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Quellcode-Bibliothek

© Kompilation durch diese Firma

[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]

Datei: README.txt   Sprache: Lisp

Original von: PVS©
(polynomial_division
 (poly_divide_TCC1 0
  (poly_divide_TCC1-1 nil 3582383554 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (rat_max application-judgement "{s: rat | s >= q AND s >= r}"
     real_defs nil)
    (int_max application-judgement "{k: int | i <= k AND j <= k}"
     real_defs nil)
    (int_plus_int_is_int application-judgement "int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil)
    (int_minus_int_is_int application-judgement "int" integers nil))
   nil))
 (poly_divide_TCC2 0
  (poly_divide_TCC2-1 nil 3582383554 ("" (subtype-tcc) nil nil) nil
   nil))
 (poly_divide_TCC3 0
  (poly_divide_TCC3-1 nil 3582383554 ("" (subtype-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil))
   nil))
 (poly_divide_TCC4 0
  (poly_divide_TCC4-1 nil 3582383554 ("" (subtype-tcc) nil nil)
   ((make_divtype const-decl "DivType" polynomial_division nil)) nil))
 (poly_divide_TCC5 0
  (poly_divide_TCC5-1 nil 3582383554
   ("" (skosimp*) (("" (assert) (("" (postpone) nil nil)) nil)) nil)
   ((real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (int_minus_int_is_int application-judgement "int" integers nil))
   nil))
 (poly_divide_TCC6 0
  (poly_divide_TCC6-1 nil 3582383554 ("" (termination-tcc) nil nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil)
    (make_divtype const-decl "DivType" polynomial_division nil))
   nil))
 (poly_divide_TCC7 0
  (poly_divide_TCC7-1 nil 3582383609 ("" (termination-tcc) nil nil)
   ((int_minus_int_is_int application-judgement "int" integers nil)
    (boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_div_nzreal_is_real application-judgement "real" reals nil)
    (make_divtype const-decl "DivType" polynomial_division nil)
    (nnint_plus_nnint_is_nnint application-judgement "nonneg_int"
     integers nil))
   nil))
 (poly_divide_TCC8 0
  (poly_divide_TCC8-1 nil 3582544163 ("" (termination-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (minus_odd_is_odd application-judgement "odd_int" integers nil))
   nil))
 (poly_divide_TCC9 0
  (poly_divide_TCC9-1 nil 3582555120 ("" (termination-tcc) nil nil)
   ((boolean nonempty-type-decl nil booleans nil)
    (bool nonempty-type-eq-decl nil booleans nil)
    (NOT const-decl "[bool -> bool]" booleans nil)
    (number nonempty-type-decl nil numbers nil)
    (number_field_pred const-decl "[number -> boolean]" number_fields
     nil)
    (number_field nonempty-type-from-decl nil number_fields nil)
    (real_pred const-decl "[number_field -> boolean]" reals nil)
    (real nonempty-type-from-decl nil reals nil)
    (>= const-decl "bool" reals nil)
    (rational_pred const-decl "[real -> boolean]" rationals nil)
    (rational nonempty-type-from-decl nil rationals nil)
    (integer_pred const-decl "[rational -> boolean]" integers nil)
    (int nonempty-type-eq-decl nil integers nil)
    (nat nonempty-type-eq-decl nil naturalnumbers nil)
    (/= const-decl "boolean" notequal nil)
    (real_ge_is_total_order name-judgement "(total_order?[real])"
     real_props nil)
    (real_gt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (real_lt_is_strict_total_order name-judgement
     "(strict_total_order?[real])" real_props nil)
    (mult_divides1 application-judgement "(divides(n))" divides nil)
    (mult_divides2 application-judgement "(divides(m))" divides nil)
    (max const-decl "{p: real | p >= m AND p >= n}" real_defs nil)
    (int_minus_int_is_int application-judgement "int" integers nil)
    (posint_plus_nnint_is_posint application-judgement "posint"
     integers nil))
   nil))
 (poly_divide_def 0
  (poly_divide_def-1 nil 3582385231
   (""
    (case "FORALL (g, h: sequence[real], i, m, n: nat):
                                                                                     h(m) /= 0 AND i<=n-m AND (n-m-i) <= n - m IMPLIES
                                                                                      LET pd = poly_divide(g, n)(h, m)((n-m-i)) IN
                                                                                        FORALL (x: real):
                                                                                          polynomial(g, n)(x) =
                                                                                           polynomial(pd`quot, pd`qdeg)(x) * polynomial(h, m)(x) +
                                                                                            polynomial(pd`rem, pd`rdeg)(x)")
    (("1" (skeep)
      (("1" (inst - "g" "h" "n-m-i" "m" "n")
        (("1" (assert)
          (("1" (split -)
            (("1" (propax) nil nil)
             ("2" (skeep)
              (("2" (assert)
                (("2" (expand "poly_divide")
                  (("2" (expand "make_divtype")
                    (("2" (expand "polynomial" + 1)
                      (("2" (expand "sigma")
                        (("2" (expand "sigma") (("2" (assert) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil)
         ("2" (assert)
          (("2" (skeep)
            (("2" (expand "poly_divide")
              (("2" (expand "make_divtype")
                (("2" (expand "polynomial" + 1)
                  (("2" (expand "sigma")
                    (("2" (expand "sigma") (("2" (assert) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     ("2" (hide 2)
      (("2"
        (case "NOT FORALL (g, h: sequence[real], i, m, n: nat):
                                                                                h(m) /= 0 AND i = n - m IMPLIES
                                                                                 LET pd = poly_divide(g, n)(h, m)(i) IN
                                                                                   FORALL (x: real):
                                                                                     polynomial(g, n)(x) =
                                                                                      polynomial(pd`quot, pd`qdeg)(x) * polynomial(h, m)(x) +
                                                                                       polynomial(pd`rem, pd`rdeg)(x)")
        (("1" (hide 2)
          (("1" (skeep)
            (("1" (replaces -1)
              (("1" (assert)
                (("1" (skeep 2)
                  (("1" (assert)
                    (("1" (name "pd" "poly_divide(g, n)(h, m)(n - m)")
                      (("1" (replace -1)
                        (("1" (expand "poly_divide" :assert? none)
                          (("1" (lift-if)
                            (("1" (split -)
                              (("1"
                                (flatten)
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "make_divtype")
                                    (("1"
                                      (replaces -2 :dir rl)
                                      (("1"
                                        (assert)
                                        (("1"
                                          (invoke
                                           (case "%1=0")
                                           (! 2 2 1))
                                          (("1" (assert) nil nil)
                                           ("2"
                                            (hide-all-but 1)
                                            (("2" (grind) nil nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2"
                                (flatten)
                                (("2"
                                  (split -)
                                  (("1"
                                    (flatten)
                                    (("1"
                                      (replaces -1)
                                      (("1"
                                        (assert)
                                        (("1"
                                          (expand "*")
                                          (("1"
                                            (expand "make_divtype")
                                            (("1"
                                              (replace -1 :dir rl)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (rewrite
                                                   "polynomial_n0")
                                                  (("1"
                                                    (rewrite
                                                     "polynomial_n0")
                                                    (("1"
                                                      (assert)
                                                      (("1"
                                                        (lemma
                                                         "scal_polynomial")
                                                        (("1"
                                                          (inst
                                                           -
                                                           "(1/h(0))*g"
                                                           "n"
                                                           "h(0)")
                                                          (("1"
                                                            (expand
                                                             "*")
                                                            (("1"
                                                              (decompose-equality
                                                               -1)
                                                              (("1"
                                                                (inst
                                                                 -
                                                                 "x")
                                                                (("1"
                                                                  (expand
                                                                   "const_fun")
                                                                  (("1"
                                                                    (replaces
                                                                     -1)
                                                                    (("1"
                                                                      (rewrite
                                                                       "poly_eq_le_degree")
                                                                      nil
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil)
                                   ("2"
                                    (flatten)
                                    (("2"
                                      (label "mz" 1)
                                      (("2"
                                        (hide "mz")
                                        (("2"
                                          (skoletin -1)
                                          (("2"
                                            (skoletin -1)
                                            (("2"
                                              (assert)
                                              (("2"
                                                (expand "make_divtype")
                                                (("2"
                                                  (assert)
                                                  (("2"
                                                    (case
                                                     "NOT polynomial(pd`quot, pd`qdeg)(x) = (g(n)/h(m))*x^(n-m)")
                                                    (("1"
                                                      (hide 5)
                                                      (("1"
                                                        (replaces
                                                         -1
                                                         +
                                                         :dir
                                                         rl)
                                                        (("1"
                                                          (assert)
                                                          (("1"
                                                            (replace
                                                             -2
                                                             +)
                                                            (("1"
                                                              (assert)
                                                              (("1"
                                                                (expand
                                                                 "polynomial")
                                                                (("1"
                                                                  (lemma
                                                                   "sigma_eq_one_arg")
                                                                  (("1"
                                                                    (inst?)
                                                                    (("1"
                                                                      (inst
                                                                       -
                                                                       "n-m")
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (split
                                                                           -)
                                                                          (("1"
                                                                            (replaces
                                                                             -1)
                                                                            (("1"
                                                                              (assert)
                                                                              (("1"
                                                                                (replaces
                                                                                 -1)
                                                                                (("1"
                                                                                  (replaces
                                                                                   -1)
                                                                                  (("1"
                                                                                    (assert)
                                                                                    (("1"
                                                                                      (lift-if)
                                                                                      (("1"
                                                                                        (ground)
                                                                                        (("1"
                                                                                          (replaces
                                                                                           -1)
                                                                                          (("1"
                                                                                            (grind)
                                                                                            nil
                                                                                            nil))
                                                                                          nil))
                                                                                        nil))
                                                                                      nil))
                                                                                    nil))
                                                                                  nil))
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("2"
                                                                            (skosimp*)
                                                                            (("2"
                                                                              (lift-if)
                                                                              (("2"
                                                                                (ground)
                                                                                nil
                                                                                nil))
                                                                              nil))
                                                                            nil)
                                                                           ("3"
                                                                            (skosimp*)
                                                                            nil
                                                                            nil))
                                                                          nil))
                                                                        nil))
                                                                      nil))
                                                                    nil))
                                                                  nil))
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil)
                                                     ("2"
                                                      (ground)
                                                      (("2"
                                                        (replaces -1)
                                                        (("2"
                                                          (lemma
                                                           "mul_x_to_n_polynomial")
                                                          (("2"
                                                            (case
                                                             "n = m")
                                                            (("1"
                                                              (assert)
                                                              (("1"
                                                                (replaces
                                                                 -1)
                                                                (("1"
                                                                  (assert)
                                                                  (("1"
                                                                    (hide
                                                                     -1)
                                                                    (("1"
                                                                      (replaces
                                                                       -3)
                                                                      (("1"
                                                                        (assert)
                                                                        (("1"
                                                                          (replace
                                                                           -1
                                                                           +
                                                                           :dir
                                                                           rl)
                                                                          (("1"
                                                                            (assert)
                                                                            (("1"
                                                                              (expand
                                                                               "polynomial"
                                                                               +
                                                                               3)
                                                                              (("1"
                                                                                (rewrite
                                                                                 "sigma_scal"
                                                                                 :dir
                                                                                 rl)
                                                                                (("1"
                                                                                  (rewrite
                                                                                   "sigma_scal_right"
                                                                                   :dir
                                                                                   rl)
                                                                                  (("1"
                                                                                    (expand
                                                                                     "polynomial")
                                                                                    (("1"
                                                                                      (expand
                                                                                       "sigma"
                                                                                       +
                                                                                       1)
                                                                                      (("1"
                                                                                        (expand
                                                                                         "sigma"
                                                                                         +
                                                                                         3)
                                                                                        (("1"
                                                                                          (case
                                                                                           "x^0 = 1")
                                                                                          (("1"
                                                                                            (replaces
                                                                                             -1)
                                                                                            (("1"
                                                                                              (assert)
                                                                                              (("1"
                                                                                                (case
                                                                                                 "NOT g(m)*x^m = h(m) * x ^ m * (g(m) / h(m))")
                                                                                                (("1"
                                                                                                  (assert)
                                                                                                  nil
                                                                                                  nil)
                                                                                                 ("2"
                                                                                                  (replaces
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--> --------------------

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--> --------------------

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