wrap (follow p (follow (ws (const ",")) (list p))) (fn (v, ((), ls)) => v :: ls), wrap (ws p) (fn v => [v]), always []] chs val ident = keep (fn ch => Char.isAlphaNum ch orelse ch = #"_") val t_ident = wrapP ident (fn s => if String.isPrefix "T_" s then SOME (String.extract (s, 2, NONE)) else NONE) val uw_ident = wrapP ident (fn s => if String.isPrefix "uw_" s andalso size s >= 4 then SOME (str (Char.toUpper (String.sub (s, 3))) ^ String.extract (s, 4, NONE)) else NONE) val field = wrap (follow t_ident (follow (const ".") uw_ident)) (fn (t, ((), f)) => (t, f)) datatype Rel = Exps of exp * exp -> prop | Props of prop * prop -> prop datatype sqexp = SqConst of Prim.t | Field of string * string | Binop of Rel * sqexp * sqexp | SqKnown of sqexp | Inj of Mono.exp | SqFunc of string * sqexp | Count fun cmp s r = wrap (const s) (fn () => Exps (fn (e1, e2) => Reln (r, [e1, e2]))) val sqbrel = altL [cmp "=" Eq, cmp "<>" Ne, cmp "<=" Le, cmp "<" Lt, cmp ">=" Ge, cmp ">" Gt, wrap (const "AND") (fn () => Props And), wrap (const "OR") (fn () => Props Or)] datatype ('a, 'b) sum = inl of 'a | inr of 'b fun string chs = case chs of String s :: chs => if size s >= 2 andalso String.sub (s, 0) = #"'" then let fun loop (cs, acc) = case cs of [] => NONE | c :: cs => if c = #"'" then SOME (String.implode (rev acc), cs) else if c = #"\\" then case cs of c :: cs => loop (cs, c :: acc) | _ => raise Fail "Iflow.string: Unmatched backslash escape" else loop (cs, c :: acc) in case loop (String.explode (String.extract (s, 1, NONE)), []) of NONE => NONE | SOME (s, []) => SOME (s, chs) | SOME (s, cs) => SOME (s, String (String.implode cs) :: chs) end else NONE | _ => NONE val prim = altL [wrap (follow (wrapP (follow (keep Char.isDigit) (follow (const ".") (keep Char.isDigit))) (fn (x, ((), y)) => Option.map Prim.Float (Real64.fromString (x ^ "." ^ y)))) (opt (const "::float8"))) #1, wrap (follow (wrapP (keep Char.isDigit) (Option.map Prim.Int o Int64.fromString)) (opt (const "::int8"))) #1, wrap (follow (opt (const "E")) (follow string (opt (const "::text")))) (Prim.String o #1 o #2)] fun known' chs = case chs of Exp (EFfi ("Basis", "sql_known"), _) :: chs => SOME ((), chs) | _ => NONE fun sqlify chs = case chs of Exp (EFfiApp ("Basis", f, [e]), _) :: chs => if String.isPrefix "sqlify" f then SOME (e, chs) else NONE | _ => NONE fun constK s = wrap (const s) (fn () => s) val funcName = altL [constK "COUNT", constK "MIN", constK "MAX", constK "SUM", constK "AVG"] fun sqexp chs = log "sqexp" (altL [wrap prim SqConst, wrap field Field, wrap known SqKnown, wrap func SqFunc, wrap (const "COUNT(*)") (fn () => Count), wrap sqlify Inj, wrap (follow (const "COALESCE(") (follow sqexp (follow (const ",") (follow (keep (fn ch => ch <> #")")) (const ")"))))) (fn ((), (e, _)) => e), wrap (follow (ws (const "(")) (follow (wrap (follow sqexp (alt (wrap (follow (ws sqbrel) (ws sqexp)) inl) (always (inr ())))) (fn (e1, sm) => case sm of inl (bo, e2) => Binop (bo, e1, e2) | inr () => e1)) (const ")"))) (fn ((), (e, ())) => e)]) chs and known chs = wrap (follow known' (follow (const "(") (follow sqexp (const ")")))) (fn ((), ((), (e, ()))) => e) chs and func chs = wrap (follow funcName (follow (const "(") (follow sqexp (const ")")))) (fn (f, ((), (e, ()))) => (f, e)) chs datatype sitem = SqField of string * string | SqExp of sqexp * string val sitem = alt (wrap field SqField) (wrap (follow sqexp (follow (const " AS ") uw_ident)) (fn (e, ((), s)) => SqExp (e, s))) val select = log "select" (wrap (follow (const "SELECT ") (list sitem)) (fn ((), ls) => ls)) val fitem = wrap (follow uw_ident (follow (const " AS ") t_ident)) (fn (t, ((), f)) => (t, f)) val from = log "from" (wrap (follow (const "FROM ") (list fitem)) (fn ((), ls) => ls)) val wher = wrap (follow (ws (const "WHERE ")) sqexp) (fn ((), ls) => ls) val query = log "query" (wrap (follow (follow select from) (opt wher)) (fn ((fs, ts), wher) => {Select = fs, From = ts, Where = wher})) datatype dml = Insert of string * (string * sqexp) list | Delete of string * sqexp val insert = log "insert" (wrapP (follow (const "INSERT INTO ") (follow uw_ident (follow (const " (") (follow (list uw_ident) (follow (const ") VALUES (") (follow (list sqexp) (const ")"))))))) (fn ((), (tab, ((), (fs, ((), (es, ())))))) => (SOME (tab, ListPair.zipEq (fs, es))) handle ListPair.UnequalLengths => NONE)) val delete = log "delete" (wrap (follow (const "DELETE FROM ") (follow uw_ident (follow (const " AS T_T WHERE ") sqexp))) (fn ((), (tab, ((), es))) => (tab, es))) val dml = log "dml" (altL [wrap insert Insert, wrap delete Delete]) fun removeDups (ls : (string * string) list) = case ls of [] => [] | x :: ls => let val ls = removeDups ls in if List.exists (fn x' => x' = x) ls then ls else x :: ls end datatype queryMode = SomeCol | AllCols of exp fun expIn rv env rvOf = let fun expIn (e, rvN) = let fun default () = let val (rvN, e) = rv rvN in (inl e, rvN) end in case e of SqConst p => (inl (Const p), rvN) | Field (v, f) => (inl (Proj (rvOf v, f)), rvN) | Binop (bo, e1, e2) => let val (e1, rvN) = expIn (e1, rvN) val (e2, rvN) = expIn (e2, rvN) in (inr (case (bo, e1, e2) of (Exps f, inl e1, inl e2) => f (e1, e2) | (Props f, inr p1, inr p2) => f (p1, p2) | _ => Unknown), rvN) end | SqKnown e => (case expIn (e, rvN) of (inl e, rvN) => (inr (Reln (Known, [e])), rvN) | _ => (inr Unknown, rvN)) | Inj e => let fun deinj e = case #1 e of ERel n => (List.nth (env, n), rvN) | EField (e, f) => let val (e, rvN) = deinj e in (Proj (e, f), rvN) end | _ => let val (rvN, e) = rv rvN in (e, rvN) end val (e, rvN) = deinj e in (inl e, rvN) end | SqFunc (f, e) => (case expIn (e, rvN) of (inl e, rvN) => (inl (Func (Other f, [e])), rvN) | _ => default ()) | Count => default () end in expIn end fun queryProp env rvN rv oe e = let fun default () = (print ("Warning: Information flow checker can't parse SQL query at " ^ ErrorMsg.spanToString (#2 e) ^ "\n"); (rvN, Unknown, Unknown, [], [])) in case parse query e of NONE => default () | SOME r => let val (rvs, rvN) = ListUtil.foldlMap (fn ((_, v), rvN) => let val (rvN, e) = rv rvN in ((v, e), rvN) end) rvN (#From r) fun rvOf v = case List.find (fn (v', _) => v' = v) rvs of NONE => raise Fail "Iflow.queryProp: Bad table variable" | SOME (_, e) => e fun usedFields e = case e of SqConst _ => [] | Field (v, f) => [(v, f)] | Binop (_, e1, e2) => removeDups (usedFields e1 @ usedFields e2) | SqKnown _ => [] | Inj _ => [] | SqFunc (_, e) => usedFields e | Count => [] val p = foldl (fn ((t, v), p) => And (p, Reln (Sql t, [rvOf v]))) True (#From r) val expIn = expIn rv env rvOf val (p, rvN) = case #Where r of NONE => (p, rvN) | SOME e => case expIn (e, rvN) of (inr p', rvN) => (And (p, p'), rvN) | _ => (p, rvN) fun normal () = case oe of SomeCol => let val (sis, rvN) = ListUtil.foldlMap (fn (si, rvN) => case si of SqField (v, f) => (Proj (rvOf v, f), rvN) | SqExp (e, f) => case expIn (e, rvN) of (inr _, _) => let val (rvN, e) = rv rvN in (e, rvN) end | (inl e, rvN) => (e, rvN)) rvN (#Select r) in (rvN, p, True, sis) end | AllCols oe => let val (p', rvN) = foldl (fn (si, (p, rvN)) => let val (p', rvN) = case si of SqField (v, f) => (Reln (Eq, [Proj (Proj (oe, v), f), Proj (rvOf v, f)]), rvN) | SqExp (e, f) => case expIn (e, rvN) of (inr p, rvN) => (Cond (Proj (oe, f), p), rvN) | (inl e, rvN) => (Reln (Eq, [Proj (oe, f), e]), rvN) in (And (p, p'), rvN) end) (True, rvN) (#Select r) in (rvN, And (p, p'), True, []) end val (rvN, p, wp, outs) = case #Select r of [SqExp (Binop (Exps bo, Count, SqConst (Prim.Int 0)), f)] => (case bo (Const (Prim.Int 1), Const (Prim.Int 2)) of Reln (Gt, [Const (Prim.Int 1), Const (Prim.Int 2)]) => (case oe of SomeCol => let val (rvN, oe) = rv rvN in (rvN, Or (Reln (Eq, [oe, Func (DtCon0 "Basis.bool.False", [])]), And (Reln (Eq, [oe, Func (DtCon0 "Basis.bool.True", [])]), p)), Reln (Eq, [oe, Func (DtCon0 "Basis.bool.True", [])]), [oe]) end | AllCols oe => let fun oeEq e = Reln (Eq, [oe, Recd [(f, e)]]) in (rvN, Or (oeEq (Func (DtCon0 "Basis.bool.False", [])), And (oeEq (Func (DtCon0 "Basis.bool.True", [])), p)), oeEq (Func (DtCon0 "Basis.bool.True", [])), []) end) | _ => normal ()) | _ => normal () in (rvN, p, wp, case #Where r of NONE => [] | SOME e => map (fn (v, f) => Proj (rvOf v, f)) (usedFields e), outs) end end fun insertProp rvN rv e = let fun default () = (print ("Warning: Information flow checker can't parse SQL query at " ^ ErrorMsg.spanToString (#2 e) ^ "\n"); Unknown) in case parse query e of NONE => default () | SOME r => let val (rvs, rvN) = ListUtil.foldlMap (fn ((_, v), rvN) => let val (rvN, e) = rv rvN in ((v, e), rvN) end) rvN (#From r) fun rvOf v = case List.find (fn (v', _) => v' = v) rvs of NONE => raise Fail "Iflow.insertProp: Bad table variable" | SOME (_, e) => e val p = foldl (fn ((t, v), p) => let val t = case v of "New" => "$New" | _ => t in And (p, Reln (Sql t, [rvOf v])) end) True (#From r) val expIn = expIn rv [] rvOf in case #Where r of NONE => p | SOME e => case expIn (e, rvN) of (inr p', _) => And (p, p') | _ => p end end fun deleteProp rvN rv e = let fun default () = (print ("Warning: Information flow checker can't parse SQL query at " ^ ErrorMsg.spanToString (#2 e) ^ "\n"); Unknown) in case parse query e of NONE => default () | SOME r => let val (rvs, rvN) = ListUtil.foldlMap (fn ((_, v), rvN) => let val (rvN, e) = rv rvN in ((v, e), rvN) end) rvN (#From r) fun rvOf v = case List.find (fn (v', _) => v' = v) rvs of NONE => raise Fail "Iflow.deleteProp: Bad table variable" | SOME (_, e) => e val p = foldl (fn ((t, v), p) => And (p, Reln (Sql t, [rvOf v]))) True (#From r) val expIn = expIn rv [] rvOf in And (Reln (Sql "$Old", [rvOf "Old"]), case #Where r of NONE => p | SOME e => case expIn (e, rvN) of (inr p', _) => And (p, p') | _ => p) end end fun evalPat env e (pt, _) = case pt of PWild => (env, True) | PVar _ => (e :: env, True) | PPrim _ => (env, True) | PCon (_, pc, NONE) => (env, Reln (PCon0 (patCon pc), [e])) | PCon (_, pc, SOME pt) => let val (env, p) = evalPat env (Func (UnCon (patCon pc), [e])) pt in (env, And (p, Reln (PCon1 (patCon pc), [e]))) end | PRecord xpts => foldl (fn ((x, pt, _), (env, p)) => let val (env, p') = evalPat env (Proj (e, x)) pt in (env, And (p', p)) end) (env, True) xpts | PNone _ => (env, Reln (PCon0 "None", [e])) | PSome (_, pt) => let val (env, p) = evalPat env (Func (UnCon "Some", [e])) pt in (env, And (p, Reln (PCon1 "Some", [e]))) end fun peq (p1, p2) = case (p1, p2) of (True, True) => true | (False, False) => true | (Unknown, Unknown) => true | (And (x1, y1), And (x2, y2)) => peq (x1, x2) andalso peq (y1, y2) | (Or (x1, y1), Or (x2, y2)) => peq (x1, x2) andalso peq (y1, y2) | (Reln (r1, es1), Reln (r2, es2)) => r1 = r2 andalso ListPair.allEq eeq (es1, es2) | (Cond (e1, p1), Cond (e2, p2)) => eeq (e1, e2) andalso peq (p1, p2) | _ => false fun removeRedundant p1 = let fun rr p2 = if peq (p1, p2) then True else case p2 of And (x, y) => And (rr x, rr y) | Or (x, y) => Or (rr x, rr y) | _ => p2 in rr end datatype cflow = Case | Where datatype flow = Data | Control of cflow type check = ErrorMsg.span * exp * prop type dml = ErrorMsg.span * prop structure St :> sig type t val create : {Var : int, Ambient : prop} -> t val curVar : t -> int val nextVar : t -> t * int val ambient : t -> prop val setAmbient : t * prop -> t val paths : t -> (check * cflow) list val addPath : t * (check * cflow) -> t val addPaths : t * (check * cflow) list -> t val clearPaths : t -> t val setPaths : t * (check * cflow) list -> t val sent : t -> (check * flow) list val addSent : t * (check * flow) -> t val setSent : t * (check * flow) list -> t val inserted : t -> dml list val addInsert : t * dml -> t val deleted : t -> dml list val addDelete : t * dml -> t end = struct type t = {Var : int, Ambient : prop, Path : (check * cflow) list, Sent : (check * flow) list, Insert : dml list, Delete : dml list} fun create {Var = v, Ambient = p} = {Var = v, Ambient = p, Path = [], Sent = [], Insert = [], Delete = []} fun curVar (t : t) = #Var t fun nextVar (t : t) = ({Var = #Var t + 1, Ambient = #Ambient t, Path = #Path t, Sent = #Sent t, Insert = #Insert t, Delete = #Delete t}, #Var t) fun ambient (t : t) = #Ambient t fun setAmbient (t : t, p) = {Var = #Var t, Ambient = p, Path = #Path t, Sent = #Sent t, Insert = #Insert t, Delete = #Delete t} fun paths (t : t) = #Path t fun addPath (t : t, c) = {Var = #Var t, Ambient = #Ambient t, Path = c :: #Path t, Sent = #Sent t, Insert = #Insert t, Delete = #Delete t} fun addPaths (t : t, cs) = {Var = #Var t, Ambient = #Ambient t, Path = cs @ #Path t, Sent = #Sent t, Insert = #Insert t, Delete = #Delete t} fun clearPaths (t : t) = {Var = #Var t, Ambient = #Ambient t, Path = [], Sent = #Sent t, Insert = #Insert t, Delete = #Delete t} fun setPaths (t : t, cs) = {Var = #Var t, Ambient = #Ambient t, Path = cs, Sent = #Sent t, Insert = #Insert t, Delete = #Delete t} fun sent (t : t) = #Sent t fun addSent (t : t, c) = {Var = #Var t, Ambient = #Ambient t, Path = #Path t, Sent = c :: #Sent t, Insert = #Insert t, Delete = #Delete t} fun setSent (t : t, cs) = {Var = #Var t, Ambient = #Ambient t, Path = #Path t, Sent = cs, Insert = #Insert t, Delete = #Delete t} fun inserted (t : t) = #Insert t fun addInsert (t : t, c) = {Var = #Var t, Ambient = #Ambient t, Path = #Path t, Sent = #Sent t, Insert = c :: #Insert t, Delete = #Delete t} fun deleted (t : t) = #Delete t fun addDelete (t : t, c) = {Var = #Var t, Ambient = #Ambient t, Path = #Path t, Sent = #Sent t, Insert = #Insert t, Delete = c :: #Delete t} end fun evalExp env (e as (_, loc), st) = let fun default () = let val (st, nv) = St.nextVar st in (Var nv, st) end fun addSent (p, e, st) = let val st = if isKnown e then st else St.addSent (st, ((loc, e, p), Data)) val st = foldl (fn ((c, fl), st) => St.addSent (st, (c, Control fl))) st (St.paths st) in St.clearPaths st end in case #1 e of EPrim p => (Const p, st) | ERel n => (List.nth (env, n), st) | ENamed _ => default () | ECon (_, pc, NONE) => (Func (DtCon0 (patCon pc), []), st) | ECon (_, pc, SOME e) => let val (e, st) = evalExp env (e, st) in (Func (DtCon1 (patCon pc), [e]), st) end | ENone _ => (Func (DtCon0 "None", []), st) | ESome (_, e) => let val (e, st) = evalExp env (e, st) in (Func (DtCon1 "Some", [e]), st) end | EFfi _ => default () | EFfiApp (m, s, es) => if m = "Basis" andalso SS.member (writers, s) then let val (es, st) = ListUtil.foldlMap (evalExp env) st es in (Recd [], foldl (fn (e, st) => addSent (St.ambient st, e, st)) st es) end else if Settings.isEffectful (m, s) andalso not (Settings.isBenignEffectful (m, s)) then default () else let val (es, st) = ListUtil.foldlMap (evalExp env) st es in (Func (Other (m ^ "." ^ s), es), st) end | EApp (e1, e2) => let val (e1, st) = evalExp env (e1, st) in case e1 of Finish => (Finish, st) | _ => default () end | EAbs _ => default () | EUnop (s, e1) => let val (e1, st) = evalExp env (e1, st) in (Func (Other s, [e1]), st) end | EBinop (s, e1, e2) => let val (e1, st) = evalExp env (e1, st) val (e2, st) = evalExp env (e2, st) in (Func (Other s, [e1, e2]), st) end | ERecord xets => let val (xes, st) = ListUtil.foldlMap (fn ((x, e, _), st) => let val (e, st) = evalExp env (e, st) in ((x, e), st) end) st xets in (Recd xes, st) end | EField (e, s) => let val (e, st) = evalExp env (e, st) in (Proj (e, s), st) end | ECase (e, pes, {result = res, ...}) => let val (e, st) = evalExp env (e, st) val (st, r) = St.nextVar st val orig = St.ambient st val origPaths = St.paths st val st = St.addPath (st, ((loc, e, orig), Case)) val (st, paths) = foldl (fn ((pt, pe), (st, paths)) => let val (env, pp) = evalPat env e pt val (pe, st') = evalExp env (pe, St.setAmbient (st, And (orig, pp))) val this = And (removeRedundant orig (St.ambient st'), Reln (Eq, [Var r, pe])) in (St.setPaths (St.setAmbient (st', Or (St.ambient st, this)), origPaths), St.paths st' @ paths) end) (St.setAmbient (st, False), []) pes val st = case #1 res of TRecord [] => St.setPaths (st, origPaths) | _ => St.setPaths (st, paths) in (Var r, St.setAmbient (st, And (orig, St.ambient st))) end | EStrcat (e1, e2) => let val (e1, st) = evalExp env (e1, st) val (e2, st) = evalExp env (e2, st) in (Func (Other "cat", [e1, e2]), st) end | EError _ => (Finish, st) | EReturnBlob {blob = b, mimeType = m, ...} => let val (b, st) = evalExp env (b, st) val (m, st) = evalExp env (m, st) in (Finish, addSent (St.ambient st, b, addSent (St.ambient st, m, st))) end | ERedirect (e, _) => let val (e, st) = evalExp env (e, st) in (Finish, addSent (St.ambient st, e, st)) end | EWrite e => let val (e, st) = evalExp env (e, st) in (Recd [], addSent (St.ambient st, e, st)) end | ESeq (e1, e2) => let val (_, st) = evalExp env (e1, st) in evalExp env (e2, st) end | ELet (_, _, e1, e2) => let val (e1, st) = evalExp env (e1, st) in evalExp (e1 :: env) (e2, st) end | EClosure (n, es) => let val (es, st) = ListUtil.foldlMap (evalExp env) st es in (Func (Other ("Cl" ^ Int.toString n), es), st) end | EQuery {query = q, body = b, initial = i, ...} => let val (_, st) = evalExp env (q, st) val (i, st) = evalExp env (i, st) val (st', r) = St.nextVar st val (st', acc) = St.nextVar st' val (b, st') = evalExp (Var acc :: Var r :: env) (b, st') val (st', qp, qwp, used, _) = queryProp env st' (fn st' => let val (st', rv) = St.nextVar st' in (st', Var rv) end) (AllCols (Var r)) q val p' = And (qp, St.ambient st') val (st, res) = if varInP acc (St.ambient st') then let val (st, r) = St.nextVar st in (st, Var r) end else let val (st, out) = St.nextVar st' val p = Or (Reln (Eq, [Var out, i]), And (Reln (Eq, [Var out, b]), p')) in (St.setAmbient (st, p), Var out) end val sent = map (fn ((loc, e, p), fl) => ((loc, e, And (qp, p)), fl)) (St.sent st') val p' = And (p', qwp) val paths = map (fn e => ((loc, e, p'), Where)) used in (res, St.addPaths (St.setSent (st, sent), paths)) end | EDml e => (case parse dml e of NONE => (print ("Warning: Information flow checker can't parse DML command at " ^ ErrorMsg.spanToString loc ^ "\n"); default ()) | SOME d => case d of Insert (tab, es) => let val (st, new) = St.nextVar st fun rv st = let val (st, n) = St.nextVar st in (st, Var n) end val expIn = expIn rv env (fn "New" => Var new | _ => raise Fail "Iflow.evalExp: Bad field expression in UPDATE") val (es, st) = ListUtil.foldlMap (fn ((x, e), st) => let val (e, st) = case expIn (e, st) of (inl e, st) => (e, st) | (inr _, _) => raise Fail ("Iflow.evalExp: Selecting " ^ "boolean expression") in ((x, e), st) end) st es in (Recd [], St.addInsert (st, (loc, And (St.ambient st, Reln (Sql "$New", [Recd es]))))) end | Delete (tab, e) => let val (st, old) = St.nextVar st fun rv st = let val (st, n) = St.nextVar st in (st, Var n) end val expIn = expIn rv env (fn "T" => Var old | _ => raise Fail "Iflow.evalExp: Bad field expression in DELETE") val (p, st) = case expIn (e, st) of (inl e, _) => raise Fail "Iflow.evalExp: DELETE with non-boolean" | (inr p, st) => (p, st) val p = And (p, And (Reln (Sql "$Old", [Var old]), Reln (Sql tab, [Var old]))) in (Recd [], St.addDelete (st, (loc, And (St.ambient st, p)))) end) | ENextval _ => default () | ESetval _ => default () | EUnurlify ((EFfiApp ("Basis", "get_cookie", _), _), _, _) => let val (st, nv) = St.nextVar st in (Var nv, St.setAmbient (st, And (St.ambient st, Reln (Known, [Var nv])))) end | EUnurlify _ => default () | EJavaScript _ => default () | ESignalReturn _ => default () | ESignalBind _ => default () | ESignalSource _ => default () | EServerCall _ => default () | ERecv _ => default () | ESleep _ => default () | ESpawn _ => default () end fun check file = let val file = MonoReduce.reduce file val file = MonoOpt.optimize file val file = Fuse.fuse file val file = MonoOpt.optimize file val file = MonoShake.shake file (*val () = Print.preface ("File", MonoPrint.p_file MonoEnv.empty file)*) val exptd = foldl (fn ((d, _), exptd) => case d of DExport (_, _, n, _, _, _) => IS.add (exptd, n) | _ => exptd) IS.empty file fun decl ((d, _), (vals, inserts, deletes, client, insert, delete)) = case d of DVal (_, n, _, e, _) => let val isExptd = IS.member (exptd, n) fun deAbs (e, env, nv, p) = case #1 e of EAbs (_, _, _, e) => deAbs (e, Var nv :: env, nv + 1, if isExptd then And (p, Reln (Known, [Var nv])) else p) | _ => (e, env, nv, p) val (e, env, nv, p) = deAbs (e, [], 1, True) val (_, st) = evalExp env (e, St.create {Var = nv, Ambient = p}) in (St.sent st @ vals, St.inserted st @ inserts, St.deleted st @ deletes, client, insert, delete) end | DPolicy pol => let fun rv rvN = (rvN + 1, Lvar rvN) in case pol of PolClient e => let val (_, p, _, _, outs) = queryProp [] 0 rv SomeCol e in (vals, inserts, deletes, (p, outs) :: client, insert, delete) end | PolInsert e => let val p = insertProp 0 rv e in (vals, inserts, deletes, client, p :: insert, delete) end | PolDelete e => let val p = deleteProp 0 rv e in (vals, inserts, deletes, client, insert, p :: delete) end end | _ => (vals, inserts, deletes, client, insert, delete) val () = reset () val (vals, inserts, deletes, client, insert, delete) = foldl decl ([], [], [], [], [], []) file val decompH = decomp true (fn (e1, e2) => e1 andalso e2 ()) val decompG = decomp false (fn (e1, e2) => e1 orelse e2 ()) fun doDml (cmds, pols) = app (fn (loc, p) => if decompH p (fn hyps => List.exists (fn p' => decompG p' (fn goals => imply (hyps, goals, NONE))) pols) then () else (ErrorMsg.errorAt loc "The information flow policy may be violated here."; Print.preface ("The state satisifies this predicate:", p_prop p))) cmds in app (fn ((loc, e, p), fl) => let fun doOne e = let val p = And (p, Reln (Eq, [Var 0, e])) in if decompH p (fn hyps => (fl <> Control Where andalso imply (hyps, [AReln (Known, [Var 0])], SOME [Var 0])) orelse List.exists (fn (p', outs) => decompG p' (fn goals => imply (hyps, goals, SOME outs))) client) then () else (ErrorMsg.errorAt loc "The information flow policy may be violated here."; Print.preface ("The state satisifies this predicate:", p_prop p)) end fun doAll e = case e of Const _ => () | Var _ => doOne e | Lvar _ => raise Fail "Iflow.doAll: Lvar" | Func (UnCon _, [_]) => doOne e | Func (_, es) => app doAll es | Recd xes => app (doAll o #2) xes | Proj _ => doOne e | Finish => () in doAll e end) vals; doDml (inserts, insert); doDml (deletes, delete) end val check = fn file => let val oldInline = Settings.getMonoInline () in (Settings.setMonoInline (case Int.maxInt of NONE => 1000000 | SOME n => n); check file; Settings.setMonoInline oldInline) handle ex => (Settings.setMonoInline oldInline; raise ex) end end