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    • Erik Martin-Dorel's avatar
      Refactoring in progress. · 4dbb200d
      Erik Martin-Dorel authored
      * Objectives:
      
      1. Remove superfluous Modules and interfaces in poly_datatypes.v ...,
      so the following are kept:
      
      Module Type BaseOps.
      Module Type PowDivOps.
      Module Type FullOps.
      Module Type ExactFullOps.
      
      Module Type PolyOps (C : PowDivOps) <: BaseOps.
      Module Type PolyIntOps (I : IntervalOps).
      
      Module FullR <: ExactFullOps.
      Module PolR <: PolyOps FullR.
      
      Module FullInt (I : IntervalOps) <: FullOps.
      Module SeqPoly (C : PowDivOps) <: PolyOps C.
      Module SeqPolyInt (I : IntervalOps) <: PolyIntOps I.
      
      The trivial module RPA has been deleted, so that the rpa record is now
      directly defined in taylor_model_int_sharp.v:
      Record rpa : Type := RPA { approx : Pol.T; error : I.type }.
      
      And the files coeff_inst.v and rpa_inst.v have been deleted.
      
      2. Always deal with polynomials over R, not over ExtendedR.
      
      This makes it possible to benefit from "real bigops", and use the fact
      that "0 * r = 0" holds over R, while it didn't over ExtendedR...
      
      3. Rework the interval-polys interface and add convenient notations:
      
      Notation "i >: x" := (contains (I.convert i) (Xreal x)) : ipoly_scope.
      
      Definition contains_pointwise pi p : Prop :=
        forall k, contains (I.convert (nth pi k)) (Xreal (PolR.nth p k)).
      Notation cpw := contains_pointwise (only parsing).
      Notation "p >:: x" := (contains_pointwise p x) : ipoly_scope.
      
      Notation eq_size pi p := (size pi = PolR.size p).
      Notation scpw pi p := (eq_size pi p /\ cpw pi p) (only parsing).
      Notation "p >::: x" := (scpw p x) (only parsing) : ipoly_scope.
      
      4. Strengthen the IntervalOps interface a little bit.
      
      In particular, the following parameters have been added:
      
      Definition propagate fi :=
        forall xi, convert xi = Inan -> convert (fi xi) = Inan.
      Definition propagate_l fi :=
        forall xi yi : type, convert xi = Inan -> convert (fi xi yi) = Inan.
      Definition propagate_r fi :=
        forall xi yi : type, convert yi = Inan -> convert (fi xi yi) = Inan.
      Parameter mask_propagate_l : propagate_l mask.
      Parameter mask_propagate_r : propagate_r mask.
      Parameter neg_propagate : propagate neg.
      Parameter inv_propagate : forall prec, propagate (inv prec).
      etc...
      
      5. Rely on Coquelicot to simplify the real-analysis proofs, and rely
      on CoqEAL_refinements to simplify the data-refinement proofs.
      
      * Remarks:
      
      - several CoqApprox proofs are still broken and need some revision.
      
      - taylor_model_float_sharp.v (which is not required by CoqInterval) is
        temporarily commented.
      
      - poly_inst_seq.v has been merged into poly_datatypes.v (temporarily?)
      4dbb200d
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