// #################################################################### /// Utility functions for manipulating AST elements /// /// author: Aleksandar Milicevic (t-alekm@microsoft.com) // #################################################################### module AstUtils open Ast open Getters open Logger open Utils let ThisLiteral = ObjLiteral("this") let NullLiteral = ObjLiteral("null") let IsLogicalOp op = [ "&&"; "||"; "==>"; "<==>" ] |> Utils.ListContains op let IsRelationalOp op = [ "="; "!="; "<"; "<="; ">"; ">="; "in"; "!in" ] |> Utils.ListContains op let AreInverseOps op1 op2 = match op1, op2 with "<" , ">" | ">" , "<" | "<=", ">=" | ">=", "<=" -> true | _ -> false let DoesImplyOp op1 op2 = match op1, op2 with | "<" , "!=" | ">" , "!=" -> true | "=" , ">=" | "=" , "<=" -> true | ">" , ">=" | "<" , "<=" -> true | _ -> false let IsCommutativeOp op = match op with "=" | "!=" -> true | _ -> false exception ExprConvFailed of string let Expr2Int e = match e with | IntLiteral(n) -> n | _ -> raise (ExprConvFailed(sprintf "not an int but: %O" e)) let Expr2Bool e = match e with | BoolLiteral(b) -> b | _ -> raise (ExprConvFailed(sprintf "not a bool but: %O" e)) let Expr2List e = match e with | SequenceExpr(elist) -> elist | _ -> raise (ExprConvFailed(sprintf "not a Seq but: %O" e)) let rec MyRewrite rewriterFunc rewriteRecurseFunc expr = match expr with | IntLiteral(_) | BoolLiteral(_) | BoxLiteral(_) | Star | VarLiteral(_) | ObjLiteral(_) | VarDeclExpr(_) | IdLiteral(_) -> match rewriterFunc expr with | Some(e) -> e | None -> expr | Dot(e, id) -> Dot(rewriteRecurseFunc e, id) | ForallExpr(vars,e) -> ForallExpr(vars, rewriteRecurseFunc e) | UnaryExpr(op,e) -> UnaryExpr(op, rewriteRecurseFunc e) | OldExpr(e) -> OldExpr(rewriteRecurseFunc e) | LCIntervalExpr(e) -> LCIntervalExpr(rewriteRecurseFunc e) | SeqLength(e) -> SeqLength(rewriteRecurseFunc e) | SelectExpr(e1, e2) -> SelectExpr(rewriteRecurseFunc e1, rewriteRecurseFunc e2) | BinaryExpr(p,op,e1,e2) -> BinaryExpr(p, op, rewriteRecurseFunc e1, rewriteRecurseFunc e2) | IteExpr(e1,e2,e3) -> IteExpr(rewriteRecurseFunc e1, rewriteRecurseFunc e2, rewriteRecurseFunc e3) | UpdateExpr(e1,e2,e3) -> UpdateExpr(rewriteRecurseFunc e1, rewriteRecurseFunc e2, rewriteRecurseFunc e3) | SequenceExpr(exs) -> SequenceExpr(exs |> List.map rewriteRecurseFunc) | SetExpr(exs) -> SetExpr(exs |> List.map rewriteRecurseFunc) | MethodCall(rcv,cname,mname,ins) -> MethodCall(rewriteRecurseFunc rcv, cname, mname, ins |> List.map rewriteRecurseFunc) | MethodOutSelect(mth,name) -> MethodOutSelect(rewriteRecurseFunc mth, name) | AssertExpr(e) -> AssertExpr(rewriteRecurseFunc e) | AssumeExpr(e) -> AssumeExpr(rewriteRecurseFunc e) let rec Rewrite rewriterFunc expr = let __RewriteOrRecurse e = match rewriterFunc e with | Some(ee) -> ee | None -> Rewrite rewriterFunc e MyRewrite rewriterFunc __RewriteOrRecurse expr // TODO: double check this! let rec RewriteBU rewriterFunc expr = let rewriteRecurseFunc e = RewriteBU rewriterFunc e // let e' = Rewrite rewriterFunc e // match rewriterFunc e' with // | Some(ee) -> ee // | None -> e' let rewriteFunc e = match rewriterFunc e with | Some(ee) -> ee | None -> e let expr' = match expr with | IntLiteral(_) | BoolLiteral(_) | BoxLiteral(_) | Star | VarLiteral(_) | ObjLiteral(_) | VarDeclExpr(_) | IdLiteral(_) -> expr | Dot(e, id) -> Dot(rewriteRecurseFunc e, id) | ForallExpr(vars,e) -> ForallExpr(vars, rewriteRecurseFunc e) | UnaryExpr(op,e) -> UnaryExpr(op, rewriteRecurseFunc e) | OldExpr(e) -> OldExpr(rewriteRecurseFunc e) | LCIntervalExpr(e) -> LCIntervalExpr(rewriteRecurseFunc e) | SeqLength(e) -> SeqLength(rewriteRecurseFunc e) | SelectExpr(e1, e2) -> SelectExpr(rewriteRecurseFunc e1, rewriteRecurseFunc e2) | BinaryExpr(p,op,e1,e2) -> BinaryExpr(p, op, rewriteRecurseFunc e1, rewriteRecurseFunc e2) | IteExpr(e1,e2,e3) -> IteExpr(rewriteRecurseFunc e1, rewriteRecurseFunc e2, rewriteRecurseFunc e3) | UpdateExpr(e1,e2,e3) -> UpdateExpr(rewriteRecurseFunc e1, rewriteRecurseFunc e2, rewriteRecurseFunc e3) | SequenceExpr(exs) -> SequenceExpr(exs |> List.map rewriteRecurseFunc) | SetExpr(exs) -> SetExpr(exs |> List.map rewriteRecurseFunc) | MethodCall(rcv,cname,mname,ins) -> MethodCall(rewriteRecurseFunc rcv, cname, mname, ins |> List.map rewriteRecurseFunc) | MethodOutSelect(mth,name) -> MethodOutSelect(rewriteRecurseFunc mth, name) | AssertExpr(e) -> AssertExpr(rewriteRecurseFunc e) | AssumeExpr(e) -> AssumeExpr(rewriteRecurseFunc e) expr' |> rewriteFunc let rec RewriteWithCtx rewriterFunc ctx expr = let __RewriteOrRecurse ctx e = match rewriterFunc ctx e with | Some(ee) -> ee | None -> RewriteWithCtx rewriterFunc ctx e match expr with | IntLiteral(_) | BoolLiteral(_) | BoxLiteral(_) | Star | VarLiteral(_) | ObjLiteral(_) | VarDeclExpr(_) | IdLiteral(_) -> match rewriterFunc ctx expr with | Some(e) -> e | None -> expr | Dot(e, id) -> Dot(__RewriteOrRecurse ctx e, id) | ForallExpr(vars,e) -> ForallExpr(vars, __RewriteOrRecurse (ctx @ vars) e) | UnaryExpr(op,e) -> UnaryExpr(op, __RewriteOrRecurse ctx e) | OldExpr(e) -> OldExpr(__RewriteOrRecurse ctx e) | LCIntervalExpr(e) -> LCIntervalExpr(__RewriteOrRecurse ctx e) | SeqLength(e) -> SeqLength(__RewriteOrRecurse ctx e) | SelectExpr(e1, e2) -> SelectExpr(__RewriteOrRecurse ctx e1, __RewriteOrRecurse ctx e2) | BinaryExpr(p,op,e1,e2) -> BinaryExpr(p, op, __RewriteOrRecurse ctx e1, __RewriteOrRecurse ctx e2) | IteExpr(e1,e2,e3) -> IteExpr(__RewriteOrRecurse ctx e1, __RewriteOrRecurse ctx e2, __RewriteOrRecurse ctx e3) | UpdateExpr(e1,e2,e3) -> UpdateExpr(__RewriteOrRecurse ctx e1, __RewriteOrRecurse ctx e2, __RewriteOrRecurse ctx e3) | SequenceExpr(exs) -> SequenceExpr(exs |> List.map (__RewriteOrRecurse ctx)) | SetExpr(exs) -> SetExpr(exs |> List.map (__RewriteOrRecurse ctx)) | MethodCall(rcv,cname,mname,ins) -> MethodCall(__RewriteOrRecurse ctx rcv, cname, mname, ins |> List.map (__RewriteOrRecurse ctx)) | MethodOutSelect(mth,name) -> MethodOutSelect(__RewriteOrRecurse ctx mth, name) | AssertExpr(e) -> AssertExpr(__RewriteOrRecurse ctx e) | AssumeExpr(e) -> AssumeExpr(__RewriteOrRecurse ctx e) // ==================================================== /// Substitutes all occurences of all IdLiterals having /// the same name as one of the variables in "vars" with /// VarLiterals, in "expr". // ==================================================== let RewriteVars vars expr = let __IdIsArg id = vars |> List.exists (fun var -> GetVarName var = id) Rewrite (fun e -> match e with | IdLiteral(id) when __IdIsArg id -> Some(VarLiteral(id)) | _ -> None) expr // ================================================ /// Substitutes all occurences of e1 with e2 in expr // ================================================ let Substitute e1 e2 expr = Rewrite (fun e -> if e = e1 then Some(e2) else None) expr // ================================================ /// Distributes the negation operator over /// arithmetic relations // ================================================ let rec DistributeNegation expr = let __Neg op = match op with | "=" -> Some("!=") | "!=" -> Some("=") | "<" -> Some(">=") | ">" -> Some("<=") | ">=" -> Some("<") | "<=" -> Some(">") | _ -> None Rewrite (fun e -> match e with | UnaryExpr("!", sub) -> match sub with | BinaryExpr(p,op,lhs,rhs) -> match __Neg op with | Some(op') -> Some(BinaryExpr(p, op', DistributeNegation lhs, DistributeNegation rhs)) | None -> None | _ -> None | _ -> None) expr let rec DescendExpr visitorFunc composeFunc leafVal expr = let __Compose elist = match elist with | [] -> leafVal | fs :: rest -> rest |> List.fold (fun acc e -> composeFunc (composeFunc acc (visitorFunc e)) (DescendExpr visitorFunc composeFunc leafVal e)) (visitorFunc fs) match expr with | IntLiteral(_) | BoolLiteral(_) | BoxLiteral(_) | Star | VarLiteral(_) | ObjLiteral(_) | VarDeclExpr(_) | IdLiteral(_) -> leafVal | AssertExpr(e) | AssumeExpr(e) | Dot(e, _) | ForallExpr(_,e) | LCIntervalExpr(e) | OldExpr(e) | UnaryExpr(_,e) | MethodOutSelect(e,_) | SeqLength(e) -> __Compose (e :: []) | SelectExpr(e1, e2) | BinaryExpr(_,_,e1,e2) -> __Compose (e1 :: e2 :: []) | IteExpr(e1,e2,e3) | UpdateExpr(e1,e2,e3) -> __Compose (e1 :: e2 :: e3 :: []) | MethodCall(rcv,_,_,aparams) -> __Compose (rcv :: aparams) | SequenceExpr(exs) | SetExpr(exs) -> __Compose exs let rec DescendExpr2 visitorFunc expr acc = let newAcc = acc |> visitorFunc expr let __Pipe elist = elist |> List.fold (fun a e -> a |> DescendExpr2 visitorFunc e) newAcc match expr with | IntLiteral(_) | BoolLiteral(_) | BoxLiteral(_) | Star | VarLiteral(_) | ObjLiteral(_) | VarDeclExpr(_) | IdLiteral(_) -> newAcc | AssertExpr(e) | AssumeExpr(e) | Dot(e, _) | ForallExpr(_,e) | LCIntervalExpr(e) | OldExpr(e) | UnaryExpr(_,e) | MethodOutSelect(e,_) | SeqLength(e) -> __Pipe (e :: []) | SelectExpr(e1, e2) | BinaryExpr(_,_,e1,e2) -> __Pipe (e1 :: e2 :: []) | IteExpr(e1,e2,e3) | UpdateExpr(e1,e2,e3) -> __Pipe (e1 :: e2 :: e3 :: []) | MethodCall(rcv,_,_,aparams) -> __Pipe (rcv :: aparams) | SequenceExpr(exs) | SetExpr(exs) -> __Pipe exs let rec DescendExpr2BU visitorFunc expr acc = let __Pipe elist = let newAcc = elist |> List.fold (fun a e -> a |> DescendExpr2 visitorFunc e) acc newAcc |> visitorFunc expr match expr with | IntLiteral(_) | BoolLiteral(_) | BoxLiteral(_) | Star | VarLiteral(_) | ObjLiteral(_) | VarDeclExpr(_) | IdLiteral(_) -> __Pipe [] | AssertExpr(e) | AssumeExpr(e) | Dot(e, _) | ForallExpr(_,e) | LCIntervalExpr(e) | OldExpr(e) | UnaryExpr(_,e) | MethodOutSelect(e,_) | SeqLength(e) -> __Pipe (e :: []) | SelectExpr(e1, e2) | BinaryExpr(_,_,e1,e2) -> __Pipe (e1 :: e2 :: []) | IteExpr(e1,e2,e3) | UpdateExpr(e1,e2,e3) -> __Pipe (e1 :: e2 :: e3 :: []) | MethodCall(rcv,_,_,aparams) -> __Pipe (rcv :: aparams) | SequenceExpr(exs) | SetExpr(exs) -> __Pipe exs let PrintGenSym (name: string) = if name.StartsWith("gensym") then name else sprintf "gensym%s" name // ===================== /// Returns TRUE literal // ===================== let TrueLiteral = BoolLiteral(true) // ===================== /// Returns FALSE literal // ===================== let FalseLiteral = BoolLiteral(false) let UnaryNeg sub = match sub with | UnaryExpr("-", s) -> s | _ -> UnaryExpr("-", sub) let UnaryNot sub = match sub with | UnaryExpr("!", s) -> s | BoolLiteral(b) -> BoolLiteral(not b) | BinaryExpr(p,"=",l,r) -> BinaryExpr(p,"!=",l,r) | BinaryExpr(p,"!=",l,r) -> BinaryExpr(p,"=",l,r) | BinaryExpr(p,"in",l,r) -> BinaryExpr(p,"!in",l,r) | BinaryExpr(p,"!in=",l,r) -> BinaryExpr(p,"in",l,r) | BinaryExpr(p,"<",l,r) -> BinaryExpr(p,">=",l,r) | BinaryExpr(p,"<=",l,r) -> BinaryExpr(p,">",l,r) | BinaryExpr(p,">",l,r) -> BinaryExpr(p,"<=",l,r) | BinaryExpr(p,">=",l,r) -> BinaryExpr(p,"<",l,r) | _ -> UnaryExpr("!", sub) // ======================================================================= /// Returns a binary AND of the two given expressions with short-circuiting // ======================================================================= let BinaryAnd (lhs: Expr) (rhs: Expr) = match lhs, rhs with | BoolLiteral(true), _ -> rhs | BoolLiteral(false), _ -> FalseLiteral | _, BoolLiteral(true) -> lhs | _, BoolLiteral(false) -> FalseLiteral | _, _ -> BinaryExpr(30, "&&", lhs, rhs) // ======================================================================= /// Returns a binary OR of the two given expressions with short-circuiting // ======================================================================= let BinaryOr (lhs: Expr) (rhs: Expr) = match lhs, rhs with | BoolLiteral(true), _ -> TrueLiteral | BoolLiteral(false), _ -> rhs | _, BoolLiteral(true) -> TrueLiteral | _, BoolLiteral(false) -> lhs | _, _ -> BinaryExpr(30, "||", lhs, rhs) // =================================================================================== /// Returns a binary IMPLIES of the two given expressions // =================================================================================== let BinaryImplies lhs rhs = match lhs, rhs with | BoolLiteral(false), _ -> TrueLiteral | BoolLiteral(true), _ -> rhs | _, BoolLiteral(true) -> lhs | _, BoolLiteral(false) -> UnaryNot(lhs) | _ -> BinaryExpr(20, "==>", lhs, rhs) // ======================================================= /// Constructors for binary EQ/NEQ of two given expressions // ======================================================= let BinaryNeq lhs rhs = match lhs, rhs with | BoolLiteral(true), x | x, BoolLiteral(true) -> UnaryNot x | BoolLiteral(false), x | x, BoolLiteral(false) -> x | _ -> BinaryExpr(40, "!=", lhs, rhs) let BinaryEq lhs rhs = match lhs, rhs with | BoolLiteral(true), x | x, BoolLiteral(true) -> x | BoolLiteral(false), x | x, BoolLiteral(false) -> UnaryNot x | _ when lhs = rhs -> TrueLiteral | _ -> BinaryExpr(40, "=", lhs, rhs) // ======================================================= /// Constructor for binary GETS // ======================================================= let BinaryGets lhs rhs = Assign(lhs, rhs) let BinaryAdd lhs rhs = BinaryExpr(55, "+", lhs, rhs) let BinarySub lhs rhs = BinaryExpr(55, "-", lhs, rhs) // ======================================================= /// Constructors for binary IN/!IN of two given expressions // ======================================================= let BinaryIn lhs rhs = match lhs, rhs with | _, SequenceExpr(elist) | _, SetExpr(elist) when elist |> List.length = 0 -> FalseLiteral | _, SequenceExpr(elist) | _, SetExpr(elist) when elist |> List.length = 1 -> BinaryEq lhs (elist.[0]) | _ -> BinaryExpr(40, "in", lhs, rhs) let BinaryNotIn lhs rhs = match lhs, rhs with | _, SequenceExpr(elist) | _, SetExpr(elist) when elist |> List.length = 0 -> TrueLiteral | _, SequenceExpr(elist) | _, SetExpr(elist) when elist |> List.length = 1 -> BinaryNeq lhs (elist.[0]) | _ -> BinaryExpr(40, "!in", lhs, rhs) // ========================================== /// Splits "expr" into a list of its conjuncts // ========================================== let rec SplitIntoConjunts expr = match expr with | BoolLiteral(true) -> [] | BinaryExpr(_,"&&",e0,e1) -> List.concat [SplitIntoConjunts e0 ; SplitIntoConjunts e1] | _ -> [expr] // ====================================== /// Applies "f" to each conjunct of "expr" // ====================================== let rec ForeachConjunct f expr = SplitIntoConjunts expr |> List.fold (fun acc e -> acc + (f e)) "" // ======================================= /// Converts a given constant to expression // ======================================= let rec Const2Expr c = match c with | IntConst(n) -> IntLiteral(n) | BoolConst(b) -> BoolLiteral(b) | BoxConst(id) -> BoxLiteral(id) | SeqConst(clist) -> let expList = clist |> List.fold (fun acc c -> Const2Expr c :: acc) [] |> List.rev SequenceExpr(expList) | SetConst(cset) -> let expSet = cset |> Set.fold (fun acc c -> Set.add (Const2Expr c) acc) Set.empty SetExpr(Set.toList expSet) | VarConst(id) -> VarLiteral(id) | ThisConst(_,_) -> ObjLiteral("this") | NewObj(name,_) -> ObjLiteral(PrintGenSym name) | NullConst -> ObjLiteral("null") | Unresolved(id) -> BoxLiteral(id) // failwithf "don't want to convert Unresolved(%s) to expr" name // | _ -> failwithf "not implemented or not supported: %O" c let rec Expr2Const e = match e with | IntLiteral(n) -> IntConst(n) | BoolLiteral(b) -> BoolConst(b) | BoxLiteral(id) -> BoxConst(id) | ObjLiteral("this") -> ThisConst("this",None) | ObjLiteral("null") -> NullConst | ObjLiteral(name) -> NewObj(name, None) | IdLiteral(id) -> Unresolved(id) | VarLiteral(id) -> VarConst(id) | SequenceExpr(elist) -> SeqConst(elist |> List.map Expr2Const) | SetExpr(elist) -> SetConst(elist |> List.map Expr2Const |> Set.ofList) | _ -> failwithf "Not a constant: %O" e let rec Expr2ConstStrict e = match e with | IntLiteral(n) -> IntConst(n) | BoolLiteral(b) -> BoolConst(b) | BoxLiteral(id) -> BoxConst(id) | ObjLiteral("this") -> ThisConst("this",None) | ObjLiteral("null") -> NullConst | ObjLiteral(name) -> NewObj(name, None) | SequenceExpr(elist) -> SeqConst(elist |> List.map Expr2ConstStrict) | SetExpr(elist) -> SetConst(elist |> List.map Expr2ConstStrict |> Set.ofList) | _ -> failwithf "Not a constant: %O" e let TryExpr2Const e = try Some(Expr2Const e) with | ex -> None let IsConstExpr e = try Expr2Const e |> ignore true with | _ -> false /////// let GetMethodPre mthd = match mthd with | Method(_,_,pre,_,_) -> pre | _ -> failwith ("not a method" + mthd.ToString()) let GetMethodPrePost mthd = let __FilterOutAssumes e = e |> SplitIntoConjunts |> List.filter (function AssumeExpr(_) -> false | _ -> true) |> List.fold BinaryAnd TrueLiteral match mthd with | Method(_,_,pre,post,_) -> __FilterOutAssumes pre,post | _ -> failwith ("not a method: " + mthd.ToString()) let GetMethodGhostPrecondition mthd = match mthd with | Method(_,_,pre,_,_) -> pre |> SplitIntoConjunts |> List.choose (function AssumeExpr(e) -> Some(e) | _ -> None) |> List.fold BinaryAnd TrueLiteral | _ -> failwith ("not a method: " + mthd.ToString()) // ============================================================== /// Returns all invariants of a component as a list of expressions // ============================================================== let GetInvariantsAsList comp = match comp with | Component(Interface(_,_,members), DataModel(_,_,_,_,inv), _) -> let clsInvs = members |> List.choose (function Invariant(exprList) -> Some(exprList) | _ -> None) |> List.concat List.append (SplitIntoConjunts inv) clsInvs | _ -> failwithf "unexpected kind of component: %O" comp /// Replaces all Old nodes with IdLiteral with name = "old_" + let RewriteOldExpr expr = expr |> RewriteBU (fun e -> match e with | OldExpr(IdLiteral(name)) -> Some(IdLiteral(RenameToOld name)) | _ -> None) let MakeOldVar var = match var with | Var(name, ty, _) -> Var(name, ty, true) let MakeOldVars varLst = varLst |> List.map MakeOldVar /// renames ALL variables to "old_"+ let MakeOld expr = expr |> RewriteBU (fun e -> match e with | IdLiteral(name) when not (name="this") -> Some(IdLiteral(RenameToOld name)) | Dot(e, name) -> Some(Dot(e, RenameToOld name)) | _ -> None) let BringToPost expr = expr |> RewriteBU (fun e -> match e with | IdLiteral(name) -> Some(IdLiteral(RenameFromOld name)) | Dot(e, name) -> Some(Dot(e, RenameFromOld name)) | _ -> None) //////////////////////// let AddReplaceMethod prog comp newMthd oldMethod = match prog, comp with | Program(clist), Component(Interface(cname, ctypeParams, members), model, code) -> let newMembers = match oldMethod with | None -> members @ [newMthd] | Some(m) -> Utils.ListReplace m newMthd members let newCls = Interface(cname, ctypeParams, newMembers) let newComp = Component(newCls, model, code) let newProg = Program(Utils.ListReplace comp newComp clist) newProg, newComp | _ -> failwithf "Invalid component: %O" comp let UnwrapAssumes e = e |> SplitIntoConjunts |> List.map (function AssumeExpr(e) -> e | x -> x) |> List.fold BinaryAnd TrueLiteral let AddPrecondition m e = match m with | Method(mn, sgn, pre, post, cstr) -> Method(mn, sgn, BinaryAnd pre (AssumeExpr(e |> UnwrapAssumes)), post, cstr) | _ -> failwithf "Not a method: %O" m let SetPrecondition m e = match m with | Method(mn, sgn, pre, post, cstr) -> Method(mn, sgn, AssumeExpr(e |> UnwrapAssumes), post, cstr) | _ -> failwithf "Not a method: %O" m //////////////////// exception EvalFailed of string exception DomainNotInferred let DefaultResolver e fldOpt = match fldOpt with | None -> e | Some(fldName) -> Dot(e, fldName) let DefaultFallbackResolver resolverFunc e = match resolverFunc e with | Some(e') -> e' | None -> e let __CheckEqual e1 e2 = match e1, e2 with | BoolLiteral(b1), BoolLiteral(b2) -> Some(b1 = b2) | IntLiteral(n1), IntLiteral(n2) -> Some(n1 = n2) | ObjLiteral(o1), ObjLiteral(o2) -> Some(o1 = o2) | SetExpr(elist1), SetExpr(elist2) -> Some(Set.ofList elist1 = Set.ofList elist2) | SequenceExpr(elist1), SequenceExpr(elist2) -> Some(elist1 = elist2) | UnaryExpr("-", sub1), sub2 | sub1, UnaryExpr("-", sub2) when sub1 = sub2 -> Some(false) | UnaryExpr("-", sub1), UnaryExpr("-", sub2) when sub1 = sub2 -> Some(true) | UnaryExpr("!", sub1), sub2 | sub1, UnaryExpr("!", sub2) when sub1 = sub2 -> Some(false) | UnaryExpr("!", sub1), UnaryExpr("-", sub2) when sub1 = sub2 -> Some(true) | _ when e1 = e2 -> Some(true) | _ -> None let EvalSym2 fullResolverFunc otherResolverFunc returnFunc ctx expr = let rec __EvalSym resolverFunc returnFunc ctx expr = let expr' = match expr with | IntLiteral(_) -> expr | BoolLiteral(_) -> expr | BoxLiteral(_) -> expr | ObjLiteral(_) -> expr | Star -> expr //TODO: can we do better? | VarDeclExpr(_) -> expr | AssertExpr(e) -> AssertExpr(__EvalSym resolverFunc returnFunc ctx e) | AssumeExpr(e) -> AssumeExpr(__EvalSym resolverFunc returnFunc ctx e) | VarLiteral(id) -> try let _,e = ctx |> List.find (fun (v,e) -> GetVarName v = id) e with | ex -> resolverFunc expr None | IdLiteral(_) -> resolverFunc expr None | Dot(e, str) -> let discr = __EvalSym resolverFunc returnFunc ctx e resolverFunc discr (Some(str)) | SeqLength(e) -> let e' = __EvalSym resolverFunc returnFunc ctx e match e' with | SequenceExpr(elist) -> IntLiteral(List.length elist) | _ -> SeqLength(e') | SequenceExpr(elist) -> let elist' = elist |> List.map (__EvalSym resolverFunc returnFunc ctx) // List.fold (fun acc e -> (__EvalSym resolverFunc returnFunc ctx e) :: acc) [] |> List.rev SequenceExpr(elist') | SetExpr(elist) -> let elist' = elist |> List.map (__EvalSym resolverFunc returnFunc ctx) //List.fold (fun acc e -> Set.add (__EvalSym resolverFunc returnFunc ctx e) acc) Set.empty SetExpr(elist' |> Set.ofList |> Set.toList) | MethodOutSelect(e,name) -> MethodOutSelect(__EvalSym resolverFunc returnFunc ctx e, name) | MethodCall(rcv,cname, mname,aparams) -> let rcv' = __EvalSym resolverFunc returnFunc ctx rcv let aparams' = aparams |> List.fold (fun acc e -> __EvalSym resolverFunc returnFunc ctx e :: acc) [] |> List.rev MethodCall(rcv', cname, mname, aparams') | LCIntervalExpr(_) -> expr | SelectExpr(lst, idx) -> let lst' = __EvalSym resolverFunc returnFunc ctx lst let idx' = __EvalSym resolverFunc returnFunc ctx idx match lst', idx' with | SequenceExpr(elist), IntLiteral(n) -> elist.[n] | SequenceExpr(elist), LCIntervalExpr(startIdx) -> let startIdx' = __EvalSym resolverFunc returnFunc ctx startIdx match startIdx' with | IntLiteral(startIdxInt) -> let rec __Skip n l = if n = 0 then l else __Skip (n-1) (List.tail l) SequenceExpr(__Skip startIdxInt elist) | _ -> SelectExpr(lst', idx') | _ -> SelectExpr(lst', idx') | UpdateExpr(lst,idx,v) -> let lst', idx', v' = __EvalSym resolverFunc returnFunc ctx lst, __EvalSym resolverFunc returnFunc ctx idx, __EvalSym resolverFunc returnFunc ctx v match lst', idx', v' with | SequenceExpr(elist), IntLiteral(n), _ -> SequenceExpr(Utils.ListSet n v' elist) | _ -> UpdateExpr(lst', idx', v') | IteExpr(c, e1, e2) -> let c' = __EvalSym fullResolverFunc returnFunc ctx c match c' with | BoolLiteral(b) -> if b then __EvalSym resolverFunc returnFunc ctx e1 else __EvalSym resolverFunc returnFunc ctx e2 | _ -> IteExpr(c', __EvalSym resolverFunc returnFunc ctx e1, __EvalSym resolverFunc returnFunc ctx e2) | BinaryExpr(p,op,e1,e2) -> let e1' = lazy (__EvalSym resolverFunc returnFunc ctx e1) let e2' = lazy (__EvalSym resolverFunc returnFunc ctx e2) let recomposed = lazy (BinaryExpr(p, op, e1'.Force(), e2'.Force())) match op with | "=" -> let e1'' = e1'.Force() let e2'' = e2'.Force() let eq = __CheckEqual e1'' e2'' match eq with | Some(b) -> BoolLiteral(b) | None -> recomposed.Force() | "!=" -> let e1'' = e1'.Force() let e2'' = e2'.Force() let eq = __CheckEqual e1'' e2'' match eq with | Some(b) -> BoolLiteral(not b) | None -> recomposed.Force() | "<" -> match e1'.Force(), e2'.Force() with | IntLiteral(n1), IntLiteral(n2) -> BoolLiteral(n1 < n2) | _ -> recomposed.Force() | "<=" -> let e1'' = e1'.Force() let e2'' = e2'.Force() let eq = __CheckEqual e1'' e2'' match eq with | Some(true) -> TrueLiteral | _ -> match e1'', e2'' with | IntLiteral(n1), IntLiteral(n2) -> BoolLiteral(n1 <= n2) | _ -> recomposed.Force() | ">" -> match e1'.Force(), e2'.Force() with | IntLiteral(n1), IntLiteral(n2) -> BoolLiteral(n1 > n2) | _ -> recomposed.Force() | ">=" -> let e1'' = e1'.Force() let e2'' = e2'.Force() let eq = __CheckEqual e1'' e2'' match eq with | Some(true) -> TrueLiteral | _ -> match e1'', e2'' with | IntLiteral(n1), IntLiteral(n2) -> BoolLiteral(n1 >= n2) | _ -> recomposed.Force() | ".." -> let e1'' = e1'.Force() let e2'' = e2'.Force() match e1'', e2'' with | IntLiteral(lo), IntLiteral(hi) -> SequenceExpr([lo .. hi] |> List.map (fun n -> IntLiteral(n))) | _ -> recomposed.Force(); | "in" -> match e1'.Force(), e2'.Force() with | _, SetExpr(s) | _, SequenceExpr(s) -> //BoolLiteral(Utils.ListContains (e1'.Force()) s) if Utils.ListContains (e1'.Force()) s then TrueLiteral else try let contains = s |> List.map Expr2ConstStrict |> Utils.ListContains (e1'.Force() |> Expr2ConstStrict) BoolLiteral(contains) with | _ -> recomposed.Force() | _ -> recomposed.Force() | "!in" -> match e1'.Force(), e2'.Force() with | _, SetExpr(s) | _, SequenceExpr(s) -> //BoolLiteral(not (Utils.ListContains (e1'.Force()) s)) if Utils.ListContains (e1'.Force()) s then FalseLiteral else try let contains = s |> List.map Expr2ConstStrict |> Utils.ListContains (e1'.Force() |> Expr2ConstStrict) BoolLiteral(not contains) with | _ -> recomposed.Force() | _ -> recomposed.Force() | "+" -> let e1'' = e1'.Force(); let e2'' = e2'.Force(); match e1'', e2'' with | IntLiteral(n1), IntLiteral(n2) -> IntLiteral(n1 + n2) | SequenceExpr(l1), SequenceExpr(l2) -> SequenceExpr(List.append l1 l2) | SetExpr(s1), SetExpr(s2) -> SetExpr(Set.union (Set.ofList s1) (Set.ofList s2) |> Set.toList) | _ -> recomposed.Force() | "-" -> match e1'.Force(), e2'.Force() with | IntLiteral(n1), IntLiteral(n2) -> IntLiteral(n1 - n2) | SetExpr(s1), SetExpr(s2) -> SetExpr(Set.difference (Set.ofList s1) (Set.ofList s2) |> Set.toList) | _ -> recomposed.Force() | "*" -> match e1'.Force(), e2'.Force() with | IntLiteral(n1), IntLiteral(n2) -> IntLiteral(n1 * n2) | _ -> recomposed.Force() | "div" -> match e1'.Force(), e2'.Force() with | IntLiteral(n1), IntLiteral(n2) -> IntLiteral(n1 / n2) | _ -> recomposed.Force() | "mod" -> match e1'.Force(), e2'.Force() with | IntLiteral(n1), IntLiteral(n2) -> IntLiteral(n1 % n2) | _ -> recomposed.Force() | "&&" -> // shortcircuit match e1'.Force() with | BoolLiteral(false) -> BoolLiteral(false) | _ -> match e1'.Force(), e2'.Force() with | _, BoolLiteral(false) -> BoolLiteral(false) | BoolLiteral(b1), BoolLiteral(b2) -> BoolLiteral(b1 && b2) | _ -> BinaryAnd (e1'.Force()) (e2'.Force()) | "||" -> // shortcircuit match e1'.Force() with | BoolLiteral(true) -> BoolLiteral(true) | _ -> match e1'.Force(), e2'.Force() with | _, BoolLiteral(true) -> BoolLiteral(true) | BoolLiteral(b1), BoolLiteral(b2) -> BoolLiteral(b1 || b2) | _ -> BinaryOr (e1'.Force()) (e2'.Force()) | "==>" -> // shortcircuit match e1'.Force() with | BoolLiteral(false) -> BoolLiteral(true) | _ -> let e1'' = e1'.Force() let e2'' = e2'.Force() BinaryImplies e1'' e2'' | "<==>" -> match e1'.Force(), e2'.Force() with | BoolLiteral(b1), BoolLiteral(b2) -> BoolLiteral(b1 = b2) | x, BoolLiteral(b) | BoolLiteral(b), x -> if b then x else UnaryNot(x) | _ -> recomposed.Force() | _ -> recomposed.Force() | OldExpr(e) -> let e' = __EvalSym resolverFunc returnFunc ctx e let recomposed = OldExpr(e') match e with | IdLiteral(name) -> resolverFunc (IdLiteral(RenameToOld name)) None | _ -> recomposed | UnaryExpr(op, e) -> let e' = __EvalSym resolverFunc returnFunc ctx e let recomposed = UnaryExpr(op, e') match op with | "!" -> match e' with | BoolLiteral(b) -> BoolLiteral(not b) | _ -> recomposed | "-" -> match e' with | IntLiteral(n) -> IntLiteral(-n) | _ -> recomposed | _ -> recomposed | ForallExpr(vars, e) -> let rec __ExhaustVar v restV vDomain = match vDomain with | vv :: restD -> let ctx' = (v,vv) :: ctx let e' = __EvalSym resolverFunc returnFunc ctx' (ForallExpr(restV, e)) let erest = __ExhaustVar v restV restD BinaryAnd e' erest | [] -> BoolLiteral(true) let rec __TraverseVars vars = match vars with | v :: restV -> try let vDom = GetVarDomain resolverFunc returnFunc ctx v e __ExhaustVar v restV vDom with | ex -> ForallExpr([v], __TraverseVars restV) | [] -> __EvalSym resolverFunc returnFunc ctx e (* --- function body starts here --- *) __TraverseVars vars if expr' = FalseLiteral then Logger.Debug "" expr' |> returnFunc and GetVarDomain resolverFunc returnFunc ctx var expr = match expr with | BinaryExpr(_, "==>", lhs, rhs) -> let conjs = SplitIntoConjunts lhs conjs |> List.fold (fun acc e -> match e with | BinaryExpr(_, "in", VarLiteral(vn), rhs) when GetVarName var = vn -> match __EvalSym resolverFunc returnFunc ctx rhs with | SetExpr(elist) | SequenceExpr(elist) -> elist |> List.append acc | x -> raise DomainNotInferred | BinaryExpr(_, op, VarLiteral(vn),oth) | BinaryExpr(_, op, oth, VarLiteral(vn)) when GetVarName var = vn && Set.ofList ["<"; "<="; ">"; ">="] |> Set.contains op -> failwith "Not implemented yet" | _ -> raise DomainNotInferred) [] | _ -> Logger.WarnLine ("unknown pattern for a quantified expression; cannot infer domain of quantified variable \"" + (GetVarName var) + "\"") raise DomainNotInferred (* --- function body starts here --- *) __EvalSym otherResolverFunc returnFunc ctx expr let EvalSym resolverFunc expr = EvalSym2 resolverFunc resolverFunc (fun e -> e) [] expr let EvalSymRet fullResolverFunc resolverFunc returnFunc expr = EvalSym2 fullResolverFunc resolverFunc returnFunc [] expr // ========================================================== /// Desugars a given expression so that all list constructors /// are expanded into explicit assignments to indexed elements // ========================================================== let MyDesugar expr removeOriginal = let rec __Desugar expr = match expr with | IntLiteral(_) | BoolLiteral(_) | BoxLiteral(_) | VarDeclExpr(_) | IdLiteral(_) | VarLiteral(_) | ObjLiteral(_) | Star | Dot(_) | SelectExpr(_) | SeqLength(_) | UpdateExpr(_) | SetExpr(_) | MethodCall(_) | MethodOutSelect(_) | SequenceExpr(_) -> expr // forall v :: v in {a1 a2 ... an} ==> e ~~~> e[v/a1] && e[v/a2] && ... && e[v/an] // forall v :: v in [a1 a2 ... an] ==> e ~~~> e[v/a1] && e[v/a2] && ... && e[v/an] | ForallExpr([Var(vn1,ty1,old1)] as v, (BinaryExpr(_, "==>", BinaryExpr(_, "in", VarLiteral(vn2), rhsCol), sub) as ee)) when vn1 = vn2 -> match rhsCol with | SetExpr(elist) | SequenceExpr(elist) -> elist |> List.fold (fun acc e -> BinaryAnd acc (__Desugar (Substitute (VarLiteral(vn2)) e sub))) TrueLiteral | _ -> ForallExpr(v, __Desugar ee) | ForallExpr(v,e) -> ForallExpr(v, __Desugar e) | LCIntervalExpr(e) -> LCIntervalExpr(__Desugar e) | OldExpr(e) -> OldExpr(__Desugar e) | UnaryExpr(op,e) -> UnaryExpr(op, __Desugar e) | AssertExpr(e) -> AssertExpr(__Desugar e) | AssumeExpr(e) -> AssumeExpr(__Desugar e) | IteExpr(c,e1,e2) -> IteExpr(c, __Desugar e1, __Desugar e2) // lst = [a1 a2 ... an] ~~~> lst = [a1 a2 ... an] && lst[0] = a1 && lst[1] = a2 && ... && lst[n-1] = an && |lst| = n | BinaryExpr(p,op,e1,e2) -> let be = BinaryExpr(p, op, __Desugar e1, __Desugar e2) let fs = if removeOriginal then TrueLiteral else be try match op with | "=" -> match EvalSym DefaultResolver e1, EvalSym DefaultResolver e2 with | SequenceExpr(l1), SequenceExpr(l2) -> let rec __fff lst1 lst2 cnt = match lst1, lst2 with | fs1 :: rest1, fs2 :: rest2 -> BinaryEq l1.[cnt] l2.[cnt] :: __fff rest1 rest2 (cnt+1) | [], [] -> [] | _ -> failwith "Lists are of different sizes" __fff l1 l2 0 |> List.fold (fun acc e -> BinaryAnd acc e) fs | e, SequenceExpr(elist) | SequenceExpr(elist), e -> let rec __fff lst cnt = match lst with | fs :: rest -> BinaryEq (SelectExpr(e, IntLiteral(cnt))) elist.[cnt] :: __fff rest (cnt+1) | [] -> [BinaryEq (SeqLength(e)) (IntLiteral(cnt))] __fff elist 0 |> List.fold (fun acc e -> BinaryAnd acc e) fs | _ -> be | _ -> be with | EvalFailed(_) as ex -> (* printfn "%O" (ex.StackTrace); *) be __Desugar expr let Desugar expr = MyDesugar expr false let DesugarAndRemove expr = MyDesugar expr true let rec DesugarLst exprLst = match exprLst with | expr :: rest -> Desugar expr :: DesugarLst rest | [] -> [] let ChangeThisReceiver receiver expr = let rec __ChangeThis locals expr = match expr with | IntLiteral(_) | BoolLiteral(_) | BoxLiteral(_) | Star | VarDeclExpr(_) | VarLiteral(_) -> expr | ObjLiteral("this") -> receiver | ObjLiteral(_) -> expr | IdLiteral("null") -> failwith "should never happen anymore" //TODO | IdLiteral("this") -> failwith "should never happen anymore" | IdLiteral(id) -> if Set.contains id locals then VarLiteral(id) else __ChangeThis locals (Dot(ObjLiteral("this"), id)) | Dot(e, id) -> Dot(__ChangeThis locals e, id) | AssertExpr(e) -> AssertExpr(__ChangeThis locals e) | AssumeExpr(e) -> AssumeExpr(__ChangeThis locals e) | ForallExpr(vars,e) -> let newLocals = vars |> List.map GetVarName |> Set.ofList |> Set.union locals ForallExpr(vars, __ChangeThis newLocals e) | LCIntervalExpr(e) -> LCIntervalExpr(__ChangeThis locals e) | OldExpr(e) -> OldExpr(__ChangeThis locals e) | UnaryExpr(op,e) -> UnaryExpr(op, __ChangeThis locals e) | SeqLength(e) -> SeqLength(__ChangeThis locals e) | SelectExpr(e1, e2) -> SelectExpr(__ChangeThis locals e1, __ChangeThis locals e2) | BinaryExpr(p,op,e1,e2) -> BinaryExpr(p, op, __ChangeThis locals e1, __ChangeThis locals e2) | IteExpr(e1,e2,e3) -> IteExpr(__ChangeThis locals e1, __ChangeThis locals e2, __ChangeThis locals e3) | UpdateExpr(e1,e2,e3) -> UpdateExpr(__ChangeThis locals e1, __ChangeThis locals e2, __ChangeThis locals e3) | SequenceExpr(exs) -> SequenceExpr(exs |> List.map (__ChangeThis locals)) | SetExpr(exs) -> SetExpr(exs |> List.map (__ChangeThis locals)) | MethodOutSelect(e, name) -> MethodOutSelect(__ChangeThis locals e, name) | MethodCall(rcv,cname, mname,aparams) -> MethodCall(__ChangeThis locals rcv, cname, mname, aparams |> List.map (__ChangeThis locals)) (* --- function body starts here --- *) __ChangeThis Set.empty expr let rec SimplifyExpr expr = let __Simplify expr = match expr with | UnaryExpr("!", sub) -> Some(UnaryNot sub) | BinaryExpr(_, "&&", l, r) -> Some(BinaryAnd l r) | BinaryExpr(_, "||", l, r) -> Some(BinaryOr l r) | BinaryExpr(_, "in", l, r) -> Some(BinaryIn l r) | BinaryExpr(_, "!in", l, r) -> Some(BinaryNotIn l r) | BinaryExpr(_, "==>", l, r) -> Some(BinaryImplies l r) | BinaryExpr(_, "=", l, r) -> Some(BinaryEq l r) | BinaryExpr(_, "!=", l, r) -> Some(BinaryNeq l r) | _ -> None RewriteBU __Simplify expr let rec ExtractTopLevelExpressions stmt = match stmt with | ExprStmt(e) -> [e] | Assign(e1, e2) -> [e1; e2] | Block(slist) -> slist |> List.fold (fun acc s -> acc @ ExtractTopLevelExpressions s) [] let rec PullUpMethodCalls stmt = let stmtList = new System.Collections.Generic.LinkedList<_>() let rec __PullUpMethodCalls expr = let newExpr = RewriteBU (fun expr -> match expr with | MethodOutSelect(_) -> let vname = SymGen.NewSymFake expr let e' = VarLiteral(vname) let var = VarDeclExpr([Var(vname,None,false)], true) let asgn = BinaryGets var expr stmtList.AddLast asgn |> ignore Some(e') | _ -> None ) expr newExpr, (stmtList |> List.ofSeq) stmtList.Clear() match stmt with | ExprStmt(e) -> let e', slist = __PullUpMethodCalls e slist @ [ExprStmt(e')] | Assign(e1, e2) -> let e2', slist = __PullUpMethodCalls e2 slist @ [Assign(e1, e2')] | Block(slist) -> slist |> List.fold (fun acc s -> acc @ PullUpMethodCalls s) [] // ========================================================== /// Very simple for now: /// - if "m" is a constructor, everything is modifiable /// - if the method's post condition contains assignments to fields, everything is modifiable /// - otherwise, all objects are immutable /// /// (TODO: instead it should read the "modifies" clause of a method and figure out what's modifiable from there) // ========================================================== let IsModifiableObj obj (c,m) = let __IsFld name = FindVar c name |> Utils.OptionToBool match m with | Method(name,_,_,_,_) when name.EndsWith("__mod__") -> true | Method(_,_,_,_,true) -> true | Method(_,_,_,post,false) -> DescendExpr2 (fun e acc -> match e with | BinaryExpr(_,"=",IdLiteral(name),r) when __IsFld name -> true | Dot(_,name) when __IsFld name -> true | _ -> acc ) post false | _ -> failwithf "expected a Method but got %O" m