diff --git a/colibri2/theories/array/array.ml b/colibri2/theories/array/array.ml
index a41d097e1529495d84d20876cb1668a9ea58cf20..4a753b9b2df8822a2d2d9176e9e13dc3f7229a34 100644
--- a/colibri2/theories/array/array.ml
+++ b/colibri2/theories/array/array.ml
@@ -30,20 +30,17 @@ let restrict_ext =
let restrict_aup =
Colibri2_stdlib.Flags.Solve.gen_register_flag
~rep:(fun flag -> (flag, "Restrict the ⇑ rule"))
- "res-aup"
+ "Array.res-aup"
let extended_comb =
Colibri2_stdlib.Flags.Solve.gen_register_flag
~rep:(fun flag -> (flag, "Extended combinators"))
- "ext-comb"
+ "Array.ext-comb"
let default_values =
Colibri2_stdlib.Flags.Solve.gen_register_flag
~rep:(fun flag -> (flag, "Default values"))
- "def-values"
-
-let db = Datastructure.Push.create Ground.pp "Array.db"
-(* Use one db per array type? *)
+ "Array.def-values"
let debug = Debug.register_info_flag ~desc:"For array theory" "Array"
let stats = Debug.register_stats_int "Array.rule"
@@ -58,14 +55,18 @@ let ind_ty_var = Expr.Ty.Var.mk "ind_ty"
let val_ty_var = Expr.Ty.Var.mk "val_ty"
let ind_ty = Expr.Ty.of_var ind_ty_var
let val_ty = Expr.Ty.of_var val_ty_var
+let alpha_ty_var = Expr.Ty.Var.mk "alpha"
+let alpha_ty = Expr.Ty.of_var alpha_ty_var
let array_ty = Expr.Ty.array ind_ty val_ty
let bind_tys tyvl ty = Expr.Ty.pi tyvl ty
+let replicate n v = List.init n (fun _ -> v)
(* Builtins *)
module Builtin = struct
type _ Expr.t +=
| Array_diff
| Array_const
+ | Array_map
| Array_default_index
| Array_default_value
@@ -79,6 +80,26 @@ module Builtin = struct
(Dolmen_std.Path.global "array_const")
(Expr.Ty.arrow [ val_ty ] array_ty)
+ let array_map : int -> Dolmen_std.Expr.term_cst =
+ let cache = Popop_stdlib.DInt.H.create 13 in
+ let get_ty i =
+ match Popop_stdlib.DInt.H.find cache i with
+ | ty -> ty
+ | exception Not_found ->
+ let ty =
+ Expr.Ty.arrow
+ (Expr.Ty.arrow (replicate i alpha_ty) val_ty
+ :: replicate i (Expr.Ty.array ind_ty alpha_ty))
+ val_ty
+ in
+ Popop_stdlib.DInt.H.add cache i ty;
+ ty
+ in
+ fun i ->
+ Expr.Id.mk ~name:"array_map" ~builtin:Array_map
+ (Dolmen_std.Path.global "array_map")
+ (get_ty i)
+
let array_default_index : Dolmen_std.Expr.term_cst =
Expr.Id.mk ~name:"array_default_index" ~builtin:Array_default_index
(Dolmen_std.Path.global "array_default_index")
@@ -116,6 +137,19 @@ module Builtin = struct
| Dolmen_loop.Typer.T.Id
{ ns = Term; name = Simple "array_default_value" } ->
app1 env s array_default_value
+ | Dolmen_loop.Typer.T.Id { ns = Term; name = Simple "array_map" } ->
+ `Term
+ (Dolmen_type.Base.term_app_list
+ (module Dolmen_loop.Typer.T)
+ env s
+ (function
+ | _ :: t as l ->
+ (* "t" should probably never be empty... *)
+ Expr.Term.apply_cst (array_map (List.length t)) [] l
+ | _ ->
+ failwith
+ "array_map needs to be applied to a function and n \
+ arrays"))
| _ -> `Not_found)
end
@@ -328,35 +362,139 @@ module Theory = struct
let l = if !extended_comb then (const_pattern, const_run) :: l else l in
List.iter (fun (p, r) -> InvertedPath.add_callback env p r) l
- let new_array env s_index_ty s_value_ty f =
- (* Extensionality rule ext: a, b ⇒ (a = b) ⋠(a[k] ≠b[k]) *)
- if not !restrict_ext then (
- Datastructure.Push.iter db env ~f:(fun f2 ->
- let subst =
- mk_subst
- [ (va, Ground.node f2); (vb, Ground.node f) ]
- [ (ind_ty_var, s_index_ty); (val_ty_var, s_value_ty) ]
- in
- Debug.dprintf2 debug "Found ext with %a" Ground.Subst.pp subst;
- let n = distinct_term_node ~subst env ta tb in
- Egraph.register env n;
- Boolean.set_true env n);
- Datastructure.Push.push db env f);
- (* ðð›¿: a |> a[ð] = 𛿠*)
- if !extended_comb then (
- let subst =
- mk_subst
- [ (va, Ground.node f) ]
- [ (ind_ty_var, s_index_ty); (val_ty_var, s_value_ty) ]
- in
- let epsilon_app = apply_def_index ta in
- let delta_app = apply_def_value ta in
- let epsilon_delta_eq =
- Expr.Term.eq (Expr.Term.select ta epsilon_app) delta_app
+ let new_array =
+ let db = Datastructure.Push.create Ground.pp "Array.db" in
+ fun env s_index_ty s_value_ty f ->
+ (* Extensionality rule ext: a, b ⇒ (a = b) ⋠(a[k] ≠b[k]) *)
+ if not !restrict_ext then (
+ Datastructure.Push.iter db env ~f:(fun f2 ->
+ let subst =
+ mk_subst
+ [ (va, Ground.node f2); (vb, Ground.node f) ]
+ [ (ind_ty_var, s_index_ty); (val_ty_var, s_value_ty) ]
+ in
+ Debug.dprintf2 debug "Found ext with %a" Ground.Subst.pp subst;
+ let n = distinct_term_node ~subst env ta tb in
+ Egraph.register env n;
+ Boolean.set_true env n);
+ Datastructure.Push.push db env f);
+ (* ðð›¿: a |> a[ð] = 𛿠*)
+ if !extended_comb then (
+ Debug.dprintf0 debug "Application of the epsilon_delta rule";
+ let subst =
+ mk_subst
+ [ (va, Ground.node f) ]
+ [ (ind_ty_var, s_index_ty); (val_ty_var, s_value_ty) ]
+ in
+ let epsilon_app = apply_def_index ta in
+ let delta_app = apply_def_value ta in
+ let epsilon_delta_eq =
+ Expr.Term.eq (Expr.Term.select ta epsilon_app) delta_app
+ in
+ let n = convert ~subst env epsilon_delta_eq in
+ Egraph.register env n;
+ Boolean.set_true env n)
+
+ let mk_vt_list pref n ty =
+ let rec aux tl n =
+ if n <= 0 then List.rev tl
+ else
+ let v = Expr.Term.Var.mk (Format.sprintf "%s%n" pref n) ty in
+ let t = Expr.Term.of_var v in
+ aux (t :: tl) (n - 1)
+ in
+ aux [] n
+
+ (* map⇓: a = map(f, b1, ..., bn), a[j] |> a[j] = f(b1[j], ..., bn[j]) *)
+ let map_adowm map_term f_term bitl =
+ let map_read_pattern =
+ Pattern.of_term_exn ~subst:Ground.Subst.empty
+ (Expr.Term.select map_term tj)
+ in
+ let map_read_run env subst =
+ Debug.dprintf2 debug "Found array_map(f,b1, ..., bn)[j] with %a"
+ Ground.Subst.pp subst;
+ let term =
+ Expr.Term.eq
+ (Expr.Term.select map_term tj)
+ (Expr.Term.apply f_term []
+ (List.map (fun bi -> Expr.Term.select bi tj) bitl))
in
- let n = convert ~subst env epsilon_delta_eq in
+ let n = convert ~subst env term in
Egraph.register env n;
- Boolean.set_true env n)
+ Boolean.set_true env n
+ in
+ (map_read_pattern, map_read_run)
+
+ (* map⇑: a = map(f, b1, ..., bn), bk[j] |> a[j] = f(b1[j], ..., bn[j]) *)
+ (* mapð›¿: a = map(f, b1, ..., bn) |> ð›¿(a) = f(ð›¿(b1), ..., ð›¿((bn)) *)
+ let map_aup map_term f_term bitl =
+ let map_pattern = Pattern.of_term_exn ~subst:Ground.Subst.empty map_term in
+ let map_run env subst =
+ Debug.dprintf2 debug "Found array_map(f,b1, ..., bn) with %a"
+ Ground.Subst.pp subst;
+ if !extended_comb then (
+ Debug.dprintf0 debug "Application of the map_aup rule";
+ let bkjl = List.map (fun bi -> Expr.Term.select bi tj) bitl in
+ let bkjl_patterns = List.map (Pattern.of_term_exn ~subst) bkjl in
+ let bkj_run =
+ let seen = ref false in
+ (* TODO: find one k for each j that is encountered, if there are
+ different k's for one j, only one of them needs to be matched. *)
+ fun env subst ->
+ if not !seen then (
+ seen := true;
+ let term =
+ Expr.Term.eq
+ (Expr.Term.select map_term tj)
+ (Expr.Term.apply f_term []
+ (List.map (fun bi -> Expr.Term.select bi tj) bitl))
+ in
+ let n = convert ~subst env term in
+ Egraph.register env n;
+ Boolean.set_true env n)
+ in
+ List.iter
+ (fun pattern -> InvertedPath.add_callback env pattern bkj_run)
+ bkjl_patterns);
+ if !default_values then (
+ Debug.dprintf0 debug "Application of the map_delta rule";
+ let d_a = Expr.Term.apply_cst Builtin.array_default_value [] [ ta ] in
+ let d_bil =
+ List.map
+ (fun bi ->
+ Expr.Term.apply_cst Builtin.array_default_value [] [ bi ])
+ bitl
+ in
+ let term = Expr.Term.eq d_a (Expr.Term.apply f_term [] d_bil) in
+ let n = convert ~subst env term in
+ Egraph.register env n;
+ Boolean.set_true env n)
+ in
+ (map_pattern, map_run)
+
+ let new_map =
+ (* Does the type matter? should it be cached? *)
+ let cache = ref Popop_stdlib.DInt.S.empty in
+ let seen i = Popop_stdlib.DInt.S.mem i !cache in
+ let add i = cache := Popop_stdlib.DInt.S.add i !cache in
+ fun env mapf_t ->
+ let mapf_s = Ground.sem mapf_t in
+ let f_arity = IArray.length mapf_s.args - 1 in
+ if not (seen f_arity) then (
+ add f_arity;
+ let b_ty = Expr.Ty.array ind_ty alpha_ty in
+ let f_ty = Expr.Ty.arrow (replicate f_arity alpha_ty) val_ty in
+ let bitl = mk_vt_list "b" f_arity b_ty in
+ let f_var = Expr.Term.Var.mk "f" f_ty in
+ let f_term = Expr.Term.of_var f_var in
+ let map_term =
+ Expr.Term.apply_cst (Builtin.array_map f_arity) [] (f_term :: bitl)
+ in
+ let map_pattern, map_run = map_adowm map_term f_term bitl in
+ let map_read_pattern, map_read_run = map_adowm map_term f_term bitl in
+ if !extended_comb then InvertedPath.add_callback env map_pattern map_run;
+ InvertedPath.add_callback env map_read_pattern map_read_run)
end
let converter env (f : Ground.t) =
@@ -486,6 +624,9 @@ let converter env (f : Ground.t) =
in
Egraph.register env eq_node;
Boolean.set_true env eq_node)
+ | { app = { builtin = Builtin.Array_map; _ }; _ }
+ when !extended_comb || !default_values ->
+ Theory.new_map env f
| _ -> ()
let init env : unit =