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Source file Cut_form.ml

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(* This file is free software, part of Zipperposition. See file "license" for more details. *)

(** {1 Universally Quantified Conjunction of Clauses} *)

open Logtk

module Fmt = CCFormat
module T = Term

type var = Term.var
type term = Term.t
type clause = Literals.t
type form = clause list

type t = {
  vars: T.VarSet.t;
  cs: form;
}
type cut_form = t

let trivial = {cs=[]; vars=T.VarSet.empty}

let make cs =
  if cs=[] then trivial
  else (
    let vars =
      Iter.of_list cs
      |> Iter.flat_map Literals.Seq.vars
      |> T.VarSet.of_iter
    and cs = CCList.sort_uniq ~cmp:Literals.compare cs in
    {cs; vars;}
  )

let vars t = t.vars
let cs t = t.cs

let hash (f:t): int = Hash.list Literals.hash f.cs
let equal f1 f2: bool = CCList.equal Literals.equal f1.cs f2.cs
let compare f1 f2 = CCList.compare Literals.compare f1.cs f2.cs

let pp out (f:t): unit =
  let pp_c = Literals.pp in
  let pp_body out () = match f.cs with
    | [c] -> pp_c out c
    | _ -> Fmt.fprintf out "@<1>∧{@[<hv>%a@]}" (Util.pp_list ~sep:"," pp_c) f.cs
  in
  if T.VarSet.is_empty f.vars then (
    pp_body out ()
  ) else (
    Fmt.fprintf out "(@[<2>forall %a.@ %a@])"
      (Util.pp_list ~sep:" " Type.pp_typed_var) (T.VarSet.to_list f.vars) pp_body ()
  )

let to_string = Fmt.to_string pp

let pp_tstp out (f:t): unit =
  let pp_c = Fmt.within "(" ")" Literals.pp_tstp in
  let pp_body out () = match f.cs with
    | [c] -> pp_c out c
    | _ -> Fmt.fprintf out "(@[%a@])" (Util.pp_list ~sep:" & " pp_c) f.cs
  in
  if T.VarSet.is_empty f.vars then (
    pp_body out ()
  ) else (
    Fmt.fprintf out "(@[<2>![%a]:@ (%a)@])"
      (Util.pp_list Type.TPTP.pp_typed_var) (T.VarSet.to_list f.vars) pp_body ()
  )

let pp_zf out (f:t): unit =
  let pp_c = Fmt.within "(" ")" Literals.pp_zf in
  let pp_body out () = match f.cs with
    | [c] -> pp_c out c
    | _ -> Fmt.fprintf out "(@[%a@])" (Util.pp_list ~sep:" && " pp_c) f.cs
  in
  if T.VarSet.is_empty f.vars then (
    pp_body out ()
  ) else (
    Fmt.fprintf out "(@[<2>forall %a.@ (%a)@])"
      (Util.pp_list Type.ZF.pp_typed_var) (T.VarSet.to_list f.vars) pp_body ()
  )

let ind_vars t =
  vars t
  |> T.VarSet.to_list
  |> List.filter
    (fun v ->
       let ty = HVar.ty v in
       (* only do induction on variables of infinite types *)
       begin match Ind_ty.as_inductive_type ty with
         | Some (ity,_) -> Ind_ty.is_recursive ity
         | None -> false
       end)

let apply_subst renaming subst (f,sc): t =
  let cs =
    List.map (fun lits -> Literals.apply_subst renaming subst (lits,sc)) f.cs
  in
  make cs

let subst1 (v:var) (t:term) (f:t): t =
  let renaming = Subst.Renaming.create () in
  let subst =
    Subst.FO.bind Subst.empty ((v:var:>InnerTerm.t HVar.t),0) (t,1)
  in
  apply_subst renaming subst (f,0)

(* find substitutions making [f1] and [f2] variants, if possible *)
let variant_ ~subst (f1,sc1)(f2,sc2): _ Iter.t =
  Unif.unif_list_com ~size:`Same subst
    ~op:(fun subst c1 c2 k ->
        Literals.variant ~subst c1 c2 (fun (subst,_tags) -> k subst))
    (f1.cs,sc1)(f2.cs,sc2)

let are_variant f1 f2: bool =
  not @@ Iter.is_empty @@ variant_ ~subst:Subst.empty (f1,1)(f2,0)

let normalize_form (f:form): form =
  let module RW = Rewrite in
  let rec simplify c =
    let lit_abs = CCArray.find_idx Literal.is_absurd c in
    begin match lit_abs with
      | None -> c
      | Some (i,_) ->
        let new_c = CCArray.except_idx c i |> Array.of_list in
        simplify new_c
    end
  in
  (* fixpoint of rewriting *)
  let rec normalize_up_to fuel (c:clause): clause Iter.t =
    assert (fuel>=0);
    if fuel=0 then Iter.return c
    else normalize_step (fuel-1) c
  and normalize_step fuel c =
    let progress=ref false in
    (* how to normalize a term/lit (with restricted resources) *)
    let rw_term t =
      let t', rules = RW.Term.normalize_term ~max_steps:10 t in
      if not (RW.Term.Rule_inst_set.is_empty rules) then progress := true;
      t'
    in
    let rw_terms c = Literals.map rw_term c
    and rw_clause c = match RW.Lit.normalize_clause c with
      | None -> [c]
      | Some (cs,_,_,_,_,_) ->
        progress := true;
        cs
    and rm_trivial =
      List.filter (fun c -> not (Literals.is_trivial c))
    in
    let cs = c |> rw_terms |> rw_clause |> rm_trivial in
    if !progress
    then normalize_form fuel cs (* normalize each result recursively *)
    else (
      (* done, just simplify *)
      Iter.of_list cs |> Iter.map simplify
    )
  and normalize_form fuel (f:form): clause Iter.t =
    Iter.of_list f |> Iter.flat_map (normalize_up_to fuel)
  in
  normalize_form 3 f |> Iter.to_rev_list

let normalize (f:t): t = cs f |> normalize_form |> make

let to_s_form (f:t) =
  let module F = TypedSTerm.Form in
  (* convert all clauses with the same variable bindings *)
  let ctx = Term.Conv.create() in
  let l = List.map (Literals.Conv.to_s_form ~ctx) (cs f) in
  F.and_ l |> F.close_forall

module Pos = struct
  module P = Position

  let bad_pos f p = Util.invalid_argf "invalid pos `%a`@ in %a" P.pp p pp f

  let clause_at f p = match p with
    | P.Stop -> bad_pos f p
    | P.Arg (n,p') ->
      let cs = cs f in
      if n<0 || n >= List.length cs then bad_pos f p;
      List.nth cs n, p'
    | _ -> bad_pos f p

  let lit_at f p =
    let c, p = clause_at f p in
    Literals.Pos.lit_at c p

  let at f p: term =
    let lit, p = lit_at f p in
    Literal.Pos.at lit p

  let replace_many f m: t =
    let l = cs f in
    P.Map.fold
      (fun p by l ->
         let n, p_c = match p with P.Arg (n,p') -> n,p' | _ -> assert false in
         let c = List.nth l n in
         let c' = Array.copy c in
         Literals.Pos.replace c' ~at:p_c ~by;
         CCList.set_at_idx n c' l)
      m l
    |> make

  let replace f ~at ~by = replace_many f (P.Map.singleton at by)
end

module Seq = struct
  let terms f =
    cs f
    |> Iter.of_list
    |> Iter.flat_map Literals.Seq.terms

  let terms_with_pos ?(subterms=true) f =
    cs f
    |> Iter.of_list
    |> Util.seq_zipi
    |> Iter.flat_map
      (fun (i,c) ->
         Iter.of_array_i c
         |> Iter.map (fun (j,lit) -> i, j, lit))
    |> Iter.flat_map
      (fun (i,j,lit) ->
         let position = Position.(arg i @@ arg j @@ stop) in
         Literal.fold_terms lit
           ~position ~ord:Ordering.none ~which:`All ~vars:true ~subterms)
end

module FV_tbl(X : Map.OrderedType) = struct
  type value = X.t

  (* approximation here, we represent it as a clause, losing the
         boolean structure. monotonicity w.r.t features should still apply *)
  let to_lits (f:cut_form) =
    cs f
    |> Iter.of_list
    |> Iter.flat_map_l Literals.to_form

  (* index for lemmas, to ensure α-equivalent lemmas have the same lit *)
  module FV = FV_tree.Make(struct
      type t = cut_form * X.t
      let compare (l1,v1)(l2,v2) =
        let open CCOrd.Infix in
        compare l1 l2 <?> (X.compare, v1, v2)

      let to_lits (l,_) = to_lits l
      let labels _ = Util.Int_set.empty
    end)

  type t = {
    mutable fv: FV.t;
  }

  let create () = {fv=FV.empty ()}

  let add t k v = t.fv <- FV.add t.fv (k,v)

  let get t k =
    FV.retrieve_alpha_equiv t.fv (to_lits k) Util.Int_set.empty
    |> Iter.find_map
      (fun (k',v) -> if are_variant k k' then Some v else None)

  let mem t k = get t k |> CCOpt.is_some

  let to_iter t = FV.iter t.fv
end