(******************************************************************************) (* *) (* Menhir *) (* *) (* François Pottier, Inria Paris *) (* Yann Régis-Gianas, PPS, Université Paris Diderot *) (* *) (* Copyright Inria. All rights reserved. This file is distributed under the *) (* terms of the GNU General Public License version 2, as described in the *) (* file LICENSE. *) (* *) (******************************************************************************) (* This module discovers information about the shape and content of the stack in each of the automaton's states. *) open Grammar module C = Conflict (* artificial dependency; ensures that [Conflict] runs first *) (* ------------------------------------------------------------------------ *) (* Compute a lower bound on the height of the stack at every state. At the same time, compute which symbols are held in this stack prefix. *) (* In order to compute (a lower bound on) the height of the stack at a state [s], we examine the LR(0) items that compose [s]. For each item, if the bullet is at position [pos], then we can be assured that the height of the stack is at least [pos]. Thus, we compute the maximum of [pos] over all items (of which there is at least one). *) (* The set of items that we use is not closed, but this does not matter; the items that would be added by the closure would not add any information regarding the height of the stack, since the bullet is at position 0 in these items. *) (* Instead of computing just the stack height, we compute, in the same manner, which symbols are on the stack at a state [s]. This is an array of symbols whose length is the height of the stack at [s]. By convention, the top of the stack is the end of the array. *) (* We first compute and tabulate this information at the level of the LR(0) automaton. *) let stack_symbols : Lr0.node -> Symbol.t array = let dummy = Array.make 0 (Symbol.T Terminal.sharp) in Misc.tabulate Lr0.n (fun node -> Item.Set.fold (fun item accu -> let _prod, _nt, rhs, pos, _length = Item.def item in if pos > Array.length accu then Array.sub rhs 0 pos else accu ) (Lr0.items node) dummy ) (* Then, it is easy to extend it to the LR(1) automaton. *) let stack_symbols (node : Lr1.node) : Symbol.t array = stack_symbols (Lr0.core (Lr1.state node)) let stack_height (node : Lr1.node) : int = Array.length (stack_symbols node) (* ------------------------------------------------------------------------ *) (* Above, we have computed a prefix of the stack at every state. We have computed the length of this prefix and the symbols that are held in this prefix of the stack. Now, compute which states may be held in this prefix. *) (* In order to compute this information, we perform an analysis of the automaton, via a least fixed fixed point computation. *) (* It is worth noting that it would be possible to use an analysis based on a least fixed point computation to discover at the same time the length of the stack prefix, the symbols that it contains, and the states that it may contain. This alternate approach, which was used until 2012/08/25, would lead us to discovering a richer invariant, that is, potentially longer prefixes. This extra information, however, was useless; computing it was a waste of time. Hence, as of 2012/08/25, the height of the stack prefix and the symbols that it contains are predicted (see above), and the least fixed computation is used only to populate these prefixes of predictable length with state information. *) (* By the way, this least fixed point analysis remains the most costly computation throughout this module. *) (* Vectors of sets of states. *) module StateVector = struct type property = Lr1.NodeSet.t list let empty = [] let rec equal v1 v2 = match v1, v2 with | [], [] -> true | states1 :: v1, states2 :: v2 -> Lr1.NodeSet.equal states1 states2 && equal v1 v2 | _, _ -> (* Because all heights are known ahead of time, we are able to (and careful to) compare only vectors of equal length. *) assert false let rec join v1 v2 = match v1, v2 with | [], [] -> [] | states1 :: v1, states2 :: v2 -> Lr1.NodeSet.union states1 states2 :: join v1 v2 | _, _ -> (* Because all heights are known ahead of time, we are able to (and careful to) compare only vectors of equal length. *) assert false let push v x = x :: v let truncate = MenhirLib.General.take end (* In order to perform the fixed point computation, we must extend our type of vectors with a bottom element. This element will not appear in the least fixed point, provided every state of the automaton is reachable. *) module StateLattice = struct type property = | Bottom | NonBottom of StateVector.property let bottom = Bottom let empty = NonBottom StateVector.empty let equal v1 v2 = match v1, v2 with | Bottom, Bottom -> true | NonBottom v1, NonBottom v2 -> StateVector.equal v1 v2 | _, _ -> false let join v1 v2 = match v1, v2 with | Bottom, v | v, Bottom -> v | NonBottom v1, NonBottom v2 -> NonBottom (StateVector.join v1 v2) let push v x = match v with | Bottom -> Bottom | NonBottom v -> NonBottom (StateVector.push v x) let truncate h v = match v with | Bottom -> Bottom | NonBottom v -> NonBottom (StateVector.truncate h v) let is_maximal _ = false end open StateLattice (* Define the fixed point. *) let stack_states : Lr1.node -> property = let module F = Fix.Make (Maps.PersistentMapsToImperativeMaps(Lr1.NodeMap)) (StateLattice) in F.lfp (fun node (get : Lr1.node -> property) -> (* We use the fact that a state has incoming transitions if and only if it is not a start state. *) match Lr1.incoming_symbol node with | None -> assert (Lr1.predecessors node = []); assert (stack_height node = 0); (* If [node] is a start state, then the stack at [node] may be (in fact, must be) the empty stack. *) empty | Some _symbol -> (* If [node] is not a start state, then include the contribution of every incoming transition. We compute a join over all predecessors. The contribution of one predecessor is the abstract value found at this predecessor, extended with a new cell for this transition, and truncated to the stack height at [node], so as to avoid obtaining a vector that is longer than expected/necessary. *) let height = stack_height node in List.fold_left (fun v predecessor -> join v (truncate height (push (get predecessor) (Lr1.NodeSet.singleton predecessor)) ) ) bottom (Lr1.predecessors node) ) (* If every state is reachable, then the least fixed point must be non-bottom everywhere, so we may view it as a function that produces a vector of sets of states. *) let stack_states (node : Lr1.node) : StateVector.property = match stack_states node with | Bottom -> (* apparently this node is unreachable *) assert false | NonBottom v -> v (* ------------------------------------------------------------------------ *) (* From the above information, deduce, for each production, the states that may appear in the stack when this production is reduced. *) (* We are careful to produce a vector of states whose length is exactly that of the production [prod]. *) let production_states : Production.index -> StateLattice.property = Production.tabulate (fun prod -> let nodes = Lr1.production_where prod in let height = Production.length prod in Lr1.NodeSet.fold (fun node accu -> join accu (truncate height (NonBottom (stack_states node)) ) ) nodes bottom ) (* ------------------------------------------------------------------------ *) (* We now determine which states must be represented, that is, explicitly pushed onto the stack. For simplicity, a state is either always represented or never represented. More fine-grained strategies, where a single state is sometimes pushed onto the stack and sometimes not pushed, depending on which outgoing transition is being taken, are conceivable, but quite tricky, and probably not worth the trouble. (1) If two states are liable to appear within a single stack cell, then one is represented if and only if the other is represented. This ensures that the structure of stacks is known everywhere and that we can propose types for stacks. (2) If a state [s] has an outgoing transition along nonterminal symbol [nt], and if the [goto] table for symbol [nt] has more than one target, then state [s] is represented. (3) If a stack cell contains more than one state and if at least one of these states is able to handle the [error] token, then these states are represented. (4) If the semantic action associated with a production mentions the [\$syntaxerror] keyword, then the state that is being reduced to (that is, the state that initiated the recognition of this production) is represented. (Indeed, it will be passed as an argument to [errorcase].) *) (* Data. *) let rep : bool UnionFind.point array = Array.init Lr1.n (fun _ -> UnionFind.fresh false) (* Getter. *) let represented state = rep.(Lr1.number state) (* Setters. *) let represent state = UnionFind.set (represented state) true let represents states = represent (Lr1.NodeSet.choose states) (* Enforce condition (1) above. *) let share (v : StateVector.property) = List.iter (fun states -> let dummy = UnionFind.fresh false in Lr1.NodeSet.iter (fun state -> UnionFind.union dummy (represented state) ) states ) v let () = Lr1.iter (fun node -> share (stack_states node) ); Production.iter (fun prod -> match production_states prod with | Bottom -> () | NonBottom v -> share v ) (* Enforce condition (2) above. *) let () = Nonterminal.iter (fun nt -> let count = Lr1.targets (fun count _ _ -> count + 1 ) 0 (Symbol.N nt) in if count > 1 then Lr1.targets (fun () sources _ -> List.iter represent sources ) () (Symbol.N nt) ) (* Enforce condition (3) above. *) let handler state = try let _ = SymbolMap.find (Symbol.T Terminal.error) (Lr1.transitions state) in true with Not_found -> try let _ = TerminalMap.lookup Terminal.error (Lr1.reductions state) in true with Not_found -> false let handlers states = Lr1.NodeSet.exists handler states let () = Lr1.iter (fun node -> let v = stack_states node in List.iter (fun states -> if Lr1.NodeSet.cardinal states >= 2 && handlers states then represents states ) v ) (* Enforce condition (4) above. *) let () = Production.iterx (fun prod -> if Action.has_syntaxerror (Production.action prod) then match production_states prod with | Bottom -> () | NonBottom v -> let sites = Lr1.production_where prod in let length = Production.length prod in if length = 0 then Lr1.NodeSet.iter represent sites else let states = List.nth v (length - 1) in represents states ) (* Define accessors. *) let represented state = UnionFind.get (represented state) let representeds states = if Lr1.NodeSet.is_empty states then assert false else represented (Lr1.NodeSet.choose states) (* Statistics. *) let () = Error.logC 1 (fun f -> let count = Lr1.fold (fun count node -> if represented node then count + 1 else count ) 0 in Printf.fprintf f "%d out of %d states are represented.\n" count Lr1.n ) (* ------------------------------------------------------------------------ *) (* Accessors for information about the stack. *) (* We describe a stack prefix as a list of cells, where each cell is a pair of a symbol and a set of states. The top of the stack is the head of the list. *) type cell = Symbol.t * Lr1.NodeSet.t type word = cell list (* This auxiliary function converts a stack-as-an-array (top of stack at the right end) to a stack-as-a-list (top of stack at list head). *) let convert a = let n = Array.length a in let rec loop i accu = if i = n then accu else loop (i + 1) (a.(i) :: accu) in loop 0 [] (* [stack s] describes the stack when the automaton is in state [s]. *) let stack node : word = List.combine (convert (stack_symbols node)) (stack_states node) (* [prodstack prod] describes the stack when production [prod] is about to be reduced. *) let prodstack prod : word = match production_states prod with | Bottom -> (* This production is never reduced. *) assert false | NonBottom v -> List.combine (convert (Production.rhs prod)) v (* [gotostack nt] is the structure of the stack when a shift transition over nonterminal [nt] is about to be taken. It consists of just one cell. *) let gotostack : Nonterminal.t -> word = Nonterminal.tabulate (fun nt -> let sources = Lr1.targets (fun accu sources _ -> List.fold_right Lr1.NodeSet.add sources accu ) Lr1.NodeSet.empty (Symbol.N nt) in [ Symbol.N nt, sources ] ) let fold f accu w = List.fold_right (fun (symbol, states) accu -> f accu (representeds states) symbol states ) w accu let fold_top f accu w = match w with | [] -> accu | (symbol, states) :: _ -> f (representeds states) symbol let print (w : word) = let b = Buffer.create 64 in fold (fun () _represented symbol _states -> Buffer.add_char b ' '; Buffer.add_string b (Symbol.print symbol) ) () w; Buffer.contents b (* ------------------------------------------------------------------------ *) (* Explain how the stack should be deconstructed when an error is found. We sometimes have a choice as too how many stack cells should be popped. Indeed, several cells in the known suffix of the stack may physically hold a state. If neither of these states handles errors, then we could jump to either. (Indeed, if we jump to one that's nearer, it will in turn pop further stack cells and jump to one that's farther.) In the interests of code size, we should pop as few stack cells as possible. So, we jump to the topmost represented state in the known suffix. *) type state = | Represented | UnRepresented of Lr1.node type instruction = | Die | DownTo of word * state let rewind node : instruction = let w = stack node in let rec rewind w = match w with | [] -> (* I believe that every stack description either is definite (that is, ends with [TailEmpty]) or contains at least one represented state. Thus, if we find an empty [w], this means that the stack is definitely empty. *) Die | ((_, states) as cell) :: w -> if representeds states then (* Here is a represented state. We will pop this cell and no more. *) DownTo ([ cell ], Represented) else if handlers states then begin (* Here is an unrepresented state that can handle errors. The cell must hold a singleton set of states, so we know which state to jump to, even though it isn't represented. *) assert (Lr1.NodeSet.cardinal states = 1); let state = Lr1.NodeSet.choose states in DownTo ([ cell ], UnRepresented state) end else (* Here is an unrepresented state that does not handle errors. Pop this cell and look further. *) match rewind w with | Die -> Die | DownTo (w, st) -> DownTo (cell :: w, st) in rewind w (* ------------------------------------------------------------------------ *) (* Machinery for the computation of which symbols must keep track of their start or end positions. *) open Keyword type variable = Symbol.t * where (* WhereStart or WhereEnd *) module M : Fix.IMPERATIVE_MAPS with type key = variable = struct type key = variable type 'data t = { mutable startp: 'data SymbolMap.t; mutable endp: 'data SymbolMap.t; } open SymbolMap let create() = { startp = empty; endp = empty } let clear m = m.startp <- empty; m.endp <- empty let add (sym, where) data m = match where with | WhereStart -> m.startp <- add sym data m.startp | WhereEnd -> m.endp <- add sym data m.endp | WhereSymbolStart -> assert false let find (sym, where) m = match where with | WhereStart -> find sym m.startp | WhereEnd -> find sym m.endp | WhereSymbolStart -> assert false let iter f m = iter (fun sym -> f (sym, WhereStart)) m.startp; iter (fun sym -> f (sym, WhereEnd)) m.endp end (* ------------------------------------------------------------------------ *) (* We now determine which positions must be kept track of. For simplicity, we do this on a per-symbol basis. That is, for each symbol, either we never keep track of position information, or we always do. In fact, we do distinguish start and end positions. This leads to computing two sets of symbols -- those that keep track of their start position and those that keep track of their end position. A symbol on the right-hand side of a production must keep track of its (start or end) position if that position is explicitly requested by a semantic action. Furthermore, if the left-hand symbol of a production must keep track of its start (resp. end) position, then the first (resp. last) symbol of its right-hand side (if there is one) must do so as well. That is, unless the right-hand side is empty. *) (* 2015/11/11. When a production [prod] is reduced, the top stack cell may be consulted for its end position. This implies that this cell must exist and must store an end position! Now, when does this happen? 1- This happens if [prod] is an epsilon production and the left-hand symbol of the production, [nt prod], keeps track of its start or end position. 2- This happens if the semantic action explicitly mentions the keyword [\$endpos(\$0)]. Now, if this happens, what should we do? a- If this happens in a state [s] whose incoming symbol is [sym], then [sym] must keep track of its end position. b- If this happens in an initial state, where the stack may be empty, then the sentinel cell at the bottom of the stack must contain an end position. Point (b) doesn't concern us here, but point (a) does. We must implement the constraint (1) \/ (2) -> (a). Point (b) is taken care of in the code back-end, where, for simplicity, we always create a sentinel cell. *) (* I will say that this is a lot more sophisticated than I would like. The code back-end has been known for its efficiency and I am trying to maintain this property -- in particular, I would like to keep track of no positions at all, if the user doesn't use any position keyword. But I am suffering. *) module S = FixSolver.Make(M)(Boolean) let record_ConVar, record_VarVar, solve = S.create() let () = (* We gather the constraints explained above in two loops. The first loop looks at every (non-start) production [prod]. The second loop looks at every (non-initial) state [s]. *) Production.iterx (fun prod -> let nt, rhs = Production.def prod and ids = Production.identifiers prod and action = Production.action prod in let length = Array.length rhs in if length > 0 then begin (* If [nt] keeps track of its start position, then the first symbol in the right-hand side must do so as well. *) record_VarVar (Symbol.N nt, WhereStart) (rhs.(0), WhereStart); (* If [nt] keeps track of its end position, then the last symbol in the right-hand side must do so as well. *) record_VarVar (Symbol.N nt, WhereEnd) (rhs.(length - 1), WhereEnd) end; KeywordSet.iter (function | SyntaxError -> () | Position (Before, _, _) -> (* Doing nothing here because [\$endpos(\$0)] is dealt with in the second loop. *) () | Position (Left, _, _) -> (* [\$startpos] and [\$endpos] have been expanded away. *) assert false | Position (_, _, FlavorLocation) -> (* [\$loc] and [\$sloc] have been expanded away. *) assert false | Position (RightNamed _, WhereSymbolStart, _) -> (* [\$symbolstartpos(x)] does not exist. *) assert false | Position (RightNamed id, where, _) -> (* If the semantic action mentions [\$startpos(\$i)], then the [i]-th symbol in the right-hand side must keep track of its start position. Similarly for end positions. *) Array.iteri (fun i id' -> if id = id' then record_ConVar true (rhs.(i), where) ) ids ) (Action.keywords action) ); (* end of loop on productions *) Lr1.iterx (fun s -> (* Let [sym] be the incoming symbol of state [s]. *) let sym = Misc.unSome (Lr1.incoming_symbol s) in (* Condition (1) in the long comment above (2015/11/11). If an epsilon production [prod] can be reduced in state [s], if its left-hand side [nt] keeps track of its start or end position, then [sym] must keep track of its end position. *) TerminalMap.iter (fun _ prods -> let prod = Misc.single prods in let nt, rhs = Production.def prod in let length = Array.length rhs in if length = 0 then begin record_VarVar (Symbol.N nt, WhereStart) (sym, WhereEnd); record_VarVar (Symbol.N nt, WhereEnd) (sym, WhereEnd) end ) (Lr1.reductions s); (* Condition (2) in the long comment above (2015/11/11). If a production can be reduced in state [s] and mentions [\$endpos(\$0)], then [sym] must keep track of its end position. *) if Lr1.has_beforeend s then record_ConVar true (sym, WhereEnd) ) let track : variable -> bool = solve() let startp symbol = track (symbol, WhereStart) let endp symbol = track (symbol, WhereEnd) let for_every_symbol (f : Symbol.t -> unit) : unit = Terminal.iter (fun t -> f (Symbol.T t)); Nonterminal.iter (fun nt -> f (Symbol.N nt)) let sum_over_every_symbol (f : Symbol.t -> bool) : int = let c = ref 0 in for_every_symbol (fun sym -> if f sym then c := !c + 1); !c let () = Error.logC 1 (fun f -> Printf.fprintf f "%d out of %d symbols keep track of their start position.\n\ %d out of %d symbols keep track of their end position.\n" (sum_over_every_symbol startp) (Terminal.n + Nonterminal.n) (sum_over_every_symbol endp) (Terminal.n + Nonterminal.n)) (* ------------------------------------------------------------------------- *) (* Miscellaneous. *) let universal symbol = Lr1.fold (fun universal s -> universal && (if represented s then SymbolMap.mem symbol (Lr1.transitions s) else true) ) true (* ------------------------------------------------------------------------ *) (* Discover which states can peek at an error. These are the states where an error token may be on the stream. These are the states that are targets of a reduce action on [error]. *) (* 2012/08/25 I am optimizing this code, whose original version I found had quadratic complexity. The problem is as follows. We can easily iterate over all states to find which states [s] have a reduce action on error. What we must find out, then, is into which state [t] this reduce action takes us. This is not easy to predict, as it depends on the contents of the stack. The original code used an overapproximation, as follows: if the reduction concerns a production whose head symbol is [nt], then all of the states that have an incoming transition labeled [nt] are potential targets. The new version of the code below relies on the same approximation, but uses two successive loops instead of two nested loops. *) let errorpeekers = (* First compute a set of symbols [nt]... *) let nts : SymbolSet.t = Lr1.fold (fun nts node -> try let prods = TerminalMap.lookup Terminal.error (Lr1.reductions node) in let prod = Misc.single prods in let nt = Production.nt prod in SymbolSet.add (Symbol.N nt) nts with Not_found -> nts ) SymbolSet.empty in (* ... then compute the set of all target states of all transitions labeled by some symbol in the set [nt]. *) SymbolSet.fold (fun nt errorpeekers -> Lr1.targets (fun errorpeekers _ target -> Lr1.NodeSet.add target errorpeekers ) errorpeekers nt ) nts Lr1.NodeSet.empty let errorpeeker node = Lr1.NodeSet.mem node errorpeekers (* ------------------------------------------------------------------------ *) let () = Time.tick "Constructing the invariant"