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generic.ml
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open [@warning "-33"] Containers
open Language
open Types
module Id = Id
let dedup cmp vec =
let prev = ref None in
Vector.filter_in_place (fun elt ->
match !prev with
| None -> prev := Some elt; true
| Some last_value ->
if Int.equal (cmp last_value elt) 0
then false
else begin
prev := Some elt;
true
end
) vec
(* let lappend_pair a (b,c) = (a,b,c) *)
type 'a query = 'a Query.t
type ('node, 'data) eclass = {
mutable id: Id.t;
nodes: 'node Vector.vector;
mutable data: 'data;
parents: ('node * Id.t) Vector.vector;
}
type ('node, 'analysis, 'data, 'permission) egraph = {
mutable version: int;
analysis: 'analysis;
uf: Id.store; (* tracks equivalence classes of
class ids *)
class_data:
('node, 'data) eclass Id.Map.t; (* maps classes to the canonical nodes
they contain, and any classes that are
children of these nodes *)
hash_cons: ('node, Id.t) Hashtbl.t; (* maps cannonical nodes to their
equivalence classes *)
pending: ('node * Id.t) Vector.vector;
pending_analysis: ('node * Id.t) Vector.vector;
}
module MakeInt (L: LANGUAGE) (* (A: ANALYSIS) *) = struct
let (.@[]) self fn = fn self [@@inline always]
(* *** Initialization *)
let init analysis = {
version=0;
analysis;
uf=Id.create_store ();
class_data=Id.Map.create 10;
hash_cons=Hashtbl.create 10;
pending=Vector.create ();
pending_analysis=Vector.create ();
}
(* *** Eclasses *)
let get_analysis self = self.analysis
let get_class_data self id =
match Id.Map.find_opt self.class_data id with
| Some data -> data
| None -> failwith @@ Printf.sprintf "attempted to set the data of an unbound class %s " (EClassId.show id)
let remove_class_data self id =
match Id.Map.find_opt self.class_data id with
| Some classes -> Id.Map.remove self.class_data id; Some classes
| None -> None
let set_data self id data =
match Id.Map.find_opt self.class_data id with
| None -> failwith @@ Printf.sprintf "attempted to set the data of an unbound class %s " (EClassId.show id)
| Some class_data -> class_data.data <- data
let get_data self id =
match Id.Map.find_opt self.class_data (Id.find self.uf id) with
| None -> failwith @@ Printf.sprintf "attempted to get the data of an unbound class %s " (EClassId.show id)
| Some class_data -> class_data.data
let canonicalise self node = L.map_children node (Id.find self.uf)
let find self vl = Id.find self.uf vl
(* *** Exports *)
(* **** Export eclasses *)
let eclasses self =
let r = Id.Map.create 10 in
Hashtbl.iter (fun node eid ->
let eid = Id.find self.uf eid in
match Id.Map.find_opt r eid with
| None -> let ls = Vector.of_list [node] in Id.Map.add r eid ls
| Some ls -> Vector.push ls node
) self.hash_cons;
r
let class_equal self cls1 cls2 =
Id.equal self.uf cls1 cls2
end
module MakePrinter (L: LANGUAGE) (A: ANALYSIS) = struct
open (MakeInt(L))
(* **** Export as dot *)
let to_dot self =
let eclasses = eclasses self in
let pp_node_by_id fmt id =
let pp_node_by_id fmt id =
let id = self.@[find] id in
begin
let vls = Id.Map.find_opt eclasses id |> Option.get_lazy Vector.create in
let open Format in
pp_print_string fmt "{";
pp_open_hovbox fmt 1;
Vector.pp
~pp_sep:(fun fmt () -> pp_print_string fmt ","; pp_print_space fmt ())
(L.pp_shape EClassId.pp) fmt vls;
pp_close_box fmt ();
pp_print_string fmt "}"
end in
pp_node_by_id fmt id in
let stmt_list =
let rev_map =
Hashtbl.to_seq self.hash_cons
|> Seq.map Pair.swap
|> Id.Map.of_seq in
let to_label id =
let to_str id =
match Id.Map.find_opt rev_map id with
| None -> Format.to_string EClassId.pp id
| Some node -> Format.to_string (L.pp_shape pp_node_by_id) node in
to_str id in
let to_id id =
Odot.Double_quoted_id (to_label id) in
let to_node_id node =
Odot.Double_quoted_id (Format.to_string (L.pp_shape pp_node_by_id) node) in
let to_subgraph_id id =
Odot.Simple_id (Printf.sprintf "cluster_%d" (Id.repr id)) in
let eclass_label eclass =
let eclass_txt = Format.to_string EClassId.pp eclass in
let data = get_data self eclass |> A.show_data in
eclass_txt ^ " = " ^ data in
let sub_graphs =
(fun f -> Fun.flip Id.Map.iter eclasses (Fun.curry f))
|> Iter.map (fun (eclass, (enodes: (Id.t L.shape, _) Vector.t)) ->
let nodes =
Vector.to_iter enodes
|> Iter.map (fun (node: Id.t L.shape) ->
let node_id = to_node_id node in
let attrs = Odot.[Simple_id "label",
Some (Double_quoted_id
(Format.to_string (L.pp_shape pp_node_by_id) node))] in
Odot.Stmt_node ((node_id, None), attrs))
|> Iter.to_list in
Odot.(Stmt_subgraph {
sub_id= Some (to_subgraph_id eclass);
sub_stmt_list=
Stmt_attr (
Attr_graph [
(Simple_id "label", Some (Double_quoted_id (eclass_label eclass)))
]) :: nodes;
})
)
|> Iter.to_list in
let edges =
(fun f -> Fun.flip Id.Map.iter eclasses (Fun.curry f))
|> Iter.flat_map (fun (_eclass, enodes) ->
Vector.to_iter enodes
|> Iter.flat_map (fun node ->
let label = to_node_id node in
Iter.of_list (L.children node)
|> Iter.map (fun child ->
let child_label = to_id child in
Odot.(Stmt_edge (
Edge_node_id (label, None),
[Edge_node_id (child_label, None)],
[]
))
)
)
)
|> Iter.to_list in
(List.append sub_graphs edges) in
Odot.{
strict=true;
kind=Digraph;
id=None;
stmt_list;
}
(* **** Print as dot *)
let pp_dot fmt st =
Format.pp_print_string fmt (Odot.string_of_graph (to_dot st))
end
module MakeExtractor (L: LANGUAGE) (E: COST with type node := Id.t L.shape) = struct
open (MakeInt(L))
let extract eg =
let eclasses = eg.@[eclasses] in
let cost_map = Id.Map.create 10 in
let node_total_cost node =
let has_cost id = Id.Map.mem cost_map (eg.@[find] id) in
if List.for_all has_cost (L.children node)
then let cost_f id = fst @@ Id.Map.find cost_map (eg.@[find] id) in Some (E.cost cost_f node)
else None in
let make_pass enodes =
let cost, node =
Vector.to_iter enodes
|> Iter.map (fun n -> (node_total_cost n, n))
|> Iter.min_exn ~lt:(fun (c1, _) (c2, _) ->
(match c1, c2 with
| None, None -> 0
| Some _, None -> -1
| None, Some _ -> 1
| Some c1, Some c2 -> E.compare c1 c2) = -1) in
Option.map (fun cost -> (cost, node)) cost in
let find_costs () =
let any_changes = ref true in
while !any_changes do
any_changes := false;
Fun.flip Id.Map.iter eclasses (fun eclass enodes ->
let pass = make_pass enodes in
match Id.Map.find_opt cost_map eclass, pass with
| None, Some nw -> Id.Map.replace cost_map eclass nw; any_changes := true
| Some ((cold, _)), Some ((cnew, _) as nw)
when E.compare cnew cold = -1 ->
Id.Map.replace cost_map eclass nw; any_changes := true
| _ -> ()
)
done in
let rec extract eid =
let eid = eg.@[find] eid in
let enode = Id.Map.find cost_map eid |> snd in
let head = L.op enode in
let children = L.children enode in
L.Mk (L.make head @@ List.map extract children) in
find_costs ();
fun result -> extract result
end
(* ** Graph *)
module MakeOps
(L: LANGUAGE)
(A: ANALYSIS)
(AM: sig
val make: (Id.t L.shape, A.t, A.data, ro) egraph -> Id.t L.shape -> A.data
val merge: A.t -> A.data -> A.data -> A.data * (bool * bool)
val modify: (Id.t L.shape, A.t, A.data, rw) egraph -> Id.t -> unit
end) =
struct
open (MakeInt (L))
module Rule = struct
type rule_output =
| Constant of L.op Query.t
| Conditional of
L.op Query.t *
((Id.t L.shape, A.t, A.data, rw) egraph -> eclass_id -> eclass_id StringMap.t -> bool)
| Dynamic of
((Id.t L.shape, A.t, A.data, rw) egraph -> eclass_id -> eclass_id StringMap.t -> L.op Query.t option)
type t = L.op Query.t * rule_output
let make_constant ~from ~into = (from, Constant into)
let make_conditional ~from ~into ~cond = (from, Conditional (into, cond))
let make_dynamic ~from ~generator = (from, Dynamic generator)
end
let new_class self =
let id = Id.make self.uf () in
Id.Map.add self.class_data id {id; nodes=Vector.create (); data=A.default; parents=Vector.create ()};
id
let freeze (graph: (_, _, _, rw) egraph) = (graph:> (_, _, _, ro) egraph)
(* Adds a node into the egraph, assuming that the cannonical version
of the node is up to date in the hash cons or
*)
let add_enode self (node: Id.t L.shape) =
let node = self.@[canonicalise] node in
let id = match Hashtbl.find_opt self.hash_cons node with
| None ->
self.version <- self.version + 1;
let id = Id.make self.uf () in
let cls = {
id;
nodes=Vector.of_list [node];
data = AM.make (freeze self) node;
parents=Vector.create ()
} in
List.iter (fun child ->
let tup = (node, id) in
Vector.push ((self.@[get_class_data] child).parents) tup
) (L.children node);
Vector.push self.pending (node,id);
Id.Map.add self.class_data id cls;
Hashtbl.add self.hash_cons node id;
AM.modify self id;
id
| Some id -> self.@[find] id in
Id.find self.uf id
let rec add_node self (L.Mk op: L.t) : Id.t =
add_enode self @@ L.map_children op (add_node self)
let rec subst self pat env =
match pat with
| Query.V id -> StringMap.find id env
| Q (sym, args) ->
let enode = L.make sym (List.map (fun arg -> self.@[subst] arg env) args) in
self.@[add_enode] enode
let merge self id1 id2 =
let (+=) va vb = Vector.append va vb in
let id1 = Id.find self.uf id1 in
let id2 = Id.find self.uf id2 in
if Id.eq_id id1 id2 then ()
else begin
self.version <- self.version + 1;
(* cls2 has fewer children *)
let id1, id2 =
if Vector.length (self.@[get_class_data] id1).parents < Vector.length (self.@[get_class_data] id2).parents
then (id2, id1)
else (id1, id2) in
(* make cls1 the new root *)
assert (Id.eq_id id1 (Id.union self.uf id1 id2));
let cls2 = self.@[remove_class_data] id2
|> Option.get_exn_or "Invariant violation" in
let cls1 = self.@[get_class_data] id1 in
assert (Id.eq_id id1 cls1.id);
self.pending += cls2.parents;
let (did_update_cls1, did_update_cls2) =
let data, res = (AM.merge self.analysis cls1.data cls2.data) in
cls1.data <- data;
res in
if did_update_cls1 then self.pending_analysis += cls1.parents;
if did_update_cls2 then self.pending_analysis += cls2.parents;
cls1.nodes += cls2.nodes;
cls1.parents += cls2.parents;
AM.modify self id1
end
let rebuild_classes self =
Id.Map.to_seq_values self.class_data |> Seq.iter (fun cls ->
Vector.map_in_place (fun node -> self.@[canonicalise] node) cls.nodes;
Vector.sort' (L.compare_shape EClassId.compare) cls.nodes;
dedup (L.compare_shape EClassId.compare) cls.nodes
)
let process_unions self =
(* let init_size = Hashtbl.length self.hash_cons in *)
while not @@ Vector.is_empty self.pending do
let rec update_hash_cons () =
match Vector.pop self.pending with
| None -> ()
| Some (node,cls) ->
let old_node = node in
let node = self.@[canonicalise] node in
if not @@ ((L.compare_shape EClassId.compare old_node node) = 0) then
Hashtbl.remove self.hash_cons old_node;
begin match (Hashtbl.find_opt self.hash_cons node) with
| None -> Hashtbl.add self.hash_cons node cls
| Some memo_cls -> self.@[merge] memo_cls cls
end;
update_hash_cons () in
update_hash_cons ();
let rec update_analysis () =
match Vector.pop self.pending_analysis with
| None -> ()
| Some (node, class_id) ->
let class_id = self.@[find] class_id in
let node_data = AM.make (freeze self) node in
let cls = self.@[get_class_data] class_id in
assert (Id.eq_id cls.id class_id);
let (did_update_left, _did_update_right) =
let data,res = AM.merge self.analysis cls.data node_data in
cls.data <- data;
res in
if did_update_left then begin
Vector.append self.pending_analysis cls.parents;
AM.modify self class_id
end;
update_analysis () in
update_analysis ()
done
(* let _final_size = Hashtbl.length self.hash_cons in
* print_endline @@ Printf.sprintf "after rebuilding size of nodes is %d => %d" init_size final_size *)
let rebuild (self: (Id.t L.shape, 'b, 'c, rw) egraph) =
process_unions self;
rebuild_classes self
(* ** Matching *)
let ematch eg (classes: (Id.t L.shape, 'a) Vector.t Id.Map.t) pattern =
let concat_map f l = Iter.concat (Iter.map f l) in
let rec enode_matches p enode env =
match[@warning "-8"] p with
| Query.Q (f, _) when not @@ L.equal_op f (L.op enode) ->
Iter.empty
| Q (_, args) ->
(fun f -> List.iter2 (Fun.curry f) args (L.children enode))
|> Iter.fold (fun envs (qvar, trm) ->
concat_map (fun env' -> match_in qvar trm env') envs) (Iter.singleton env)
and match_in p eid env =
let eid = find eg eid in
match p with
| V id -> begin
match StringMap.find_opt id env with
| None -> Iter.singleton (StringMap.add id eid env)
| Some eid' when Id.eq_id eid eid' -> Iter.singleton env
| _ -> Iter.empty
end
| p ->
match Id.Map.find_opt classes eid with
| Some v -> Vector.to_iter v |> concat_map (fun enode -> enode_matches p enode env)
| None -> Iter.empty
in
(fun f -> Id.Map.iter (Fun.curry f) classes)
|> concat_map (fun (eid, _) ->
Iter.map (fun s -> (eid, s)) (match_in pattern eid StringMap.empty))
let find_matches eg =
let eclasses = eclasses eg in
fun rule -> ematch eg eclasses rule
let iter_children self cls =
(* let old_cls = cls in *)
let cls = (self.@[find] cls) in
Id.Map.find_opt (eclasses self) cls |> Option.map Vector.to_iter |> Option.get_or ~default:Iter.empty
module BuildRunner (S : SCHEDULER with type 'a egraph := (Id.t L.shape, A.t, A.data, rw) egraph
and type rule := Rule.t) = struct
(* ** Rewriting System *)
let apply_rules scheduler iteration (eg: (Id.t L.shape, _, _, _) egraph) (rules : (Rule.t * S.data) array) =
let find_matches = find_matches eg in
let for_each_match =
Iter.of_array rules
|> Iter.flat_map (fun ((from_rule, to_rule), meta_data) ->
S.guard_rule_usage eg scheduler meta_data iteration (fun () -> find_matches from_rule)
|> Iter.map (fun (eid,env) -> (to_rule, eid, env))
) in
for_each_match begin fun (to_rule, eid, env) ->
match to_rule with
| Rule.Constant to_rule ->
let new_eid = subst eg to_rule env in
merge eg eid new_eid
| Conditional (to_rule, cond) ->
if cond eg eid env then
let new_eid = subst eg to_rule env in
merge eg eid new_eid
else ()
| Dynamic cond ->
match cond eg eid env with
| None -> ()
| Some to_rule ->
let new_eid = subst eg to_rule env in
merge eg eid new_eid
end;
rebuild eg
let run_until_saturation ?scheduler ?(node_limit=`Bounded 10_000) ?(fuel=`Bounded 30) ?until eg rules =
let scheduler = match scheduler with None -> S.default () | Some scheduler -> scheduler in
let rules = Iter.of_list rules
|> Iter.map (fun rule -> (rule, S.create_rule_metadata scheduler rule))
|> Iter.to_array in
let rule_data () = Array.to_iter rules |> Iter.map snd in
match fuel, node_limit, until with
| `Unbounded, `Unbounded, None ->
let rec loop last_version ind =
apply_rules scheduler ind eg rules;
if not @@ Int.equal eg.version last_version
then loop eg.version (ind + 1)
else if S.should_stop scheduler ind (rule_data ()) then () else loop eg.version (ind + 1) in
loop eg.version 0; true
| `Unbounded, `Unbounded, Some pred ->
let rec loop last_version ind =
apply_rules scheduler ind eg rules;
if not @@ Int.equal eg.version last_version
then if pred eg then false else loop eg.version (ind + 1)
else if S.should_stop scheduler ind (rule_data ()) then true else loop eg.version (ind + 1) in
loop eg.version 0
| `Unbounded, `Bounded node_limit, None ->
let rec loop last_version ind =
apply_rules scheduler ind eg rules;
if not @@ Int.equal eg.version last_version
then if Hashtbl.length eg.hash_cons < node_limit
then loop eg.version (ind + 1)
else false
else if S.should_stop scheduler ind (rule_data ()) then true else loop eg.version (ind + 1) in
loop eg.version 0
| `Unbounded, `Bounded node_limit, Some pred ->
let rec loop last_version ind =
apply_rules scheduler ind eg rules;
if not @@ Int.equal eg.version last_version
then if Hashtbl.length eg.hash_cons < node_limit
then if pred eg then false else loop eg.version (ind + 1)
else false
else if S.should_stop scheduler ind (rule_data ()) then true else loop eg.version (ind + 1) in
loop eg.version 0
| `Bounded fuel, `Unbounded, None ->
let rec loop last_version ind =
apply_rules scheduler ind eg rules;
if not @@ Int.equal eg.version last_version
then if fuel > ind
then loop eg.version (ind + 1)
else false
else if S.should_stop scheduler ind (rule_data ()) then true else loop eg.version (ind + 1) in
loop eg.version 0
| `Bounded fuel, `Unbounded, Some pred ->
let rec loop last_version ind =
apply_rules scheduler ind eg rules;
if not @@ Int.equal eg.version last_version
then if fuel > ind
then if pred eg then false else loop eg.version (ind + 1)
else false
else if S.should_stop scheduler ind (rule_data ()) then true else loop eg.version (ind + 1) in
loop eg.version 0
| `Bounded fuel, `Bounded node_limit, None ->
let rec loop last_version ind =
apply_rules scheduler ind eg rules;
if not @@ Int.equal eg.version last_version
then if fuel > ind && Hashtbl.length eg.hash_cons < node_limit
then loop eg.version (ind + 1)
else false
else if S.should_stop scheduler ind (rule_data ()) then true else loop eg.version (ind + 1) in
loop eg.version 0
| `Bounded fuel, `Bounded node_limit, Some pred ->
let rec loop last_version ind =
apply_rules scheduler ind eg rules;
if not @@ Int.equal eg.version last_version
then if fuel > ind && Hashtbl.length eg.hash_cons < node_limit
then if pred eg then false else loop eg.version (ind + 1)
else false
else if S.should_stop scheduler ind (rule_data ()) then true else loop eg.version (ind + 1) in
loop eg.version 0
end
include (BuildRunner (Scheduler.Backoff))
let apply_rules (eg: (Id.t L.shape, _, _, _) egraph) (rules : Rule.t list) =
let find_matches = find_matches eg in
let for_each_match =
Iter.of_list rules
|> Iter.flat_map
(fun (from_rule, to_rule) ->
find_matches from_rule
|> Iter.map (fun (eid,env) -> (to_rule, eid, env))
) in
for_each_match begin fun (to_rule, eid, env) ->
match to_rule with
| Rule.Constant to_rule ->
let new_eid = subst eg to_rule env in
merge eg eid new_eid
| Conditional (to_rule, cond) ->
if cond eg eid env then
let new_eid = subst eg to_rule env in
merge eg eid new_eid
else ()
| Dynamic cond ->
match cond eg eid env with
| None -> ()
| Some to_rule ->
let new_eid = subst eg to_rule env in
merge eg eid new_eid
end;
rebuild eg
end
module Make
(L: LANGUAGE)
(A: ANALYSIS)
(MakeAnalysisOps: functor
(S: GRAPH_API
with type 'p t = (Id.t L.shape, A.t, A.data, 'p) egraph
and type analysis := A.t
and type data := A.data
and type 'a shape := 'a L.shape
and type node := L.t) -> sig
val make: (Id.t L.shape, A.t, A.data, ro) egraph -> Id.t L.shape -> A.data
val merge: A.t -> A.data -> A.data -> A.data * (bool * bool)
val modify: (Id.t L.shape, A.t, A.data, rw) egraph -> Id.t -> unit
end)
= struct
module rec EGraph : sig
type 'p t = (Id.t L.shape, A.t, A.data, 'p) egraph
module Rule: sig
type t
val make_constant : from:L.op query -> into:L.op query -> t
val make_conditional :
from:L.op query ->
into:L.op query ->
cond:((Id.t L.shape, A.t, A.data, rw) egraph -> eclass_id -> eclass_id StringMap.t -> bool) ->
t
val make_dynamic :
from:L.op query ->
generator:((Id.t L.shape, A.t, A.data, rw) egraph ->
eclass_id -> eclass_id StringMap.t -> L.op query option) ->
t
end
val freeze : rw t -> ro t
val init : A.t -> 'p t
val class_equal: ro t -> eclass_id -> eclass_id -> bool
val new_class : rw t -> eclass_id
val set_data : rw t -> eclass_id -> A.data -> unit
val get_data : _ t -> eclass_id -> A.data
val get_analysis : rw t -> A.t
val canonicalise : rw t -> Id.t L.shape -> Id.t L.shape
val find : ro t -> eclass_id -> eclass_id
(* val append_to_worklist : rw t -> eclass_id -> unit *)
val eclasses: rw t -> (Id.t L.shape, Vector.rw) Vector.t Id.Map.t
(* val pp : Format.formatter -> (Id.t L.shape, 'a, A.data, _) egraph -> unit *)
val to_dot : (Id.t L.shape, A.t, A.data, _) egraph -> Odot.graph
val pp_dot : Format.formatter -> (Id.t L.shape, A.t, A.data, _) egraph -> unit
val add_node : rw t -> L.t -> eclass_id
val merge : rw t -> eclass_id -> eclass_id -> unit
val iter_children : ro t -> eclass_id -> Id.t L.shape Iter.t
val rebuild : rw t -> unit
val find_matches : ro t -> L.op query -> (eclass_id * eclass_id StringMap.t) Iter.t
val apply_rules : (Id.t L.shape, A.t, A.data, rw) egraph -> Rule.t list -> unit
val run_until_saturation:
?scheduler:Scheduler.Backoff.t ->
?node_limit:[`Bounded of int | `Unbounded] ->
?fuel:[`Bounded of int | `Unbounded] ->
?until:((Id.t L.shape, A.t, A.data, rw) egraph -> bool) -> (Id.t L.shape, A.t, A.data, rw) egraph -> Rule.t list -> bool
module BuildRunner (S : SCHEDULER
with type 'a egraph := (Id.t L.shape, A.t, A.data, rw) egraph
and type rule := Rule.t) :
sig
val apply_rules :
S.t ->
int ->
(Id.t L.shape, A.t, A.data, rw) egraph ->
(Rule.t * S.data) array -> unit
val run_until_saturation :
?scheduler:S.t ->
?node_limit:[`Bounded of int | `Unbounded] ->
?fuel:[`Bounded of int | `Unbounded] ->
?until:((Id.t L.shape, A.t, A.data, rw) egraph -> bool) ->
(Id.t L.shape, A.t, A.data, rw) egraph -> Rule.t list -> bool
end
end
= struct
let _unsafe = 10
type 'p t = (Id.t L.shape, A.t, A.data, 'p) egraph
include (MakeInt (L))
include (MakePrinter (L) (A))
include (MakeOps (L) (A) (Analysis))
end
and Analysis : sig
val make: (Id.t L.shape, A.t, A.data, ro) egraph -> Id.t L.shape -> A.data
val merge: A.t -> A.data -> A.data -> A.data * (bool * bool)
val modify: (Id.t L.shape, A.t, A.data, rw) egraph -> Id.t -> unit
end = MakeAnalysisOps (EGraph)
include EGraph
end