(* 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 type representative exception Contradiction exception Undetermined val database : unit -> database val representative : database * exp -> representative val assert : database * atom -> unit val check : database * atom -> bool val p_database : database Print.printer 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 | VFinish | Nothing type representative = node ref val finish = ref (Node {Rep = ref NONE, Cons = ref SM.empty, Variety = VFinish, Known = ref false}) 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 => case #Variety (unNode n) of Nothing => string ("?" ^ Int.toString (Unsafe.cast n)) | 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) => box [string "{", p_list (fn (x, n) => box [string x, space, string "=", space, p_rep n]) (SM.listItemsi m), string "}"] | 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]) (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 = (#Known (unNode r) := true; case #Variety (unNode r) of Dt1 (_, r) => markKnown r | Recrd xes => SM.app markKnown (!xes) | _ => ()) 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 false}) 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 false}) 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 false}) 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 false}) 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), 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 false}) 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 false}) val r'' = ref (Node {Rep = ref NONE, Cons = #Cons (unNode r), Variety = Recrd (ref (SM.insert (SM.empty, f, r'))), 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]) => markKnown (representative (db, e)) | (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, _) => (#Rep (unNode r1) := SOME r2; if !(#Known (unNode r1)) andalso not (!(#Known (unNode r2))) then markKnown r2 else (); #Cons (unNode r2) := SM.unionWith #1 (!(#Cons (unNode r2)), !(#Cons (unNode r1))); compactFuncs ()) | (_, Nothing) => (#Rep (unNode r2) := SOME r1; if !(#Known (unNode r2)) andalso not (!(#Known (unNode r1))) then markKnown r1 else (); #Cons (unNode r1) := SM.unionWith #1 (!(#Cons (unNode r1)), !(#Cons (unNode r2))); compactFuncs ()) | _ => raise Contradiction 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]) => !(#Known (unNode (representative (db, e)))) | (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 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 (p1, p2) = (reset (); decomp true (fn (e1, e2) => e1 andalso e2 ()) p1 (fn hyps => decomp false (fn (e1, e2) => e1 orelse e2 ()) p2 (fn goals => let fun gls goals onFail acc = case goals of [] => (let val cc = Cc.database () val () = app (fn a => Cc.assert (cc, a)) hyps in (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 orelse onFail ()) handle Cc.Contradiction => onFail () end handle Cc.Undetermined => onFail ()) | AReln (Sql gf, [ge]) :: goals => let fun hps hyps = case hyps of [] => onFail () | 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 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})) 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 of exp | AllCols of exp fun queryProp env rvN rv oe e = case parse query e of NONE => (print ("Warning: Information flow checker can't parse SQL query at " ^ ErrorMsg.spanToString (#2 e) ^ "\n"); (rvN, Var 0, Unknown, [])) | SOME r => let val (rvN, count) = rv rvN 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) fun expIn e = case e of SqConst p => inl (Const p) | Field (v, f) => inl (Proj (rvOf v, f)) | Binop (bo, e1, e2) => inr (case (bo, expIn e1, expIn e2) of (Exps f, inl e1, inl e2) => f (e1, e2) | (Props f, inr p1, inr p2) => f (p1, p2) | _ => Unknown) | SqKnown e => inr (case expIn e of inl e => Reln (Known, [e]) | _ => Unknown) | Inj e => let fun deinj (e, _) = case e of ERel n => List.nth (env, n) | EField (e, f) => Proj (deinj e, f) | _ => raise Fail "Iflow: non-variable injected into query" in inl (deinj e) end | SqFunc (f, e) => inl (case expIn e of inl e => Func (Other f, [e]) | _ => raise Fail ("Iflow: non-expresion passed to function " ^ f)) | Count => inl count val p = case #Where r of NONE => p | SOME e => case expIn e of inr p' => And (p, p') | _ => p in (rvN, count, And (p, case oe of SomeCol oe => foldl (fn (si, p) => let val p' = case si of SqField (v, f) => Reln (Eq, [oe, Proj (rvOf v, f)]) | SqExp (e, f) => case expIn e of inr _ => Unknown | inl e => Reln (Eq, [oe, e]) in Or (p, p') end) False (#Select r) | AllCols oe => foldl (fn (si, p) => let val p' = case si of SqField (v, f) => Reln (Eq, [Proj (Proj (oe, v), f), Proj (rvOf v, f)]) | SqExp (e, f) => case expIn e of inr p => Cond (Proj (oe, f), p) | inl e => Reln (Eq, [Proj (oe, f), e]) in And (p, p') end) True (#Select r)), case #Where r of NONE => [] | SOME e => map (fn (v, f) => Proj (rvOf v, f)) (usedFields e)) 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 fun evalExp env (e as (_, loc), st as (nv, p, sent)) = let fun default () = ((*Print.preface ("Default" ^ Int.toString nv, MonoPrint.p_exp MonoEnv.empty e);*) (Var nv, (nv+1, p, sent))) fun addSent (p, e, sent) = if isKnown e then sent else (loc, e, p) :: sent 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 [], (#1 st, p, foldl (fn (e, sent) => addSent (#2 st, e, sent)) sent 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, _) => let val (e, st) = evalExp env (e, st) val r = #1 st val st = (r + 1, #2 st, #3 st) val orig = #2 st val st = foldl (fn ((pt, pe), st) => let val (env, pp) = evalPat env e pt val (pe, st') = evalExp env (pe, (#1 st, And (orig, pp), #3 st)) val this = And (removeRedundant orig (#2 st'), Reln (Eq, [Var r, pe])) in (#1 st', Or (#2 st, this), #3 st') end) (#1 st, False, #3 st) pes in (Var r, (#1 st, And (orig, #2 st), #3 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, (#1 st, p, addSent (#2 st, b, addSent (#2 st, m, sent)))) end | ERedirect (e, _) => let val (e, st) = evalExp env (e, st) in (Finish, (#1 st, p, addSent (#2 st, e, sent))) end | EWrite e => let val (e, st) = evalExp env (e, st) in (Recd [], (#1 st, p, addSent (#2 st, e, sent))) 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 r = #1 st val acc = #1 st + 1 val st' = (#1 st + 2, #2 st, #3 st) val (b, st') = evalExp (Var acc :: Var r :: env) (b, st') val (rvN, count, qp, used) = queryProp env (#1 st') (fn rvN => (rvN + 1, Var rvN)) (AllCols (Var r)) q val p' = And (qp, #2 st') val (nvs, p, res) = if varInP acc (#2 st') then (#1 st + 1, #2 st, Var r) else let val out = rvN val p = Or (Reln (Eq, [Var out, i]), And (Reln (Eq, [Var out, b]), And (Reln (Gt, [count, Const (Prim.Int 0)]), p'))) in (out + 1, p, Var out) end val sent = map (fn (loc, e, p) => (loc, e, And (qp, p))) (#3 st') val sent = map (fn e => (loc, e, p')) used @ sent in (res, (nvs, p, sent)) end | EDml _ => default () | ENextval _ => default () | ESetval _ => default () | EUnurlify ((EFfiApp ("Basis", "get_cookie", _), _), _, _) => (Var nv, (nv + 1, And (p, Reln (Known, [Var nv])), sent)) | 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 () = 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, pols)) = 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 (e, (_, p, sent)) = evalExp env (e, (nv, p, [])) in (sent @ vals, pols) end | DPolicy (PolClient e) => (vals, #3 (queryProp [] 0 (fn rvN => (rvN + 1, Lvar rvN)) (SomeCol (Var 0)) e) :: pols) | _ => (vals, pols) val () = reset () val (vals, pols) = foldl decl ([], []) file in app (fn (loc, e, p) => let fun doOne e = let val p = And (p, Reln (Eq, [Var 0, e])) in if List.exists (fn pol => if imply (p, pol) then (if !debug then Print.prefaces "Match" [("Hyp", p_prop p), ("Goal", p_prop pol)] else (); true) else false) pols then () else (ErrorMsg.errorAt loc "The information flow policy may be violated here."; Print.preface ("The state satisifes this predicate:", p_prop p)) end fun doAll e = case e of Const _ => () | Var _ => doOne e | Lvar _ => raise Fail "Iflow.doAll: Lvar" | Func (UnCon _, [e]) => doOne e | Func (_, es) => app doAll es | Recd xes => app (doAll o #2) xes | Proj _ => doOne e | Finish => () in doAll e end) vals 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