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authorGravatar fbesson <fbesson@85f007b7-540e-0410-9357-904b9bb8a0f7>2011-05-20 17:01:54 +0000
committerGravatar fbesson <fbesson@85f007b7-540e-0410-9357-904b9bb8a0f7>2011-05-20 17:01:54 +0000
commit7da3e3d85c88eb42e932230048cb0db255474b5d (patch)
tree0cd987e72b528d88c5a2a6bbcfa1d0718a74efa6 /plugins/micromega/micromega.ml
parent4c6c284ddc6db47f070026ad68b5c29f6737c4a0 (diff)
added support to handle division by a constant over R
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14147 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'plugins/micromega/micromega.ml')
-rw-r--r--plugins/micromega/micromega.ml3371
1 files changed, 2856 insertions, 515 deletions
diff --git a/plugins/micromega/micromega.ml b/plugins/micromega/micromega.ml
index 39b6cd2a3..564126d24 100644
--- a/plugins/micromega/micromega.ml
+++ b/plugins/micromega/micromega.ml
@@ -1,3 +1,6 @@
+type __ = Obj.t
+let __ = let rec f _ = Obj.repr f in Obj.repr f
+
(** val negb : bool -> bool **)
let negb = function
@@ -8,6 +11,23 @@ type nat =
| O
| S of nat
+(** val fst : ('a1 * 'a2) -> 'a1 **)
+
+let fst = function
+| x,y -> x
+
+(** val snd : ('a1 * 'a2) -> 'a2 **)
+
+let snd = function
+| x,y -> y
+
+(** val app : 'a1 list -> 'a1 list -> 'a1 list **)
+
+let rec app l m =
+ match l with
+ | [] -> m
+ | a::l1 -> a::(app l1 m)
+
type comparison =
| Eq
| Lt
@@ -20,12 +40,28 @@ let compOpp = function
| Lt -> Gt
| Gt -> Lt
-(** val app : 'a1 list -> 'a1 list -> 'a1 list **)
+type compareSpecT =
+| CompEqT
+| CompLtT
+| CompGtT
-let rec app l m =
- match l with
- | [] -> m
- | a::l1 -> a::(app l1 m)
+(** val compareSpec2Type : comparison -> compareSpecT **)
+
+let compareSpec2Type = function
+| Eq -> CompEqT
+| Lt -> CompLtT
+| Gt -> CompGtT
+
+type 'a compSpecT = compareSpecT
+
+(** val compSpec2Type : 'a1 -> 'a1 -> comparison -> 'a1 compSpecT **)
+
+let compSpec2Type x y c =
+ compareSpec2Type c
+
+type 'a sig0 =
+ 'a
+ (* singleton inductive, whose constructor was exist *)
(** val plus : nat -> nat -> nat **)
@@ -34,181 +70,1927 @@ let rec plus n0 m =
| O -> m
| S p -> S (plus p m)
+(** val nat_iter : nat -> ('a1 -> 'a1) -> 'a1 -> 'a1 **)
+
+let rec nat_iter n0 f x =
+ match n0 with
+ | O -> x
+ | S n' -> f (nat_iter n' f x)
+
type positive =
| XI of positive
| XO of positive
| XH
-(** val psucc : positive -> positive **)
-
-let rec psucc = function
-| XI p -> XO (psucc p)
-| XO p -> XI p
-| XH -> XO XH
-
-(** val pplus : positive -> positive -> positive **)
-
-let rec pplus x y =
- match x with
- | XI p ->
- (match y with
- | XI q0 -> XO (pplus_carry p q0)
- | XO q0 -> XI (pplus p q0)
- | XH -> XO (psucc p))
- | XO p ->
- (match y with
- | XI q0 -> XI (pplus p q0)
- | XO q0 -> XO (pplus p q0)
- | XH -> XI p)
- | XH ->
- (match y with
- | XI q0 -> XO (psucc q0)
- | XO q0 -> XI q0
- | XH -> XO XH)
-
-(** val pplus_carry : positive -> positive -> positive **)
-
-and pplus_carry x y =
- match x with
- | XI p ->
- (match y with
- | XI q0 -> XI (pplus_carry p q0)
- | XO q0 -> XO (pplus_carry p q0)
- | XH -> XI (psucc p))
- | XO p ->
- (match y with
- | XI q0 -> XO (pplus_carry p q0)
- | XO q0 -> XI (pplus p q0)
- | XH -> XO (psucc p))
- | XH ->
- (match y with
- | XI q0 -> XI (psucc q0)
- | XO q0 -> XO (psucc q0)
- | XH -> XI XH)
-
-(** val p_of_succ_nat : nat -> positive **)
-
-let rec p_of_succ_nat = function
-| O -> XH
-| S x -> psucc (p_of_succ_nat x)
-
-(** val pdouble_minus_one : positive -> positive **)
-
-let rec pdouble_minus_one = function
-| XI p -> XI (XO p)
-| XO p -> XI (pdouble_minus_one p)
-| XH -> XH
-
-type positive_mask =
-| IsNul
-| IsPos of positive
-| IsNeg
-
-(** val pdouble_plus_one_mask : positive_mask -> positive_mask **)
-
-let pdouble_plus_one_mask = function
-| IsNul -> IsPos XH
-| IsPos p -> IsPos (XI p)
-| IsNeg -> IsNeg
-
-(** val pdouble_mask : positive_mask -> positive_mask **)
-
-let pdouble_mask = function
-| IsPos p -> IsPos (XO p)
-| x0 -> x0
-
-(** val pdouble_minus_two : positive -> positive_mask **)
-
-let pdouble_minus_two = function
-| XI p -> IsPos (XO (XO p))
-| XO p -> IsPos (XO (pdouble_minus_one p))
-| XH -> IsNul
-
-(** val pminus_mask : positive -> positive -> positive_mask **)
-
-let rec pminus_mask x y =
- match x with
- | XI p ->
- (match y with
- | XI q0 -> pdouble_mask (pminus_mask p q0)
- | XO q0 -> pdouble_plus_one_mask (pminus_mask p q0)
- | XH -> IsPos (XO p))
- | XO p ->
- (match y with
- | XI q0 -> pdouble_plus_one_mask (pminus_mask_carry p q0)
- | XO q0 -> pdouble_mask (pminus_mask p q0)
- | XH -> IsPos (pdouble_minus_one p))
- | XH ->
- (match y with
- | XH -> IsNul
- | _ -> IsNeg)
-
-(** val pminus_mask_carry : positive -> positive -> positive_mask **)
-
-and pminus_mask_carry x y =
- match x with
- | XI p ->
- (match y with
- | XI q0 -> pdouble_plus_one_mask (pminus_mask_carry p q0)
- | XO q0 -> pdouble_mask (pminus_mask p q0)
- | XH -> IsPos (pdouble_minus_one p))
- | XO p ->
- (match y with
- | XI q0 -> pdouble_mask (pminus_mask_carry p q0)
- | XO q0 -> pdouble_plus_one_mask (pminus_mask_carry p q0)
- | XH -> pdouble_minus_two p)
- | XH -> IsNeg
-
-(** val pminus : positive -> positive -> positive **)
-
-let pminus x y =
- match pminus_mask x y with
- | IsPos z0 -> z0
- | _ -> XH
-
-(** val pmult : positive -> positive -> positive **)
-
-let rec pmult x y =
- match x with
- | XI p -> pplus y (XO (pmult p y))
- | XO p -> XO (pmult p y)
- | XH -> y
-
-(** val psize : positive -> nat **)
-
-let rec psize = function
-| XI p2 -> S (psize p2)
-| XO p2 -> S (psize p2)
-| XH -> S O
-
-(** val pcompare : positive -> positive -> comparison -> comparison **)
-
-let rec pcompare x y r =
- match x with
- | XI p ->
- (match y with
- | XI q0 -> pcompare p q0 r
- | XO q0 -> pcompare p q0 Gt
- | XH -> Gt)
- | XO p ->
- (match y with
- | XI q0 -> pcompare p q0 Lt
- | XO q0 -> pcompare p q0 r
- | XH -> Gt)
- | XH ->
- (match y with
- | XH -> r
- | _ -> Lt)
-
type n =
| N0
| Npos of positive
-(** val n_of_nat : nat -> n **)
+type z =
+| Z0
+| Zpos of positive
+| Zneg of positive
-let n_of_nat = function
-| O -> N0
-| S n' -> Npos (p_of_succ_nat n')
+module type TotalOrder' =
+ sig
+ type t
+ end
+
+module MakeOrderTac =
+ functor (O:TotalOrder') ->
+ struct
+
+ end
+
+module MaxLogicalProperties =
+ functor (O:TotalOrder') ->
+ functor (M:sig
+ val max : O.t -> O.t -> O.t
+ end) ->
+ struct
+ module T = MakeOrderTac(O)
+ end
+
+module Pos =
+ struct
+ type t = positive
+
+ (** val succ : positive -> positive **)
+
+ let rec succ = function
+ | XI p -> XO (succ p)
+ | XO p -> XI p
+ | XH -> XO XH
+
+ (** val add : positive -> positive -> positive **)
+
+ let rec add x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> XO (add_carry p q0)
+ | XO q0 -> XI (add p q0)
+ | XH -> XO (succ p))
+ | XO p ->
+ (match y with
+ | XI q0 -> XI (add p q0)
+ | XO q0 -> XO (add p q0)
+ | XH -> XI p)
+ | XH ->
+ (match y with
+ | XI q0 -> XO (succ q0)
+ | XO q0 -> XI q0
+ | XH -> XO XH)
+
+ (** val add_carry : positive -> positive -> positive **)
+
+ and add_carry x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> XI (add_carry p q0)
+ | XO q0 -> XO (add_carry p q0)
+ | XH -> XI (succ p))
+ | XO p ->
+ (match y with
+ | XI q0 -> XO (add_carry p q0)
+ | XO q0 -> XI (add p q0)
+ | XH -> XO (succ p))
+ | XH ->
+ (match y with
+ | XI q0 -> XI (succ q0)
+ | XO q0 -> XO (succ q0)
+ | XH -> XI XH)
+
+ (** val pred_double : positive -> positive **)
+
+ let rec pred_double = function
+ | XI p -> XI (XO p)
+ | XO p -> XI (pred_double p)
+ | XH -> XH
+
+ (** val pred : positive -> positive **)
+
+ let pred = function
+ | XI p -> XO p
+ | XO p -> pred_double p
+ | XH -> XH
+
+ (** val pred_N : positive -> n **)
+
+ let pred_N = function
+ | XI p -> Npos (XO p)
+ | XO p -> Npos (pred_double p)
+ | XH -> N0
+
+ type mask =
+ | IsNul
+ | IsPos of positive
+ | IsNeg
+
+ (** val mask_rect : 'a1 -> (positive -> 'a1) -> 'a1 -> mask -> 'a1 **)
+
+ let mask_rect f f0 f1 = function
+ | IsNul -> f
+ | IsPos x -> f0 x
+ | IsNeg -> f1
+
+ (** val mask_rec : 'a1 -> (positive -> 'a1) -> 'a1 -> mask -> 'a1 **)
+
+ let mask_rec f f0 f1 = function
+ | IsNul -> f
+ | IsPos x -> f0 x
+ | IsNeg -> f1
+
+ (** val succ_double_mask : mask -> mask **)
+
+ let succ_double_mask = function
+ | IsNul -> IsPos XH
+ | IsPos p -> IsPos (XI p)
+ | IsNeg -> IsNeg
+
+ (** val double_mask : mask -> mask **)
+
+ let double_mask = function
+ | IsPos p -> IsPos (XO p)
+ | x0 -> x0
+
+ (** val double_pred_mask : positive -> mask **)
+
+ let double_pred_mask = function
+ | XI p -> IsPos (XO (XO p))
+ | XO p -> IsPos (XO (pred_double p))
+ | XH -> IsNul
+
+ (** val pred_mask : mask -> mask **)
+
+ let pred_mask = function
+ | IsPos q0 ->
+ (match q0 with
+ | XH -> IsNul
+ | _ -> IsPos (pred q0))
+ | _ -> IsNeg
+
+ (** val sub_mask : positive -> positive -> mask **)
+
+ let rec sub_mask x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> double_mask (sub_mask p q0)
+ | XO q0 -> succ_double_mask (sub_mask p q0)
+ | XH -> IsPos (XO p))
+ | XO p ->
+ (match y with
+ | XI q0 -> succ_double_mask (sub_mask_carry p q0)
+ | XO q0 -> double_mask (sub_mask p q0)
+ | XH -> IsPos (pred_double p))
+ | XH ->
+ (match y with
+ | XH -> IsNul
+ | _ -> IsNeg)
+
+ (** val sub_mask_carry : positive -> positive -> mask **)
+
+ and sub_mask_carry x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> succ_double_mask (sub_mask_carry p q0)
+ | XO q0 -> double_mask (sub_mask p q0)
+ | XH -> IsPos (pred_double p))
+ | XO p ->
+ (match y with
+ | XI q0 -> double_mask (sub_mask_carry p q0)
+ | XO q0 -> succ_double_mask (sub_mask_carry p q0)
+ | XH -> double_pred_mask p)
+ | XH -> IsNeg
+
+ (** val sub : positive -> positive -> positive **)
+
+ let sub x y =
+ match sub_mask x y with
+ | IsPos z0 -> z0
+ | _ -> XH
+
+ (** val mul : positive -> positive -> positive **)
+
+ let rec mul x y =
+ match x with
+ | XI p -> add y (XO (mul p y))
+ | XO p -> XO (mul p y)
+ | XH -> y
+
+ (** val iter : positive -> ('a1 -> 'a1) -> 'a1 -> 'a1 **)
+
+ let rec iter n0 f x =
+ match n0 with
+ | XI n' -> f (iter n' f (iter n' f x))
+ | XO n' -> iter n' f (iter n' f x)
+ | XH -> f x
+
+ (** val pow : positive -> positive -> positive **)
+
+ let pow x y =
+ iter y (mul x) XH
+
+ (** val div2 : positive -> positive **)
+
+ let div2 = function
+ | XI p2 -> p2
+ | XO p2 -> p2
+ | XH -> XH
+
+ (** val div2_up : positive -> positive **)
+
+ let div2_up = function
+ | XI p2 -> succ p2
+ | XO p2 -> p2
+ | XH -> XH
+
+ (** val size_nat : positive -> nat **)
+
+ let rec size_nat = function
+ | XI p2 -> S (size_nat p2)
+ | XO p2 -> S (size_nat p2)
+ | XH -> S O
+
+ (** val size : positive -> positive **)
+
+ let rec size = function
+ | XI p2 -> succ (size p2)
+ | XO p2 -> succ (size p2)
+ | XH -> XH
+
+ (** val compare_cont : positive -> positive -> comparison -> comparison **)
+
+ let rec compare_cont x y r =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> compare_cont p q0 r
+ | XO q0 -> compare_cont p q0 Gt
+ | XH -> Gt)
+ | XO p ->
+ (match y with
+ | XI q0 -> compare_cont p q0 Lt
+ | XO q0 -> compare_cont p q0 r
+ | XH -> Gt)
+ | XH ->
+ (match y with
+ | XH -> r
+ | _ -> Lt)
+
+ (** val compare : positive -> positive -> comparison **)
+
+ let compare x y =
+ compare_cont x y Eq
+
+ (** val min : positive -> positive -> positive **)
+
+ let min p p' =
+ match compare p p' with
+ | Gt -> p'
+ | _ -> p
+
+ (** val max : positive -> positive -> positive **)
+
+ let max p p' =
+ match compare p p' with
+ | Gt -> p
+ | _ -> p'
+
+ (** val eqb : positive -> positive -> bool **)
+
+ let rec eqb p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> eqb p2 q1
+ | _ -> false)
+ | XO p2 ->
+ (match q0 with
+ | XO q1 -> eqb p2 q1
+ | _ -> false)
+ | XH ->
+ (match q0 with
+ | XH -> true
+ | _ -> false)
+
+ (** val leb : positive -> positive -> bool **)
+
+ let leb x y =
+ match compare x y with
+ | Gt -> false
+ | _ -> true
+
+ (** val ltb : positive -> positive -> bool **)
+
+ let ltb x y =
+ match compare x y with
+ | Lt -> true
+ | _ -> false
+
+ (** val sqrtrem_step :
+ (positive -> positive) -> (positive -> positive) -> (positive * mask)
+ -> positive * mask **)
+
+ let sqrtrem_step f g = function
+ | s,y ->
+ (match y with
+ | IsPos r ->
+ let s' = XI (XO s) in
+ let r' = g (f r) in
+ if leb s' r' then (XI s),(sub_mask r' s') else (XO s),(IsPos r')
+ | _ -> (XO s),(sub_mask (g (f XH)) (XO (XO XH))))
+
+ (** val sqrtrem : positive -> positive * mask **)
+
+ let rec sqrtrem = function
+ | XI p2 ->
+ (match p2 with
+ | XI p3 -> sqrtrem_step (fun x -> XI x) (fun x -> XI x) (sqrtrem p3)
+ | XO p3 -> sqrtrem_step (fun x -> XO x) (fun x -> XI x) (sqrtrem p3)
+ | XH -> XH,(IsPos (XO XH)))
+ | XO p2 ->
+ (match p2 with
+ | XI p3 -> sqrtrem_step (fun x -> XI x) (fun x -> XO x) (sqrtrem p3)
+ | XO p3 -> sqrtrem_step (fun x -> XO x) (fun x -> XO x) (sqrtrem p3)
+ | XH -> XH,(IsPos XH))
+ | XH -> XH,IsNul
+
+ (** val sqrt : positive -> positive **)
+
+ let sqrt p =
+ fst (sqrtrem p)
+
+ (** val gcdn : nat -> positive -> positive -> positive **)
+
+ let rec gcdn n0 a b =
+ match n0 with
+ | O -> XH
+ | S n1 ->
+ (match a with
+ | XI a' ->
+ (match b with
+ | XI b' ->
+ (match compare a' b' with
+ | Eq -> a
+ | Lt -> gcdn n1 (sub b' a') a
+ | Gt -> gcdn n1 (sub a' b') b)
+ | XO b0 -> gcdn n1 a b0
+ | XH -> XH)
+ | XO a0 ->
+ (match b with
+ | XI p -> gcdn n1 a0 b
+ | XO b0 -> XO (gcdn n1 a0 b0)
+ | XH -> XH)
+ | XH -> XH)
+
+ (** val gcd : positive -> positive -> positive **)
+
+ let gcd a b =
+ gcdn (plus (size_nat a) (size_nat b)) a b
+
+ (** val ggcdn :
+ nat -> positive -> positive -> positive * (positive * positive) **)
+
+ let rec ggcdn n0 a b =
+ match n0 with
+ | O -> XH,(a,b)
+ | S n1 ->
+ (match a with
+ | XI a' ->
+ (match b with
+ | XI b' ->
+ (match compare a' b' with
+ | Eq -> a,(XH,XH)
+ | Lt ->
+ let g,p = ggcdn n1 (sub b' a') a in
+ let ba,aa = p in g,(aa,(add aa (XO ba)))
+ | Gt ->
+ let g,p = ggcdn n1 (sub a' b') b in
+ let ab,bb = p in g,((add bb (XO ab)),bb))
+ | XO b0 ->
+ let g,p = ggcdn n1 a b0 in let aa,bb = p in g,(aa,(XO bb))
+ | XH -> XH,(a,XH))
+ | XO a0 ->
+ (match b with
+ | XI p ->
+ let g,p2 = ggcdn n1 a0 b in let aa,bb = p2 in g,((XO aa),bb)
+ | XO b0 -> let g,p = ggcdn n1 a0 b0 in (XO g),p
+ | XH -> XH,(a,XH))
+ | XH -> XH,(XH,b))
+
+ (** val ggcd : positive -> positive -> positive * (positive * positive) **)
+
+ let ggcd a b =
+ ggcdn (plus (size_nat a) (size_nat b)) a b
+
+ (** val coq_Nsucc_double : n -> n **)
+
+ let coq_Nsucc_double = function
+ | N0 -> Npos XH
+ | Npos p -> Npos (XI p)
+
+ (** val coq_Ndouble : n -> n **)
+
+ let coq_Ndouble = function
+ | N0 -> N0
+ | Npos p -> Npos (XO p)
+
+ (** val coq_lor : positive -> positive -> positive **)
+
+ let rec coq_lor p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> XI (coq_lor p2 q1)
+ | XO q1 -> XI (coq_lor p2 q1)
+ | XH -> p)
+ | XO p2 ->
+ (match q0 with
+ | XI q1 -> XI (coq_lor p2 q1)
+ | XO q1 -> XO (coq_lor p2 q1)
+ | XH -> XI p2)
+ | XH ->
+ (match q0 with
+ | XO q1 -> XI q1
+ | _ -> q0)
+
+ (** val coq_land : positive -> positive -> n **)
+
+ let rec coq_land p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> coq_Nsucc_double (coq_land p2 q1)
+ | XO q1 -> coq_Ndouble (coq_land p2 q1)
+ | XH -> Npos XH)
+ | XO p2 ->
+ (match q0 with
+ | XI q1 -> coq_Ndouble (coq_land p2 q1)
+ | XO q1 -> coq_Ndouble (coq_land p2 q1)
+ | XH -> N0)
+ | XH ->
+ (match q0 with
+ | XO q1 -> N0
+ | _ -> Npos XH)
+
+ (** val ldiff : positive -> positive -> n **)
+
+ let rec ldiff p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> coq_Ndouble (ldiff p2 q1)
+ | XO q1 -> coq_Nsucc_double (ldiff p2 q1)
+ | XH -> Npos (XO p2))
+ | XO p2 ->
+ (match q0 with
+ | XI q1 -> coq_Ndouble (ldiff p2 q1)
+ | XO q1 -> coq_Ndouble (ldiff p2 q1)
+ | XH -> Npos p)
+ | XH ->
+ (match q0 with
+ | XO q1 -> Npos XH
+ | _ -> N0)
+
+ (** val coq_lxor : positive -> positive -> n **)
+
+ let rec coq_lxor p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> coq_Ndouble (coq_lxor p2 q1)
+ | XO q1 -> coq_Nsucc_double (coq_lxor p2 q1)
+ | XH -> Npos (XO p2))
+ | XO p2 ->
+ (match q0 with
+ | XI q1 -> coq_Nsucc_double (coq_lxor p2 q1)
+ | XO q1 -> coq_Ndouble (coq_lxor p2 q1)
+ | XH -> Npos (XI p2))
+ | XH ->
+ (match q0 with
+ | XI q1 -> Npos (XO q1)
+ | XO q1 -> Npos (XI q1)
+ | XH -> N0)
+
+ (** val shiftl_nat : positive -> nat -> positive **)
+
+ let shiftl_nat p n0 =
+ nat_iter n0 (fun x -> XO x) p
+
+ (** val shiftr_nat : positive -> nat -> positive **)
+
+ let shiftr_nat p n0 =
+ nat_iter n0 div2 p
+
+ (** val shiftl : positive -> n -> positive **)
+
+ let shiftl p = function
+ | N0 -> p
+ | Npos n1 -> iter n1 (fun x -> XO x) p
+
+ (** val shiftr : positive -> n -> positive **)
+
+ let shiftr p = function
+ | N0 -> p
+ | Npos n1 -> iter n1 div2 p
+
+ (** val testbit_nat : positive -> nat -> bool **)
+
+ let rec testbit_nat p n0 =
+ match p with
+ | XI p2 ->
+ (match n0 with
+ | O -> true
+ | S n' -> testbit_nat p2 n')
+ | XO p2 ->
+ (match n0 with
+ | O -> false
+ | S n' -> testbit_nat p2 n')
+ | XH ->
+ (match n0 with
+ | O -> true
+ | S n1 -> false)
+
+ (** val testbit : positive -> n -> bool **)
+
+ let rec testbit p n0 =
+ match p with
+ | XI p2 ->
+ (match n0 with
+ | N0 -> true
+ | Npos n1 -> testbit p2 (pred_N n1))
+ | XO p2 ->
+ (match n0 with
+ | N0 -> false
+ | Npos n1 -> testbit p2 (pred_N n1))
+ | XH ->
+ (match n0 with
+ | N0 -> true
+ | Npos p2 -> false)
+
+ (** val iter_op : ('a1 -> 'a1 -> 'a1) -> positive -> 'a1 -> 'a1 **)
+
+ let rec iter_op op p a =
+ match p with
+ | XI p2 -> op a (iter_op op p2 (op a a))
+ | XO p2 -> iter_op op p2 (op a a)
+ | XH -> a
+
+ (** val to_nat : positive -> nat **)
+
+ let to_nat x =
+ iter_op plus x (S O)
+
+ (** val of_nat : nat -> positive **)
+
+ let rec of_nat = function
+ | O -> XH
+ | S x ->
+ (match x with
+ | O -> XH
+ | S n1 -> succ (of_nat x))
+
+ (** val of_succ_nat : nat -> positive **)
+
+ let rec of_succ_nat = function
+ | O -> XH
+ | S x -> succ (of_succ_nat x)
+ end
+
+module Coq_Pos =
+ struct
+ module Coq__1 = struct
+ type t = positive
+ end
+ type t = Coq__1.t
+
+ (** val succ : positive -> positive **)
+
+ let rec succ = function
+ | XI p -> XO (succ p)
+ | XO p -> XI p
+ | XH -> XO XH
+
+ (** val add : positive -> positive -> positive **)
+
+ let rec add x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> XO (add_carry p q0)
+ | XO q0 -> XI (add p q0)
+ | XH -> XO (succ p))
+ | XO p ->
+ (match y with
+ | XI q0 -> XI (add p q0)
+ | XO q0 -> XO (add p q0)
+ | XH -> XI p)
+ | XH ->
+ (match y with
+ | XI q0 -> XO (succ q0)
+ | XO q0 -> XI q0
+ | XH -> XO XH)
+
+ (** val add_carry : positive -> positive -> positive **)
+
+ and add_carry x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> XI (add_carry p q0)
+ | XO q0 -> XO (add_carry p q0)
+ | XH -> XI (succ p))
+ | XO p ->
+ (match y with
+ | XI q0 -> XO (add_carry p q0)
+ | XO q0 -> XI (add p q0)
+ | XH -> XO (succ p))
+ | XH ->
+ (match y with
+ | XI q0 -> XI (succ q0)
+ | XO q0 -> XO (succ q0)
+ | XH -> XI XH)
+
+ (** val pred_double : positive -> positive **)
+
+ let rec pred_double = function
+ | XI p -> XI (XO p)
+ | XO p -> XI (pred_double p)
+ | XH -> XH
+
+ (** val pred : positive -> positive **)
+
+ let pred = function
+ | XI p -> XO p
+ | XO p -> pred_double p
+ | XH -> XH
+
+ (** val pred_N : positive -> n **)
+
+ let pred_N = function
+ | XI p -> Npos (XO p)
+ | XO p -> Npos (pred_double p)
+ | XH -> N0
+
+ type mask = Pos.mask =
+ | IsNul
+ | IsPos of positive
+ | IsNeg
+
+ (** val mask_rect : 'a1 -> (positive -> 'a1) -> 'a1 -> mask -> 'a1 **)
+
+ let mask_rect f f0 f1 = function
+ | IsNul -> f
+ | IsPos x -> f0 x
+ | IsNeg -> f1
+
+ (** val mask_rec : 'a1 -> (positive -> 'a1) -> 'a1 -> mask -> 'a1 **)
+
+ let mask_rec f f0 f1 = function
+ | IsNul -> f
+ | IsPos x -> f0 x
+ | IsNeg -> f1
+
+ (** val succ_double_mask : mask -> mask **)
+
+ let succ_double_mask = function
+ | IsNul -> IsPos XH
+ | IsPos p -> IsPos (XI p)
+ | IsNeg -> IsNeg
+
+ (** val double_mask : mask -> mask **)
+
+ let double_mask = function
+ | IsPos p -> IsPos (XO p)
+ | x0 -> x0
+
+ (** val double_pred_mask : positive -> mask **)
+
+ let double_pred_mask = function
+ | XI p -> IsPos (XO (XO p))
+ | XO p -> IsPos (XO (pred_double p))
+ | XH -> IsNul
+
+ (** val pred_mask : mask -> mask **)
+
+ let pred_mask = function
+ | IsPos q0 ->
+ (match q0 with
+ | XH -> IsNul
+ | _ -> IsPos (pred q0))
+ | _ -> IsNeg
+
+ (** val sub_mask : positive -> positive -> mask **)
+
+ let rec sub_mask x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> double_mask (sub_mask p q0)
+ | XO q0 -> succ_double_mask (sub_mask p q0)
+ | XH -> IsPos (XO p))
+ | XO p ->
+ (match y with
+ | XI q0 -> succ_double_mask (sub_mask_carry p q0)
+ | XO q0 -> double_mask (sub_mask p q0)
+ | XH -> IsPos (pred_double p))
+ | XH ->
+ (match y with
+ | XH -> IsNul
+ | _ -> IsNeg)
+
+ (** val sub_mask_carry : positive -> positive -> mask **)
+
+ and sub_mask_carry x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> succ_double_mask (sub_mask_carry p q0)
+ | XO q0 -> double_mask (sub_mask p q0)
+ | XH -> IsPos (pred_double p))
+ | XO p ->
+ (match y with
+ | XI q0 -> double_mask (sub_mask_carry p q0)
+ | XO q0 -> succ_double_mask (sub_mask_carry p q0)
+ | XH -> double_pred_mask p)
+ | XH -> IsNeg
+
+ (** val sub : positive -> positive -> positive **)
+
+ let sub x y =
+ match sub_mask x y with
+ | IsPos z0 -> z0
+ | _ -> XH
+
+ (** val mul : positive -> positive -> positive **)
+
+ let rec mul x y =
+ match x with
+ | XI p -> add y (XO (mul p y))
+ | XO p -> XO (mul p y)
+ | XH -> y
+
+ (** val iter : positive -> ('a1 -> 'a1) -> 'a1 -> 'a1 **)
+
+ let rec iter n0 f x =
+ match n0 with
+ | XI n' -> f (iter n' f (iter n' f x))
+ | XO n' -> iter n' f (iter n' f x)
+ | XH -> f x
+
+ (** val pow : positive -> positive -> positive **)
+
+ let pow x y =
+ iter y (mul x) XH
+
+ (** val div2 : positive -> positive **)
+
+ let div2 = function
+ | XI p2 -> p2
+ | XO p2 -> p2
+ | XH -> XH
+
+ (** val div2_up : positive -> positive **)
+
+ let div2_up = function
+ | XI p2 -> succ p2
+ | XO p2 -> p2
+ | XH -> XH
+
+ (** val size_nat : positive -> nat **)
+
+ let rec size_nat = function
+ | XI p2 -> S (size_nat p2)
+ | XO p2 -> S (size_nat p2)
+ | XH -> S O
+
+ (** val size : positive -> positive **)
+
+ let rec size = function
+ | XI p2 -> succ (size p2)
+ | XO p2 -> succ (size p2)
+ | XH -> XH
+
+ (** val compare_cont : positive -> positive -> comparison -> comparison **)
+
+ let rec compare_cont x y r =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> compare_cont p q0 r
+ | XO q0 -> compare_cont p q0 Gt
+ | XH -> Gt)
+ | XO p ->
+ (match y with
+ | XI q0 -> compare_cont p q0 Lt
+ | XO q0 -> compare_cont p q0 r
+ | XH -> Gt)
+ | XH ->
+ (match y with
+ | XH -> r
+ | _ -> Lt)
+
+ (** val compare : positive -> positive -> comparison **)
+
+ let compare x y =
+ compare_cont x y Eq
+
+ (** val min : positive -> positive -> positive **)
+
+ let min p p' =
+ match compare p p' with
+ | Gt -> p'
+ | _ -> p
+
+ (** val max : positive -> positive -> positive **)
+
+ let max p p' =
+ match compare p p' with
+ | Gt -> p
+ | _ -> p'
+
+ (** val eqb : positive -> positive -> bool **)
+
+ let rec eqb p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> eqb p2 q1
+ | _ -> false)
+ | XO p2 ->
+ (match q0 with
+ | XO q1 -> eqb p2 q1
+ | _ -> false)
+ | XH ->
+ (match q0 with
+ | XH -> true
+ | _ -> false)
+
+ (** val leb : positive -> positive -> bool **)
+
+ let leb x y =
+ match compare x y with
+ | Gt -> false
+ | _ -> true
+
+ (** val ltb : positive -> positive -> bool **)
+
+ let ltb x y =
+ match compare x y with
+ | Lt -> true
+ | _ -> false
+
+ (** val sqrtrem_step :
+ (positive -> positive) -> (positive -> positive) -> (positive * mask)
+ -> positive * mask **)
+
+ let sqrtrem_step f g = function
+ | s,y ->
+ (match y with
+ | IsPos r ->
+ let s' = XI (XO s) in
+ let r' = g (f r) in
+ if leb s' r' then (XI s),(sub_mask r' s') else (XO s),(IsPos r')
+ | _ -> (XO s),(sub_mask (g (f XH)) (XO (XO XH))))
+
+ (** val sqrtrem : positive -> positive * mask **)
+
+ let rec sqrtrem = function
+ | XI p2 ->
+ (match p2 with
+ | XI p3 -> sqrtrem_step (fun x -> XI x) (fun x -> XI x) (sqrtrem p3)
+ | XO p3 -> sqrtrem_step (fun x -> XO x) (fun x -> XI x) (sqrtrem p3)
+ | XH -> XH,(IsPos (XO XH)))
+ | XO p2 ->
+ (match p2 with
+ | XI p3 -> sqrtrem_step (fun x -> XI x) (fun x -> XO x) (sqrtrem p3)
+ | XO p3 -> sqrtrem_step (fun x -> XO x) (fun x -> XO x) (sqrtrem p3)
+ | XH -> XH,(IsPos XH))
+ | XH -> XH,IsNul
+
+ (** val sqrt : positive -> positive **)
+
+ let sqrt p =
+ fst (sqrtrem p)
+
+ (** val gcdn : nat -> positive -> positive -> positive **)
+
+ let rec gcdn n0 a b =
+ match n0 with
+ | O -> XH
+ | S n1 ->
+ (match a with
+ | XI a' ->
+ (match b with
+ | XI b' ->
+ (match compare a' b' with
+ | Eq -> a
+ | Lt -> gcdn n1 (sub b' a') a
+ | Gt -> gcdn n1 (sub a' b') b)
+ | XO b0 -> gcdn n1 a b0
+ | XH -> XH)
+ | XO a0 ->
+ (match b with
+ | XI p -> gcdn n1 a0 b
+ | XO b0 -> XO (gcdn n1 a0 b0)
+ | XH -> XH)
+ | XH -> XH)
+
+ (** val gcd : positive -> positive -> positive **)
+
+ let gcd a b =
+ gcdn (plus (size_nat a) (size_nat b)) a b
+
+ (** val ggcdn :
+ nat -> positive -> positive -> positive * (positive * positive) **)
+
+ let rec ggcdn n0 a b =
+ match n0 with
+ | O -> XH,(a,b)
+ | S n1 ->
+ (match a with
+ | XI a' ->
+ (match b with
+ | XI b' ->
+ (match compare a' b' with
+ | Eq -> a,(XH,XH)
+ | Lt ->
+ let g,p = ggcdn n1 (sub b' a') a in
+ let ba,aa = p in g,(aa,(add aa (XO ba)))
+ | Gt ->
+ let g,p = ggcdn n1 (sub a' b') b in
+ let ab,bb = p in g,((add bb (XO ab)),bb))
+ | XO b0 ->
+ let g,p = ggcdn n1 a b0 in let aa,bb = p in g,(aa,(XO bb))
+ | XH -> XH,(a,XH))
+ | XO a0 ->
+ (match b with
+ | XI p ->
+ let g,p2 = ggcdn n1 a0 b in let aa,bb = p2 in g,((XO aa),bb)
+ | XO b0 -> let g,p = ggcdn n1 a0 b0 in (XO g),p
+ | XH -> XH,(a,XH))
+ | XH -> XH,(XH,b))
+
+ (** val ggcd : positive -> positive -> positive * (positive * positive) **)
+
+ let ggcd a b =
+ ggcdn (plus (size_nat a) (size_nat b)) a b
+
+ (** val coq_Nsucc_double : n -> n **)
+
+ let coq_Nsucc_double = function
+ | N0 -> Npos XH
+ | Npos p -> Npos (XI p)
+
+ (** val coq_Ndouble : n -> n **)
+
+ let coq_Ndouble = function
+ | N0 -> N0
+ | Npos p -> Npos (XO p)
+
+ (** val coq_lor : positive -> positive -> positive **)
+
+ let rec coq_lor p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> XI (coq_lor p2 q1)
+ | XO q1 -> XI (coq_lor p2 q1)
+ | XH -> p)
+ | XO p2 ->
+ (match q0 with
+ | XI q1 -> XI (coq_lor p2 q1)
+ | XO q1 -> XO (coq_lor p2 q1)
+ | XH -> XI p2)
+ | XH ->
+ (match q0 with
+ | XO q1 -> XI q1
+ | _ -> q0)
+
+ (** val coq_land : positive -> positive -> n **)
+
+ let rec coq_land p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> coq_Nsucc_double (coq_land p2 q1)
+ | XO q1 -> coq_Ndouble (coq_land p2 q1)
+ | XH -> Npos XH)
+ | XO p2 ->
+ (match q0 with
+ | XI q1 -> coq_Ndouble (coq_land p2 q1)
+ | XO q1 -> coq_Ndouble (coq_land p2 q1)
+ | XH -> N0)
+ | XH ->
+ (match q0 with
+ | XO q1 -> N0
+ | _ -> Npos XH)
+
+ (** val ldiff : positive -> positive -> n **)
+
+ let rec ldiff p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> coq_Ndouble (ldiff p2 q1)
+ | XO q1 -> coq_Nsucc_double (ldiff p2 q1)
+ | XH -> Npos (XO p2))
+ | XO p2 ->
+ (match q0 with
+ | XI q1 -> coq_Ndouble (ldiff p2 q1)
+ | XO q1 -> coq_Ndouble (ldiff p2 q1)
+ | XH -> Npos p)
+ | XH ->
+ (match q0 with
+ | XO q1 -> Npos XH
+ | _ -> N0)
+
+ (** val coq_lxor : positive -> positive -> n **)
+
+ let rec coq_lxor p q0 =
+ match p with
+ | XI p2 ->
+ (match q0 with
+ | XI q1 -> coq_Ndouble (coq_lxor p2 q1)
+ | XO q1 -> coq_Nsucc_double (coq_lxor p2 q1)
+ | XH -> Npos (XO p2))
+ | XO p2 ->
+ (match q0 with
+ | XI q1 -> coq_Nsucc_double (coq_lxor p2 q1)
+ | XO q1 -> coq_Ndouble (coq_lxor p2 q1)
+ | XH -> Npos (XI p2))
+ | XH ->
+ (match q0 with
+ | XI q1 -> Npos (XO q1)
+ | XO q1 -> Npos (XI q1)
+ | XH -> N0)
+
+ (** val shiftl_nat : positive -> nat -> positive **)
+
+ let shiftl_nat p n0 =
+ nat_iter n0 (fun x -> XO x) p
+
+ (** val shiftr_nat : positive -> nat -> positive **)
+
+ let shiftr_nat p n0 =
+ nat_iter n0 div2 p
+
+ (** val shiftl : positive -> n -> positive **)
+
+ let shiftl p = function
+ | N0 -> p
+ | Npos n1 -> iter n1 (fun x -> XO x) p
+
+ (** val shiftr : positive -> n -> positive **)
+
+ let shiftr p = function
+ | N0 -> p
+ | Npos n1 -> iter n1 div2 p
+
+ (** val testbit_nat : positive -> nat -> bool **)
+
+ let rec testbit_nat p n0 =
+ match p with
+ | XI p2 ->
+ (match n0 with
+ | O -> true
+ | S n' -> testbit_nat p2 n')
+ | XO p2 ->
+ (match n0 with
+ | O -> false
+ | S n' -> testbit_nat p2 n')
+ | XH ->
+ (match n0 with
+ | O -> true
+ | S n1 -> false)
+
+ (** val testbit : positive -> n -> bool **)
+
+ let rec testbit p n0 =
+ match p with
+ | XI p2 ->
+ (match n0 with
+ | N0 -> true
+ | Npos n1 -> testbit p2 (pred_N n1))
+ | XO p2 ->
+ (match n0 with
+ | N0 -> false
+ | Npos n1 -> testbit p2 (pred_N n1))
+ | XH ->
+ (match n0 with
+ | N0 -> true
+ | Npos p2 -> false)
+
+ (** val iter_op : ('a1 -> 'a1 -> 'a1) -> positive -> 'a1 -> 'a1 **)
+
+ let rec iter_op op p a =
+ match p with
+ | XI p2 -> op a (iter_op op p2 (op a a))
+ | XO p2 -> iter_op op p2 (op a a)
+ | XH -> a
+
+ (** val to_nat : positive -> nat **)
+
+ let to_nat x =
+ iter_op plus x (S O)
+
+ (** val of_nat : nat -> positive **)
+
+ let rec of_nat = function
+ | O -> XH
+ | S x ->
+ (match x with
+ | O -> XH
+ | S n1 -> succ (of_nat x))
+
+ (** val of_succ_nat : nat -> positive **)
+
+ let rec of_succ_nat = function
+ | O -> XH
+ | S x -> succ (of_succ_nat x)
+
+ (** val eq_dec : positive -> positive -> bool **)
+
+ let rec eq_dec p y0 =
+ match p with
+ | XI p2 ->
+ (match y0 with
+ | XI p3 -> eq_dec p2 p3
+ | _ -> false)
+ | XO p2 ->
+ (match y0 with
+ | XO p3 -> eq_dec p2 p3
+ | _ -> false)
+ | XH ->
+ (match y0 with
+ | XH -> true
+ | _ -> false)
+
+ (** val peano_rect : 'a1 -> (positive -> 'a1 -> 'a1) -> positive -> 'a1 **)
+
+ let rec peano_rect a f p =
+ let f2 = peano_rect (f XH a) (fun p2 x -> f (succ (XO p2)) (f (XO p2) x))
+ in
+ (match p with
+ | XI q0 -> f (XO q0) (f2 q0)
+ | XO q0 -> f2 q0
+ | XH -> a)
+
+ (** val peano_rec : 'a1 -> (positive -> 'a1 -> 'a1) -> positive -> 'a1 **)
+
+ let peano_rec =
+ peano_rect
+
+ type coq_PeanoView =
+ | PeanoOne
+ | PeanoSucc of positive * coq_PeanoView
+
+ (** val coq_PeanoView_rect :
+ 'a1 -> (positive -> coq_PeanoView -> 'a1 -> 'a1) -> positive ->
+ coq_PeanoView -> 'a1 **)
+
+ let rec coq_PeanoView_rect f f0 p = function
+ | PeanoOne -> f
+ | PeanoSucc (p3, p4) -> f0 p3 p4 (coq_PeanoView_rect f f0 p3 p4)
+
+ (** val coq_PeanoView_rec :
+ 'a1 -> (positive -> coq_PeanoView -> 'a1 -> 'a1) -> positive ->
+ coq_PeanoView -> 'a1 **)
+
+ let rec coq_PeanoView_rec f f0 p = function
+ | PeanoOne -> f
+ | PeanoSucc (p3, p4) -> f0 p3 p4 (coq_PeanoView_rec f f0 p3 p4)
+
+ (** val peanoView_xO : positive -> coq_PeanoView -> coq_PeanoView **)
+
+ let rec peanoView_xO p = function
+ | PeanoOne -> PeanoSucc (XH, PeanoOne)
+ | PeanoSucc (p2, q1) ->
+ PeanoSucc ((succ (XO p2)), (PeanoSucc ((XO p2), (peanoView_xO p2 q1))))
+
+ (** val peanoView_xI : positive -> coq_PeanoView -> coq_PeanoView **)
+
+ let rec peanoView_xI p = function
+ | PeanoOne -> PeanoSucc ((succ XH), (PeanoSucc (XH, PeanoOne)))
+ | PeanoSucc (p2, q1) ->
+ PeanoSucc ((succ (XI p2)), (PeanoSucc ((XI p2), (peanoView_xI p2 q1))))
+
+ (** val peanoView : positive -> coq_PeanoView **)
+
+ let rec peanoView = function
+ | XI p2 -> peanoView_xI p2 (peanoView p2)
+ | XO p2 -> peanoView_xO p2 (peanoView p2)
+ | XH -> PeanoOne
+
+ (** val coq_PeanoView_iter :
+ 'a1 -> (positive -> 'a1 -> 'a1) -> positive -> coq_PeanoView -> 'a1 **)
+
+ let rec coq_PeanoView_iter a f p = function
+ | PeanoOne -> a
+ | PeanoSucc (p2, q1) -> f p2 (coq_PeanoView_iter a f p2 q1)
+
+ (** val switch_Eq : comparison -> comparison -> comparison **)
+
+ let switch_Eq c = function
+ | Eq -> c
+ | x -> x
+
+ (** val mask2cmp : mask -> comparison **)
+
+ let mask2cmp = function
+ | IsNul -> Eq
+ | IsPos p2 -> Gt
+ | IsNeg -> Lt
+
+ module T =
+ struct
+
+ end
+
+ module ORev =
+ struct
+ type t = Coq__1.t
+ end
+
+ module MRev =
+ struct
+ (** val max : t -> t -> t **)
+
+ let max x y =
+ min y x
+ end
+
+ module MPRev = MaxLogicalProperties(ORev)(MRev)
+
+ module P =
+ struct
+ (** val max_case_strong :
+ t -> t -> (t -> t -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1)
+ -> 'a1 **)
+
+ let max_case_strong n0 m compat hl hr =
+ let c = compSpec2Type n0 m (compare n0 m) in
+ (match c with
+ | CompGtT -> compat n0 (max n0 m) __ (hl __)
+ | _ -> compat m (max n0 m) __ (hr __))
+
+ (** val max_case :
+ t -> t -> (t -> t -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 **)
+
+ let max_case n0 m x x0 x1 =
+ max_case_strong n0 m x (fun _ -> x0) (fun _ -> x1)
+
+ (** val max_dec : t -> t -> bool **)
+
+ let max_dec n0 m =
+ max_case n0 m (fun x y _ h0 -> h0) true false
+
+ (** val min_case_strong :
+ t -> t -> (t -> t -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1)
+ -> 'a1 **)
+
+ let min_case_strong n0 m compat hl hr =
+ let c = compSpec2Type n0 m (compare n0 m) in
+ (match c with
+ | CompGtT -> compat m (min n0 m) __ (hr __)
+ | _ -> compat n0 (min n0 m) __ (hl __))
+
+ (** val min_case :
+ t -> t -> (t -> t -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 **)
+
+ let min_case n0 m x x0 x1 =
+ min_case_strong n0 m x (fun _ -> x0) (fun _ -> x1)
+
+ (** val min_dec : t -> t -> bool **)
+
+ let min_dec n0 m =
+ min_case n0 m (fun x y _ h0 -> h0) true false
+ end
+
+ (** val max_case_strong : t -> t -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **)
+
+ let max_case_strong n0 m x x0 =
+ P.max_case_strong n0 m (fun x1 y _ x2 -> x2) x x0
+
+ (** val max_case : t -> t -> 'a1 -> 'a1 -> 'a1 **)
+
+ let max_case n0 m x x0 =
+ max_case_strong n0 m (fun _ -> x) (fun _ -> x0)
+
+ (** val max_dec : t -> t -> bool **)
+
+ let max_dec =
+ P.max_dec
+
+ (** val min_case_strong : t -> t -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **)
+
+ let min_case_strong n0 m x x0 =
+ P.min_case_strong n0 m (fun x1 y _ x2 -> x2) x x0
+
+ (** val min_case : t -> t -> 'a1 -> 'a1 -> 'a1 **)
+
+ let min_case n0 m x x0 =
+ min_case_strong n0 m (fun _ -> x) (fun _ -> x0)
+
+ (** val min_dec : t -> t -> bool **)
+
+ let min_dec =
+ P.min_dec
+ end
+
+module N =
+ struct
+ type t = n
+
+ (** val zero : n **)
+
+ let zero =
+ N0
+
+ (** val one : n **)
+
+ let one =
+ Npos XH
+
+ (** val two : n **)
+
+ let two =
+ Npos (XO XH)
+
+ (** val succ_double : n -> n **)
+
+ let succ_double = function
+ | N0 -> Npos XH
+ | Npos p -> Npos (XI p)
+
+ (** val double : n -> n **)
+
+ let double = function
+ | N0 -> N0
+ | Npos p -> Npos (XO p)
+
+ (** val succ : n -> n **)
+
+ let succ = function
+ | N0 -> Npos XH
+ | Npos p -> Npos (Coq_Pos.succ p)
+
+ (** val pred : n -> n **)
+
+ let pred = function
+ | N0 -> N0
+ | Npos p -> Coq_Pos.pred_N p
+
+ (** val succ_pos : n -> positive **)
+
+ let succ_pos = function
+ | N0 -> XH
+ | Npos p -> Coq_Pos.succ p
+
+ (** val add : n -> n -> n **)
+
+ let add n0 m =
+ match n0 with
+ | N0 -> m
+ | Npos p ->
+ (match m with
+ | N0 -> n0
+ | Npos q0 -> Npos (Coq_Pos.add p q0))
+
+ (** val sub : n -> n -> n **)
+
+ let sub n0 m =
+ match n0 with
+ | N0 -> N0
+ | Npos n' ->
+ (match m with
+ | N0 -> n0
+ | Npos m' ->
+ (match Coq_Pos.sub_mask n' m' with
+ | Coq_Pos.IsPos p -> Npos p
+ | _ -> N0))
+
+ (** val mul : n -> n -> n **)
+
+ let mul n0 m =
+ match n0 with
+ | N0 -> N0
+ | Npos p ->
+ (match m with
+ | N0 -> N0
+ | Npos q0 -> Npos (Coq_Pos.mul p q0))
+
+ (** val compare : n -> n -> comparison **)
+
+ let compare n0 m =
+ match n0 with
+ | N0 ->
+ (match m with
+ | N0 -> Eq
+ | Npos m' -> Lt)
+ | Npos n' ->
+ (match m with
+ | N0 -> Gt
+ | Npos m' -> Coq_Pos.compare n' m')
+
+ (** val eqb : n -> n -> bool **)
+
+ let rec eqb n0 m =
+ match n0 with
+ | N0 ->
+ (match m with
+ | N0 -> true
+ | Npos p -> false)
+ | Npos p ->
+ (match m with
+ | N0 -> false
+ | Npos q0 -> Coq_Pos.eqb p q0)
+
+ (** val leb : n -> n -> bool **)
+
+ let leb x y =
+ match compare x y with
+ | Gt -> false
+ | _ -> true
+
+ (** val ltb : n -> n -> bool **)
+
+ let ltb x y =
+ match compare x y with
+ | Lt -> true
+ | _ -> false
+
+ (** val min : n -> n -> n **)
+
+ let min n0 n' =
+ match compare n0 n' with
+ | Gt -> n'
+ | _ -> n0
+
+ (** val max : n -> n -> n **)
+
+ let max n0 n' =
+ match compare n0 n' with
+ | Gt -> n0
+ | _ -> n'
+
+ (** val div2 : n -> n **)
+
+ let div2 = function
+ | N0 -> N0
+ | Npos p2 ->
+ (match p2 with
+ | XI p -> Npos p
+ | XO p -> Npos p
+ | XH -> N0)
+
+ (** val even : n -> bool **)
+
+ let even = function
+ | N0 -> true
+ | Npos p ->
+ (match p with
+ | XO p2 -> true
+ | _ -> false)
+
+ (** val odd : n -> bool **)
+
+ let odd n0 =
+ negb (even n0)
+
+ (** val pow : n -> n -> n **)
+
+ let pow n0 = function
+ | N0 -> Npos XH
+ | Npos p2 ->
+ (match n0 with
+ | N0 -> N0
+ | Npos q0 -> Npos (Coq_Pos.pow q0 p2))
+
+ (** val log2 : n -> n **)
+
+ let log2 = function
+ | N0 -> N0
+ | Npos p2 ->
+ (match p2 with
+ | XI p -> Npos (Coq_Pos.size p)
+ | XO p -> Npos (Coq_Pos.size p)
+ | XH -> N0)
+
+ (** val size : n -> n **)
+
+ let size = function
+ | N0 -> N0
+ | Npos p -> Npos (Coq_Pos.size p)
+
+ (** val size_nat : n -> nat **)
+
+ let size_nat = function
+ | N0 -> O
+ | Npos p -> Coq_Pos.size_nat p
+
+ (** val pos_div_eucl : positive -> n -> n * n **)
+
+ let rec pos_div_eucl a b =
+ match a with
+ | XI a' ->
+ let q0,r = pos_div_eucl a' b in
+ let r' = succ_double r in
+ if leb b r' then (succ_double q0),(sub r' b) else (double q0),r'
+ | XO a' ->
+ let q0,r = pos_div_eucl a' b in
+ let r' = double r in
+ if leb b r' then (succ_double q0),(sub r' b) else (double q0),r'
+ | XH ->
+ (match b with
+ | N0 -> N0,(Npos XH)
+ | Npos p ->
+ (match p with
+ | XH -> (Npos XH),N0
+ | _ -> N0,(Npos XH)))
+
+ (** val div_eucl : n -> n -> n * n **)
+
+ let div_eucl a b =
+ match a with
+ | N0 -> N0,N0
+ | Npos na ->
+ (match b with
+ | N0 -> N0,a
+ | Npos p -> pos_div_eucl na b)
+
+ (** val div : n -> n -> n **)
+
+ let div a b =
+ fst (div_eucl a b)
+
+ (** val modulo : n -> n -> n **)
+
+ let modulo a b =
+ snd (div_eucl a b)
+
+ (** val gcd : n -> n -> n **)
+
+ let gcd a b =
+ match a with
+ | N0 -> b
+ | Npos p ->
+ (match b with
+ | N0 -> a
+ | Npos q0 -> Npos (Coq_Pos.gcd p q0))
+
+ (** val ggcd : n -> n -> n * (n * n) **)
+
+ let ggcd a b =
+ match a with
+ | N0 -> b,(N0,(Npos XH))
+ | Npos p ->
+ (match b with
+ | N0 -> a,((Npos XH),N0)
+ | Npos q0 ->
+ let g,p2 = Coq_Pos.ggcd p q0 in
+ let aa,bb = p2 in (Npos g),((Npos aa),(Npos bb)))
+
+ (** val sqrtrem : n -> n * n **)
+
+ let sqrtrem = function
+ | N0 -> N0,N0
+ | Npos p ->
+ let s,m = Coq_Pos.sqrtrem p in
+ (match m with
+ | Coq_Pos.IsPos r -> (Npos s),(Npos r)
+ | _ -> (Npos s),N0)
+
+ (** val sqrt : n -> n **)
+
+ let sqrt = function
+ | N0 -> N0
+ | Npos p -> Npos (Coq_Pos.sqrt p)
+
+ (** val coq_lor : n -> n -> n **)
+
+ let coq_lor n0 m =
+ match n0 with
+ | N0 -> m
+ | Npos p ->
+ (match m with
+ | N0 -> n0
+ | Npos q0 -> Npos (Coq_Pos.coq_lor p q0))
+
+ (** val coq_land : n -> n -> n **)
+
+ let coq_land n0 m =
+ match n0 with
+ | N0 -> N0
+ | Npos p ->
+ (match m with
+ | N0 -> N0
+ | Npos q0 -> Coq_Pos.coq_land p q0)
+
+ (** val ldiff : n -> n -> n **)
+
+ let rec ldiff n0 m =
+ match n0 with
+ | N0 -> N0
+ | Npos p ->
+ (match m with
+ | N0 -> n0
+ | Npos q0 -> Coq_Pos.ldiff p q0)
+
+ (** val coq_lxor : n -> n -> n **)
+
+ let coq_lxor n0 m =
+ match n0 with
+ | N0 -> m
+ | Npos p ->
+ (match m with
+ | N0 -> n0
+ | Npos q0 -> Coq_Pos.coq_lxor p q0)
+
+ (** val shiftl_nat : n -> nat -> n **)
+
+ let shiftl_nat a n0 =
+ nat_iter n0 double a
+
+ (** val shiftr_nat : n -> nat -> n **)
+
+ let shiftr_nat a n0 =
+ nat_iter n0 div2 a
+
+ (** val shiftl : n -> n -> n **)
+
+ let shiftl a n0 =
+ match a with
+ | N0 -> N0
+ | Npos a0 -> Npos (Coq_Pos.shiftl a0 n0)
+
+ (** val shiftr : n -> n -> n **)
+
+ let shiftr a = function
+ | N0 -> a
+ | Npos p -> Coq_Pos.iter p div2 a
+
+ (** val testbit_nat : n -> nat -> bool **)
+
+ let testbit_nat = function
+ | N0 -> (fun x -> false)
+ | Npos p -> Coq_Pos.testbit_nat p
+
+ (** val testbit : n -> n -> bool **)
+
+ let testbit a n0 =
+ match a with
+ | N0 -> false
+ | Npos p -> Coq_Pos.testbit p n0
+
+ (** val to_nat : n -> nat **)
+
+ let to_nat = function
+ | N0 -> O
+ | Npos p -> Coq_Pos.to_nat p
+
+ (** val of_nat : nat -> n **)
+
+ let of_nat = function
+ | O -> N0
+ | S n' -> Npos (Coq_Pos.of_succ_nat n')
+
+ (** val iter : n -> ('a1 -> 'a1) -> 'a1 -> 'a1 **)
+
+ let iter n0 f x =
+ match n0 with
+ | N0 -> x
+ | Npos p -> Coq_Pos.iter p f x
+
+ (** val eq_dec : n -> n -> bool **)
+
+ let eq_dec n0 m =
+ match n0 with
+ | N0 ->
+ (match m with
+ | N0 -> true
+ | Npos p -> false)
+ | Npos x ->
+ (match m with
+ | N0 -> false
+ | Npos p2 -> Coq_Pos.eq_dec x p2)
+
+ (** val discr : n -> positive option **)
+
+ let discr = function
+ | N0 -> None
+ | Npos p -> Some p
+
+ (** val binary_rect :
+ 'a1 -> (n -> 'a1 -> 'a1) -> (n -> 'a1 -> 'a1) -> n -> 'a1 **)
+
+ let binary_rect f0 f2 fS2 n0 =
+ let f2' = fun p -> f2 (Npos p) in
+ let fS2' = fun p -> fS2 (Npos p) in
+ (match n0 with
+ | N0 -> f0
+ | Npos p ->
+ let rec f = function
+ | XI p3 -> fS2' p3 (f p3)
+ | XO p3 -> f2' p3 (f p3)
+ | XH -> fS2 N0 f0
+ in f p)
+
+ (** val binary_rec :
+ 'a1 -> (n -> 'a1 -> 'a1) -> (n -> 'a1 -> 'a1) -> n -> 'a1 **)
+
+ let binary_rec =
+ binary_rect
+
+ (** val peano_rect : 'a1 -> (n -> 'a1 -> 'a1) -> n -> 'a1 **)
+
+ let peano_rect f0 f n0 =
+ let f' = fun p -> f (Npos p) in
+ (match n0 with
+ | N0 -> f0
+ | Npos p -> Coq_Pos.peano_rect (f N0 f0) f' p)
+
+ (** val peano_rec : 'a1 -> (n -> 'a1 -> 'a1) -> n -> 'a1 **)
+
+ let peano_rec =
+ peano_rect
+
+ module BootStrap =
+ struct
+
+ end
+
+ (** val recursion : 'a1 -> (n -> 'a1 -> 'a1) -> n -> 'a1 **)
+
+ let recursion x =
+ peano_rect x
+
+ module OrderElts =
+ struct
+ type t = n
+ end
+
+ module OrderTac = MakeOrderTac(OrderElts)
+
+ module NZPowP =
+ struct
+
+ end
+
+ module NZSqrtP =
+ struct
+
+ end
+
+ (** val sqrt_up : n -> n **)
+
+ let sqrt_up a =
+ match compare N0 a with
+ | Lt -> succ (sqrt (pred a))
+ | _ -> N0
+
+ (** val log2_up : n -> n **)
+
+ let log2_up a =
+ match compare (Npos XH) a with
+ | Lt -> succ (log2 (pred a))
+ | _ -> N0
+
+ module NZDivP =
+ struct
+
+ end
+
+ (** val lcm : n -> n -> n **)
+
+ let lcm a b =
+ mul a (div b (gcd a b))
+
+ (** val b2n : bool -> n **)
+
+ let b2n = function
+ | true -> Npos XH
+ | false -> N0
+
+ (** val setbit : n -> n -> n **)
+
+ let setbit a n0 =
+ coq_lor a (shiftl (Npos XH) n0)
+
+ (** val clearbit : n -> n -> n **)
+
+ let clearbit a n0 =
+ ldiff a (shiftl (Npos XH) n0)
+
+ (** val ones : n -> n **)
+
+ let ones n0 =
+ pred (shiftl (Npos XH) n0)
+
+ (** val lnot : n -> n -> n **)
+
+ let lnot a n0 =
+ coq_lxor a (ones n0)
+
+ module T =
+ struct
+
+ end
+
+ module ORev =
+ struct
+ type t = n
+ end
+
+ module MRev =
+ struct
+ (** val max : n -> n -> n **)
+
+ let max x y =
+ min y x
+ end
+
+ module MPRev = MaxLogicalProperties(ORev)(MRev)
+
+ module P =
+ struct
+ (** val max_case_strong :
+ n -> n -> (n -> n -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1)
+ -> 'a1 **)
+
+ let max_case_strong n0 m compat hl hr =
+ let c = compSpec2Type n0 m (compare n0 m) in
+ (match c with
+ | CompGtT -> compat n0 (max n0 m) __ (hl __)
+ | _ -> compat m (max n0 m) __ (hr __))
+
+ (** val max_case :
+ n -> n -> (n -> n -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 **)
+
+ let max_case n0 m x x0 x1 =
+ max_case_strong n0 m x (fun _ -> x0) (fun _ -> x1)
+
+ (** val max_dec : n -> n -> bool **)
+
+ let max_dec n0 m =
+ max_case n0 m (fun x y _ h0 -> h0) true false
+
+ (** val min_case_strong :
+ n -> n -> (n -> n -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1)
+ -> 'a1 **)
+
+ let min_case_strong n0 m compat hl hr =
+ let c = compSpec2Type n0 m (compare n0 m) in
+ (match c with
+ | CompGtT -> compat m (min n0 m) __ (hr __)
+ | _ -> compat n0 (min n0 m) __ (hl __))
+
+ (** val min_case :
+ n -> n -> (n -> n -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 **)
+
+ let min_case n0 m x x0 x1 =
+ min_case_strong n0 m x (fun _ -> x0) (fun _ -> x1)
+
+ (** val min_dec : n -> n -> bool **)
+
+ let min_dec n0 m =
+ min_case n0 m (fun x y _ h0 -> h0) true false
+ end
+
+ (** val max_case_strong : n -> n -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **)
+
+ let max_case_strong n0 m x x0 =
+ P.max_case_strong n0 m (fun x1 y _ x2 -> x2) x x0
+
+ (** val max_case : n -> n -> 'a1 -> 'a1 -> 'a1 **)
+
+ let max_case n0 m x x0 =
+ max_case_strong n0 m (fun _ -> x) (fun _ -> x0)
+
+ (** val max_dec : n -> n -> bool **)
+
+ let max_dec =
+ P.max_dec
+
+ (** val min_case_strong : n -> n -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **)
+
+ let min_case_strong n0 m x x0 =
+ P.min_case_strong n0 m (fun x1 y _ x2 -> x2) x x0
+
+ (** val min_case : n -> n -> 'a1 -> 'a1 -> 'a1 **)
+
+ let min_case n0 m x x0 =
+ min_case_strong n0 m (fun _ -> x) (fun _ -> x0)
+
+ (** val min_dec : n -> n -> bool **)
+
+ let min_dec =
+ P.min_dec
+ end
(** val pow_pos : ('a1 -> 'a1 -> 'a1) -> 'a1 -> positive -> 'a1 **)
@@ -228,268 +2010,773 @@ let rec nth n0 l default =
| S m ->
(match l with
| [] -> default
- | x::t0 -> nth m t0 default)
+ | x::t1 -> nth m t1 default)
(** val map : ('a1 -> 'a2) -> 'a1 list -> 'a2 list **)
let rec map f = function
| [] -> []
-| a::t0 -> (f a)::(map f t0)
+| a::t1 -> (f a)::(map f t1)
(** val fold_right : ('a2 -> 'a1 -> 'a1) -> 'a1 -> 'a2 list -> 'a1 **)
let rec fold_right f a0 = function
| [] -> a0
-| b::t0 -> f b (fold_right f a0 t0)
-
-type z =
-| Z0
-| Zpos of positive
-| Zneg of positive
-
-(** val zdouble_plus_one : z -> z **)
-
-let zdouble_plus_one = function
-| Z0 -> Zpos XH
-| Zpos p -> Zpos (XI p)
-| Zneg p -> Zneg (pdouble_minus_one p)
-
-(** val zdouble_minus_one : z -> z **)
-
-let zdouble_minus_one = function
-| Z0 -> Zneg XH
-| Zpos p -> Zpos (pdouble_minus_one p)
-| Zneg p -> Zneg (XI p)
-
-(** val zdouble : z -> z **)
-
-let zdouble = function
-| Z0 -> Z0
-| Zpos p -> Zpos (XO p)
-| Zneg p -> Zneg (XO p)
-
-(** val zPminus : positive -> positive -> z **)
-
-let rec zPminus x y =
- match x with
- | XI p ->
- (match y with
- | XI q0 -> zdouble (zPminus p q0)
- | XO q0 -> zdouble_plus_one (zPminus p q0)
- | XH -> Zpos (XO p))
- | XO p ->
- (match y with
- | XI q0 -> zdouble_minus_one (zPminus p q0)
- | XO q0 -> zdouble (zPminus p q0)
- | XH -> Zpos (pdouble_minus_one p))
- | XH ->
- (match y with
- | XI q0 -> Zneg (XO q0)
- | XO q0 -> Zneg (pdouble_minus_one q0)
- | XH -> Z0)
-
-(** val zplus : z -> z -> z **)
-
-let zplus x y =
- match x with
- | Z0 -> y
- | Zpos x' ->
- (match y with
- | Z0 -> Zpos x'
- | Zpos y' -> Zpos (pplus x' y')
- | Zneg y' ->
- (match pcompare x' y' Eq with
- | Eq -> Z0
- | Lt -> Zneg (pminus y' x')
- | Gt -> Zpos (pminus x' y')))
- | Zneg x' ->
- (match y with
- | Z0 -> Zneg x'
- | Zpos y' ->
- (match pcompare x' y' Eq with
- | Eq -> Z0
- | Lt -> Zpos (pminus y' x')
- | Gt -> Zneg (pminus x' y'))
- | Zneg y' -> Zneg (pplus x' y'))
-
-(** val zopp : z -> z **)
-
-let zopp = function
-| Z0 -> Z0
-| Zpos x0 -> Zneg x0
-| Zneg x0 -> Zpos x0
-
-(** val zminus : z -> z -> z **)
-
-let zminus m n0 =
- zplus m (zopp n0)
-
-(** val zmult : z -> z -> z **)
-
-let zmult x y =
- match x with
+| b::t1 -> f b (fold_right f a0 t1)
+
+module Z =
+ struct
+ type t = z
+
+ (** val zero : z **)
+
+ let zero =
+ Z0
+
+ (** val one : z **)
+
+ let one =
+ Zpos XH
+
+ (** val two : z **)
+
+ let two =
+ Zpos (XO XH)
+
+ (** val double : z -> z **)
+
+ let double = function
| Z0 -> Z0
- | Zpos x' ->
- (match y with
- | Z0 -> Z0
- | Zpos y' -> Zpos (pmult x' y')
- | Zneg y' -> Zneg (pmult x' y'))
- | Zneg x' ->
- (match y with
- | Z0 -> Z0
- | Zpos y' -> Zneg (pmult x' y')
- | Zneg y' -> Zpos (pmult x' y'))
-
-(** val zcompare : z -> z -> comparison **)
-
-let zcompare x y =
- match x with
- | Z0 ->
- (match y with
- | Z0 -> Eq
- | Zpos y' -> Lt
- | Zneg y' -> Gt)
- | Zpos x' ->
- (match y with
- | Zpos y' -> pcompare x' y' Eq
- | _ -> Gt)
- | Zneg x' ->
- (match y with
- | Zneg y' -> compOpp (pcompare x' y' Eq)
- | _ -> Lt)
-
-(** val zmax : z -> z -> z **)
-
-let zmax n0 m =
- match zcompare n0 m with
- | Lt -> m
- | _ -> n0
-
-(** val zabs : z -> z **)
-
-let zabs = function
-| Zneg p -> Zpos p
-| x -> x
-
-(** val zle_bool : z -> z -> bool **)
-
-let zle_bool x y =
- match zcompare x y with
- | Gt -> false
- | _ -> true
-
-(** val zge_bool : z -> z -> bool **)
-
-let zge_bool x y =
- match zcompare x y with
- | Lt -> false
- | _ -> true
-
-(** val zgt_bool : z -> z -> bool **)
-
-let zgt_bool x y =
- match zcompare x y with
- | Gt -> true
- | _ -> false
+ | Zpos p -> Zpos (XO p)
+ | Zneg p -> Zneg (XO p)
+
+ (** val succ_double : z -> z **)
+
+ let succ_double = function
+ | Z0 -> Zpos XH
+ | Zpos p -> Zpos (XI p)
+ | Zneg p -> Zneg (Coq_Pos.pred_double p)
+
+ (** val pred_double : z -> z **)
+
+ let pred_double = function
+ | Z0 -> Zneg XH
+ | Zpos p -> Zpos (Coq_Pos.pred_double p)
+ | Zneg p -> Zneg (XI p)
+
+ (** val pos_sub : positive -> positive -> z **)
+
+ let rec pos_sub x y =
+ match x with
+ | XI p ->
+ (match y with
+ | XI q0 -> double (pos_sub p q0)
+ | XO q0 -> succ_double (pos_sub p q0)
+ | XH -> Zpos (XO p))
+ | XO p ->
+ (match y with
+ | XI q0 -> pred_double (pos_sub p q0)
+ | XO q0 -> double (pos_sub p q0)
+ | XH -> Zpos (Coq_Pos.pred_double p))
+ | XH ->
+ (match y with
+ | XI q0 -> Zneg (XO q0)
+ | XO q0 -> Zneg (Coq_Pos.pred_double q0)
+ | XH -> Z0)
+
+ (** val add : z -> z -> z **)
+
+ let add x y =
+ match x with
+ | Z0 -> y
+ | Zpos x' ->
+ (match y with
+ | Z0 -> x
+ | Zpos y' -> Zpos (Coq_Pos.add x' y')
+ | Zneg y' -> pos_sub x' y')
+ | Zneg x' ->
+ (match y with
+ | Z0 -> x
+ | Zpos y' -> pos_sub y' x'
+ | Zneg y' -> Zneg (Coq_Pos.add x' y'))
+
+ (** val opp : z -> z **)
+
+ let opp = function
+ | Z0 -> Z0
+ | Zpos x0 -> Zneg x0
+ | Zneg x0 -> Zpos x0
+
+ (** val succ : z -> z **)
+
+ let succ x =
+ add x (Zpos XH)
+
+ (** val pred : z -> z **)
+
+ let pred x =
+ add x (Zneg XH)
+
+ (** val sub : z -> z -> z **)
+
+ let sub m n0 =
+ add m (opp n0)
+
+ (** val mul : z -> z -> z **)
+
+ let mul x y =
+ match x with
+ | Z0 -> Z0
+ | Zpos x' ->
+ (match y with
+ | Z0 -> Z0
+ | Zpos y' -> Zpos (Coq_Pos.mul x' y')
+ | Zneg y' -> Zneg (Coq_Pos.mul x' y'))
+ | Zneg x' ->
+ (match y with
+ | Z0 -> Z0
+ | Zpos y' -> Zneg (Coq_Pos.mul x' y')
+ | Zneg y' -> Zpos (Coq_Pos.mul x' y'))
+
+ (** val pow_pos : z -> positive -> z **)
+
+ let pow_pos z0 n0 =
+ Coq_Pos.iter n0 (mul z0) (Zpos XH)
+
+ (** val pow : z -> z -> z **)
+
+ let pow x = function
+ | Z0 -> Zpos XH
+ | Zpos p -> pow_pos x p
+ | Zneg p -> Z0
+
+ (** val compare : z -> z -> comparison **)
+
+ let compare x y =
+ match x with
+ | Z0 ->
+ (match y with
+ | Z0 -> Eq
+ | Zpos y' -> Lt
+ | Zneg y' -> Gt)
+ | Zpos x' ->
+ (match y with
+ | Zpos y' -> Coq_Pos.compare x' y'
+ | _ -> Gt)
+ | Zneg x' ->
+ (match y with
+ | Zneg y' -> compOpp (Coq_Pos.compare x' y')
+ | _ -> Lt)
+
+ (** val sgn : z -> z **)
+
+ let sgn = function
+ | Z0 -> Z0
+ | Zpos p -> Zpos XH
+ | Zneg p -> Zneg XH
+
+ (** val leb : z -> z -> bool **)
+
+ let leb x y =
+ match compare x y with
+ | Gt -> false
+ | _ -> true
+
+ (** val geb : z -> z -> bool **)
+
+ let geb x y =
+ match compare x y with
+ | Lt -> false
+ | _ -> true
+
+ (** val ltb : z -> z -> bool **)
+
+ let ltb x y =
+ match compare x y with
+ | Lt -> true
+ | _ -> false
+
+ (** val gtb : z -> z -> bool **)
+
+ let gtb x y =
+ match compare x y with
+ | Gt -> true
+ | _ -> false
+
+ (** val eqb : z -> z -> bool **)
+
+ let rec eqb x y =
+ match x with
+ | Z0 ->
+ (match y with
+ | Z0 -> true
+ | _ -> false)
+ | Zpos p ->
+ (match y with
+ | Zpos q0 -> Coq_Pos.eqb p q0
+ | _ -> false)
+ | Zneg p ->
+ (match y with
+ | Zneg q0 -> Coq_Pos.eqb p q0
+ | _ -> false)
+
+ (** val max : z -> z -> z **)
+
+ let max n0 m =
+ match compare n0 m with
+ | Lt -> m
+ | _ -> n0
+
+ (** val min : z -> z -> z **)
+
+ let min n0 m =
+ match compare n0 m with
+ | Gt -> m
+ | _ -> n0
+
+ (** val abs : z -> z **)
+
+ let abs = function
+ | Zneg p -> Zpos p
+ | x -> x
+
+ (** val abs_nat : z -> nat **)
+
+ let abs_nat = function
+ | Z0 -> O
+ | Zpos p -> Coq_Pos.to_nat p
+ | Zneg p -> Coq_Pos.to_nat p
+
+ (** val abs_N : z -> n **)
+
+ let abs_N = function
+ | Z0 -> N0
+ | Zpos p -> Npos p
+ | Zneg p -> Npos p
+
+ (** val to_nat : z -> nat **)
+
+ let to_nat = function
+ | Zpos p -> Coq_Pos.to_nat p
+ | _ -> O
+
+ (** val to_N : z -> n **)
+
+ let to_N = function
+ | Zpos p -> Npos p
+ | _ -> N0
+
+ (** val of_nat : nat -> z **)
+
+ let of_nat = function
+ | O -> Z0
+ | S n1 -> Zpos (Coq_Pos.of_succ_nat n1)
+
+ (** val of_N : n -> z **)
+
+ let of_N = function
+ | N0 -> Z0
+ | Npos p -> Zpos p
+
+ (** val iter : z -> ('a1 -> 'a1) -> 'a1 -> 'a1 **)
+
+ let iter n0 f x =
+ match n0 with
+ | Zpos p -> Coq_Pos.iter p f x
+ | _ -> x
+
+ (** val pos_div_eucl : positive -> z -> z * z **)
+
+ let rec pos_div_eucl a b =
+ match a with
+ | XI a' ->
+ let q0,r = pos_div_eucl a' b in
+ let r' = add (mul (Zpos (XO XH)) r) (Zpos XH) in
+ if gtb b r'
+ then (mul (Zpos (XO XH)) q0),r'
+ else (add (mul (Zpos (XO XH)) q0) (Zpos XH)),(sub r' b)
+ | XO a' ->
+ let q0,r = pos_div_eucl a' b in
+ let r' = mul (Zpos (XO XH)) r in
+ if gtb b r'
+ then (mul (Zpos (XO XH)) q0),r'
+ else (add (mul (Zpos (XO XH)) q0) (Zpos XH)),(sub r' b)
+ | XH -> if geb b (Zpos (XO XH)) then Z0,(Zpos XH) else (Zpos XH),Z0
+
+ (** val div_eucl : z -> z -> z * z **)
+
+ let div_eucl a b =
+ match a with
+ | Z0 -> Z0,Z0
+ | Zpos a' ->
+ (match b with
+ | Z0 -> Z0,Z0
+ | Zpos p -> pos_div_eucl a' b
+ | Zneg b' ->
+ let q0,r = pos_div_eucl a' (Zpos b') in
+ (match r with
+ | Z0 -> (opp q0),Z0
+ | _ -> (opp (add q0 (Zpos XH))),(add b r)))
+ | Zneg a' ->
+ (match b with
+ | Z0 -> Z0,Z0
+ | Zpos p ->
+ let q0,r = pos_div_eucl a' b in
+ (match r with
+ | Z0 -> (opp q0),Z0
+ | _ -> (opp (add q0 (Zpos XH))),(sub b r))
+ | Zneg b' -> let q0,r = pos_div_eucl a' (Zpos b') in q0,(opp r))
+
+ (** val div : z -> z -> z **)
+
+ let div a b =
+ let q0,x = div_eucl a b in q0
+
+ (** val modulo : z -> z -> z **)
+
+ let modulo a b =
+ let x,r = div_eucl a b in r
+
+ (** val quotrem : z -> z -> z * z **)
+
+ let quotrem a b =
+ match a with
+ | Z0 -> Z0,Z0
+ | Zpos a0 ->
+ (match b with
+ | Z0 -> Z0,a
+ | Zpos b0 ->
+ let q0,r = N.pos_div_eucl a0 (Npos b0) in (of_N q0),(of_N r)
+ | Zneg b0 ->
+ let q0,r = N.pos_div_eucl a0 (Npos b0) in (opp (of_N q0)),(of_N r))
+ | Zneg a0 ->
+ (match b with
+ | Z0 -> Z0,a
+ | Zpos b0 ->
+ let q0,r = N.pos_div_eucl a0 (Npos b0) in
+ (opp (of_N q0)),(opp (of_N r))
+ | Zneg b0 ->
+ let q0,r = N.pos_div_eucl a0 (Npos b0) in (of_N q0),(opp (of_N r)))
+
+ (** val quot : z -> z -> z **)
+
+ let quot a b =
+ fst (quotrem a b)
+
+ (** val rem : z -> z -> z **)
+
+ let rem a b =
+ snd (quotrem a b)
+
+ (** val even : z -> bool **)
+
+ let even = function
+ | Z0 -> true
+ | Zpos p ->
+ (match p with
+ | XO p2 -> true
+ | _ -> false)
+ | Zneg p ->
+ (match p with
+ | XO p2 -> true
+ | _ -> false)
+
+ (** val odd : z -> bool **)
+
+ let odd = function
+ | Z0 -> false
+ | Zpos p ->
+ (match p with
+ | XO p2 -> false
+ | _ -> true)
+ | Zneg p ->
+ (match p with
+ | XO p2 -> false
+ | _ -> true)
+
+ (** val div2 : z -> z **)
+
+ let div2 = function
+ | Z0 -> Z0
+ | Zpos p ->
+ (match p with
+ | XH -> Z0
+ | _ -> Zpos (Coq_Pos.div2 p))
+ | Zneg p -> Zneg (Coq_Pos.div2_up p)
+
+ (** val quot2 : z -> z **)
+
+ let quot2 = function
+ | Z0 -> Z0
+ | Zpos p ->
+ (match p with
+ | XH -> Z0
+ | _ -> Zpos (Coq_Pos.div2 p))
+ | Zneg p ->
+ (match p with
+ | XH -> Z0
+ | _ -> Zneg (Coq_Pos.div2 p))
+
+ (** val log2 : z -> z **)
+
+ let log2 = function
+ | Zpos p2 ->
+ (match p2 with
+ | XI p -> Zpos (Coq_Pos.size p)
+ | XO p -> Zpos (Coq_Pos.size p)
+ | XH -> Z0)
+ | _ -> Z0
+
+ (** val sqrtrem : z -> z * z **)
+
+ let sqrtrem = function
+ | Zpos p ->
+ let s,m = Coq_Pos.sqrtrem p in
+ (match m with
+ | Coq_Pos.IsPos r -> (Zpos s),(Zpos r)
+ | _ -> (Zpos s),Z0)
+ | _ -> Z0,Z0
+
+ (** val sqrt : z -> z **)
+
+ let sqrt = function
+ | Zpos p -> Zpos (Coq_Pos.sqrt p)
+ | _ -> Z0
+
+ (** val gcd : z -> z -> z **)
+
+ let gcd a b =
+ match a with
+ | Z0 -> abs b
+ | Zpos a0 ->
+ (match b with
+ | Z0 -> abs a
+ | Zpos b0 -> Zpos (Coq_Pos.gcd a0 b0)
+ | Zneg b0 -> Zpos (Coq_Pos.gcd a0 b0))
+ | Zneg a0 ->
+ (match b with
+ | Z0 -> abs a
+ | Zpos b0 -> Zpos (Coq_Pos.gcd a0 b0)
+ | Zneg b0 -> Zpos (Coq_Pos.gcd a0 b0))
+
+ (** val ggcd : z -> z -> z * (z * z) **)
+
+ let ggcd a b =
+ match a with
+ | Z0 -> (abs b),(Z0,(sgn b))
+ | Zpos a0 ->
+ (match b with
+ | Z0 -> (abs a),((sgn a),Z0)
+ | Zpos b0 ->
+ let g,p = Coq_Pos.ggcd a0 b0 in
+ let aa,bb = p in (Zpos g),((Zpos aa),(Zpos bb))
+ | Zneg b0 ->
+ let g,p = Coq_Pos.ggcd a0 b0 in
+ let aa,bb = p in (Zpos g),((Zpos aa),(Zneg bb)))
+ | Zneg a0 ->
+ (match b with
+ | Z0 -> (abs a),((sgn a),Z0)
+ | Zpos b0 ->
+ let g,p = Coq_Pos.ggcd a0 b0 in
+ let aa,bb = p in (Zpos g),((Zneg aa),(Zpos bb))
+ | Zneg b0 ->
+ let g,p = Coq_Pos.ggcd a0 b0 in
+ let aa,bb = p in (Zpos g),((Zneg aa),(Zneg bb)))
+
+ (** val testbit : z -> z -> bool **)
+
+ let testbit a = function
+ | Z0 -> odd a
+ | Zpos p ->
+ (match a with
+ | Z0 -> false
+ | Zpos a0 -> Coq_Pos.testbit a0 (Npos p)
+ | Zneg a0 -> negb (N.testbit (Coq_Pos.pred_N a0) (Npos p)))
+ | Zneg p -> false
+
+ (** val shiftl : z -> z -> z **)
+
+ let shiftl a = function
+ | Z0 -> a
+ | Zpos p -> Coq_Pos.iter p (mul (Zpos (XO XH))) a
+ | Zneg p -> Coq_Pos.iter p div2 a
+
+ (** val shiftr : z -> z -> z **)
+
+ let shiftr a n0 =
+ shiftl a (opp n0)
+
+ (** val coq_lor : z -> z -> z **)
+
+ let coq_lor a b =
+ match a with
+ | Z0 -> b
+ | Zpos a0 ->
+ (match b with
+ | Z0 -> a
+ | Zpos b0 -> Zpos (Coq_Pos.coq_lor a0 b0)
+ | Zneg b0 -> Zneg (N.succ_pos (N.ldiff (Coq_Pos.pred_N b0) (Npos a0))))
+ | Zneg a0 ->
+ (match b with
+ | Z0 -> a
+ | Zpos b0 -> Zneg (N.succ_pos (N.ldiff (Coq_Pos.pred_N a0) (Npos b0)))
+ | Zneg b0 ->
+ Zneg
+ (N.succ_pos (N.coq_land (Coq_Pos.pred_N a0) (Coq_Pos.pred_N b0))))
+
+ (** val coq_land : z -> z -> z **)
+
+ let coq_land a b =
+ match a with
+ | Z0 -> Z0
+ | Zpos a0 ->
+ (match b with
+ | Z0 -> Z0
+ | Zpos b0 -> of_N (Coq_Pos.coq_land a0 b0)
+ | Zneg b0 -> of_N (N.ldiff (Npos a0) (Coq_Pos.pred_N b0)))
+ | Zneg a0 ->
+ (match b with
+ | Z0 -> Z0
+ | Zpos b0 -> of_N (N.ldiff (Npos b0) (Coq_Pos.pred_N a0))
+ | Zneg b0 ->
+ Zneg
+ (N.succ_pos (N.coq_lor (Coq_Pos.pred_N a0) (Coq_Pos.pred_N b0))))
+
+ (** val ldiff : z -> z -> z **)
+
+ let ldiff a b =
+ match a with
+ | Z0 -> Z0
+ | Zpos a0 ->
+ (match b with
+ | Z0 -> a
+ | Zpos b0 -> of_N (Coq_Pos.ldiff a0 b0)
+ | Zneg b0 -> of_N (N.coq_land (Npos a0) (Coq_Pos.pred_N b0)))
+ | Zneg a0 ->
+ (match b with
+ | Z0 -> a
+ | Zpos b0 ->
+ Zneg (N.succ_pos (N.coq_lor (Coq_Pos.pred_N a0) (Npos b0)))
+ | Zneg b0 -> of_N (N.ldiff (Coq_Pos.pred_N b0) (Coq_Pos.pred_N a0)))
+
+ (** val coq_lxor : z -> z -> z **)
+
+ let coq_lxor a b =
+ match a with
+ | Z0 -> b
+ | Zpos a0 ->
+ (match b with
+ | Z0 -> a
+ | Zpos b0 -> of_N (Coq_Pos.coq_lxor a0 b0)
+ | Zneg b0 ->
+ Zneg (N.succ_pos (N.coq_lxor (Npos a0) (Coq_Pos.pred_N b0))))
+ | Zneg a0 ->
+ (match b with
+ | Z0 -> a
+ | Zpos b0 ->
+ Zneg (N.succ_pos (N.coq_lxor (Coq_Pos.pred_N a0) (Npos b0)))
+ | Zneg b0 -> of_N (N.coq_lxor (Coq_Pos.pred_N a0) (Coq_Pos.pred_N b0)))
+
+ (** val eq_dec : z -> z -> bool **)
+
+ let eq_dec x y =
+ match x with
+ | Z0 ->
+ (match y with
+ | Z0 -> true
+ | _ -> false)
+ | Zpos x0 ->
+ (match y with
+ | Zpos p2 -> Coq_Pos.eq_dec x0 p2
+ | _ -> false)
+ | Zneg x0 ->
+ (match y with
+ | Zneg p2 -> Coq_Pos.eq_dec x0 p2
+ | _ -> false)
+
+ module BootStrap =
+ struct
+
+ end
+
+ module OrderElts =
+ struct
+ type t = z
+ end
+
+ module OrderTac = MakeOrderTac(OrderElts)
+
+ (** val sqrt_up : z -> z **)
+
+ let sqrt_up a =
+ match compare Z0 a with
+ | Lt -> succ (sqrt (pred a))
+ | _ -> Z0
+
+ (** val log2_up : z -> z **)
+
+ let log2_up a =
+ match compare (Zpos XH) a with
+ | Lt -> succ (log2 (pred a))
+ | _ -> Z0
+
+ module NZDivP =
+ struct
+
+ end
+
+ module Quot2Div =
+ struct
+ (** val div : z -> z -> z **)
+
+ let div =
+ quot
+
+ (** val modulo : z -> z -> z **)
+
+ let modulo =
+ rem
+ end
+
+ module NZQuot =
+ struct
+
+ end
+
+ (** val lcm : z -> z -> z **)
+
+ let lcm a b =
+ abs (mul a (div b (gcd a b)))
+
+ (** val b2z : bool -> z **)
+
+ let b2z = function
+ | true -> Zpos XH
+ | false -> Z0
+
+ (** val setbit : z -> z -> z **)
+
+ let setbit a n0 =
+ coq_lor a (shiftl (Zpos XH) n0)
+
+ (** val clearbit : z -> z -> z **)
+
+ let clearbit a n0 =
+ ldiff a (shiftl (Zpos XH) n0)
+
+ (** val lnot : z -> z **)
+
+ let lnot a =
+ pred (opp a)
+
+ (** val ones : z -> z **)
+
+ let ones n0 =
+ pred (shiftl (Zpos XH) n0)
+
+ module T =
+ struct
+
+ end
+
+ module ORev =
+ struct
+ type t = z
+ end
+
+ module MRev =
+ struct
+ (** val max : z -> z -> z **)
+
+ let max x y =
+ min y x
+ end
+
+ module MPRev = MaxLogicalProperties(ORev)(MRev)
+
+ module P =
+ struct
+ (** val max_case_strong :
+ z -> z -> (z -> z -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1)
+ -> 'a1 **)
+
+ let max_case_strong n0 m compat hl hr =
+ let c = compSpec2Type n0 m (compare n0 m) in
+ (match c with
+ | CompGtT -> compat n0 (max n0 m) __ (hl __)
+ | _ -> compat m (max n0 m) __ (hr __))
+
+ (** val max_case :
+ z -> z -> (z -> z -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 **)
+
+ let max_case n0 m x x0 x1 =
+ max_case_strong n0 m x (fun _ -> x0) (fun _ -> x1)
+
+ (** val max_dec : z -> z -> bool **)
+
+ let max_dec n0 m =
+ max_case n0 m (fun x y _ h0 -> h0) true false
+
+ (** val min_case_strong :
+ z -> z -> (z -> z -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1)
+ -> 'a1 **)
+
+ let min_case_strong n0 m compat hl hr =
+ let c = compSpec2Type n0 m (compare n0 m) in
+ (match c with
+ | CompGtT -> compat m (min n0 m) __ (hr __)
+ | _ -> compat n0 (min n0 m) __ (hl __))
+
+ (** val min_case :
+ z -> z -> (z -> z -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 **)
+
+ let min_case n0 m x x0 x1 =
+ min_case_strong n0 m x (fun _ -> x0) (fun _ -> x1)
+
+ (** val min_dec : z -> z -> bool **)
+
+ let min_dec n0 m =
+ min_case n0 m (fun x y _ h0 -> h0) true false
+ end
+
+ (** val max_case_strong : z -> z -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **)
+
+ let max_case_strong n0 m x x0 =
+ P.max_case_strong n0 m (fun x1 y _ x2 -> x2) x x0
+
+ (** val max_case : z -> z -> 'a1 -> 'a1 -> 'a1 **)
+
+ let max_case n0 m x x0 =
+ max_case_strong n0 m (fun _ -> x) (fun _ -> x0)
+
+ (** val max_dec : z -> z -> bool **)
+
+ let max_dec =
+ P.max_dec
+
+ (** val min_case_strong : z -> z -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 **)
+
+ let min_case_strong n0 m x x0 =
+ P.min_case_strong n0 m (fun x1 y _ x2 -> x2) x x0
+
+ (** val min_case : z -> z -> 'a1 -> 'a1 -> 'a1 **)
+
+ let min_case n0 m x x0 =
+ min_case_strong n0 m (fun _ -> x) (fun _ -> x0)
+
+ (** val min_dec : z -> z -> bool **)
+
+ let min_dec =
+ P.min_dec
+ end
(** val zeq_bool : z -> z -> bool **)
let zeq_bool x y =
- match zcompare x y with
+ match Z.compare x y with
| Eq -> true
| _ -> false
-(** val pgcdn : nat -> positive -> positive -> positive **)
-
-let rec pgcdn n0 a b =
- match n0 with
- | O -> XH
- | S n1 ->
- (match a with
- | XI a' ->
- (match b with
- | XI b' ->
- (match pcompare a' b' Eq with
- | Eq -> a
- | Lt -> pgcdn n1 (pminus b' a') a
- | Gt -> pgcdn n1 (pminus a' b') b)
- | XO b0 -> pgcdn n1 a b0
- | XH -> XH)
- | XO a0 ->
- (match b with
- | XI p -> pgcdn n1 a0 b
- | XO b0 -> XO (pgcdn n1 a0 b0)
- | XH -> XH)
- | XH -> XH)
-
-(** val pgcd : positive -> positive -> positive **)
-
-let pgcd a b =
- pgcdn (plus (psize a) (psize b)) a b
-
-(** val zgcd : z -> z -> z **)
-
-let zgcd a b =
- match a with
- | Z0 -> zabs b
- | Zpos a0 ->
- (match b with
- | Z0 -> zabs a
- | Zpos b0 -> Zpos (pgcd a0 b0)
- | Zneg b0 -> Zpos (pgcd a0 b0))
- | Zneg a0 ->
- (match b with
- | Z0 -> zabs a
- | Zpos b0 -> Zpos (pgcd a0 b0)
- | Zneg b0 -> Zpos (pgcd a0 b0))
-
-(** val zdiv_eucl_POS : positive -> z -> z * z **)
-
-let rec zdiv_eucl_POS a b =
- match a with
- | XI a' ->
- let q0,r = zdiv_eucl_POS a' b in
- let r' = zplus (zmult (Zpos (XO XH)) r) (Zpos XH) in
- if zgt_bool b r'
- then (zmult (Zpos (XO XH)) q0),r'
- else (zplus (zmult (Zpos (XO XH)) q0) (Zpos XH)),(zminus r' b)
- | XO a' ->
- let q0,r = zdiv_eucl_POS a' b in
- let r' = zmult (Zpos (XO XH)) r in
- if zgt_bool b r'
- then (zmult (Zpos (XO XH)) q0),r'
- else (zplus (zmult (Zpos (XO XH)) q0) (Zpos XH)),(zminus r' b)
- | XH -> if zge_bool b (Zpos (XO XH)) then Z0,(Zpos XH) else (Zpos XH),Z0
-
-(** val zdiv_eucl : z -> z -> z * z **)
-
-let zdiv_eucl a b =
- match a with
- | Z0 -> Z0,Z0
- | Zpos a' ->
- (match b with
- | Z0 -> Z0,Z0
- | Zpos p -> zdiv_eucl_POS a' b
- | Zneg b' ->
- let q0,r = zdiv_eucl_POS a' (Zpos b') in
- (match r with
- | Z0 -> (zopp q0),Z0
- | _ -> (zopp (zplus q0 (Zpos XH))),(zplus b r)))
- | Zneg a' ->
- (match b with
- | Z0 -> Z0,Z0
- | Zpos p ->
- let q0,r = zdiv_eucl_POS a' b in
- (match r with
- | Z0 -> (zopp q0),Z0
- | _ -> (zopp (zplus q0 (Zpos XH))),(zminus b r))
- | Zneg b' -> let q0,r = zdiv_eucl_POS a' (Zpos b') in q0,(zopp r))
-
-(** val zdiv : z -> z -> z **)
-
-let zdiv a b =
- let q0,x = zdiv_eucl a b in q0
-
type 'c pol =
| Pc of 'c
| Pinj of positive * 'c pol
@@ -516,14 +2803,14 @@ let rec peq ceqb p p' =
| Pinj (j, q0) ->
(match p' with
| Pinj (j', q') ->
- (match pcompare j j' Eq with
+ (match Coq_Pos.compare j j' with
| Eq -> peq ceqb q0 q'
| _ -> false)
| _ -> false)
| PX (p2, i, q0) ->
(match p' with
| PX (p'0, i', q') ->
- (match pcompare i i' Eq with
+ (match Coq_Pos.compare i i' with
| Eq -> if peq ceqb p2 p'0 then peq ceqb q0 q' else false
| _ -> false)
| _ -> false)
@@ -532,7 +2819,7 @@ let rec peq ceqb p p' =
let mkPinj j p = match p with
| Pc c -> p
-| Pinj (j', q0) -> Pinj ((pplus j j'), q0)
+| Pinj (j', q0) -> Pinj ((Coq_Pos.add j j'), q0)
| PX (p2, p3, p4) -> Pinj (j, p)
(** val mkPinj_pred : positive -> 'a1 pol -> 'a1 pol **)
@@ -540,7 +2827,7 @@ let mkPinj j p = match p with
let mkPinj_pred j p =
match j with
| XI j0 -> Pinj ((XO j0), p)
- | XO j0 -> Pinj ((pdouble_minus_one j0), p)
+ | XO j0 -> Pinj ((Coq_Pos.pred_double j0), p)
| XH -> p
(** val mkPX :
@@ -551,7 +2838,9 @@ let mkPX cO ceqb p i q0 =
| Pc c -> if ceqb c cO then mkPinj XH q0 else PX (p, i, q0)
| Pinj (p2, p3) -> PX (p, i, q0)
| PX (p', i', q') ->
- if peq ceqb q' (p0 cO) then PX (p', (pplus i' i), q0) else PX (p, i, q0)
+ if peq ceqb q' (p0 cO)
+ then PX (p', (Coq_Pos.add i' i), q0)
+ else PX (p, i, q0)
(** val mkXi : 'a1 -> 'a1 -> positive -> 'a1 pol **)
@@ -593,14 +2882,14 @@ let rec psubC csub p c =
let rec paddI cadd pop q0 j = function
| Pc c -> mkPinj j (paddC cadd q0 c)
| Pinj (j', q') ->
- (match zPminus j' j with
+ (match Z.pos_sub j' j with
| Z0 -> mkPinj j (pop q' q0)
| Zpos k -> mkPinj j (pop (Pinj (k, q')) q0)
| Zneg k -> mkPinj j' (paddI cadd pop q0 k q'))
| PX (p2, i, q') ->
(match j with
| XI j0 -> PX (p2, i, (paddI cadd pop q0 (XO j0) q'))
- | XO j0 -> PX (p2, i, (paddI cadd pop q0 (pdouble_minus_one j0) q'))
+ | XO j0 -> PX (p2, i, (paddI cadd pop q0 (Coq_Pos.pred_double j0) q'))
| XH -> PX (p2, i, (pop q' q0)))
(** val psubI :
@@ -610,14 +2899,15 @@ let rec paddI cadd pop q0 j = function
let rec psubI cadd copp pop q0 j = function
| Pc c -> mkPinj j (paddC cadd (popp copp q0) c)
| Pinj (j', q') ->
- (match zPminus j' j with
+ (match Z.pos_sub j' j with
| Z0 -> mkPinj j (pop q' q0)
| Zpos k -> mkPinj j (pop (Pinj (k, q')) q0)
| Zneg k -> mkPinj j' (psubI cadd copp pop q0 k q'))
| PX (p2, i, q') ->
(match j with
| XI j0 -> PX (p2, i, (psubI cadd copp pop q0 (XO j0) q'))
- | XO j0 -> PX (p2, i, (psubI cadd copp pop q0 (pdouble_minus_one j0) q'))
+ | XO j0 ->
+ PX (p2, i, (psubI cadd copp pop q0 (Coq_Pos.pred_double j0) q'))
| XH -> PX (p2, i, (pop q' q0)))
(** val paddX :
@@ -629,10 +2919,10 @@ let rec paddX cO ceqb pop p' i' p = match p with
| Pinj (j, q') ->
(match j with
| XI j0 -> PX (p', i', (Pinj ((XO j0), q')))
- | XO j0 -> PX (p', i', (Pinj ((pdouble_minus_one j0), q')))
+ | XO j0 -> PX (p', i', (Pinj ((Coq_Pos.pred_double j0), q')))
| XH -> PX (p', i', q'))
| PX (p2, i, q') ->
- (match zPminus i i' with
+ (match Z.pos_sub i i' with
| Z0 -> mkPX cO ceqb (pop p2 p') i q'
| Zpos k -> mkPX cO ceqb (pop (PX (p2, k, (p0 cO))) p') i' q'
| Zneg k -> mkPX cO ceqb (paddX cO ceqb pop p' k p2) i q')
@@ -646,10 +2936,10 @@ let rec psubX cO copp ceqb pop p' i' p = match p with
| Pinj (j, q') ->
(match j with
| XI j0 -> PX ((popp copp p'), i', (Pinj ((XO j0), q')))
- | XO j0 -> PX ((popp copp p'), i', (Pinj ((pdouble_minus_one j0), q')))
+ | XO j0 -> PX ((popp copp p'), i', (Pinj ((Coq_Pos.pred_double j0), q')))
| XH -> PX ((popp copp p'), i', q'))
| PX (p2, i, q') ->
- (match zPminus i i' with
+ (match Z.pos_sub i i' with
| Z0 -> mkPX cO ceqb (pop p2 p') i q'
| Zpos k -> mkPX cO ceqb (pop (PX (p2, k, (p0 cO))) p') i' q'
| Zneg k -> mkPX cO ceqb (psubX cO copp ceqb pop p' k p2) i q')
@@ -669,10 +2959,10 @@ let rec padd cO cadd ceqb p = function
| XI j0 -> PX (p'0, i', (padd cO cadd ceqb (Pinj ((XO j0), q0)) q'))
| XO j0 ->
PX (p'0, i',
- (padd cO cadd ceqb (Pinj ((pdouble_minus_one j0), q0)) q'))
+ (padd cO cadd ceqb (Pinj ((Coq_Pos.pred_double j0), q0)) q'))
| XH -> PX (p'0, i', (padd cO cadd ceqb q0 q')))
| PX (p2, i, q0) ->
- (match zPminus i i' with
+ (match Z.pos_sub i i' with
| Z0 ->
mkPX cO ceqb (padd cO cadd ceqb p2 p'0) i (padd cO cadd ceqb q0 q')
| Zpos k ->
@@ -699,11 +2989,11 @@ let rec psub cO cadd csub copp ceqb p = function
(psub cO cadd csub copp ceqb (Pinj ((XO j0), q0)) q'))
| XO j0 ->
PX ((popp copp p'0), i',
- (psub cO cadd csub copp ceqb (Pinj ((pdouble_minus_one j0), q0))
+ (psub cO cadd csub copp ceqb (Pinj ((Coq_Pos.pred_double j0), q0))
q'))
| XH -> PX ((popp copp p'0), i', (psub cO cadd csub copp ceqb q0 q')))
| PX (p2, i, q0) ->
- (match zPminus i i' with
+ (match Z.pos_sub i i' with
| Z0 ->
mkPX cO ceqb (psub cO cadd csub copp ceqb p2 p'0) i
(psub cO cadd csub copp ceqb q0 q')
@@ -743,7 +3033,7 @@ let pmulC cO cI cmul ceqb p c =
let rec pmulI cO cI cmul ceqb pmul0 q0 j = function
| Pc c -> mkPinj j (pmulC cO cI cmul ceqb q0 c)
| Pinj (j', q') ->
- (match zPminus j' j with
+ (match Z.pos_sub j' j with
| Z0 -> mkPinj j (pmul0 q' q0)
| Zpos k -> mkPinj j (pmul0 (Pinj (k, q')) q0)
| Zneg k -> mkPinj j' (pmulI cO cI cmul ceqb pmul0 q0 k q'))
@@ -754,7 +3044,7 @@ let rec pmulI cO cI cmul ceqb pmul0 q0 j = function
(pmulI cO cI cmul ceqb pmul0 q0 (XO j') q')
| XO j' ->
mkPX cO ceqb (pmulI cO cI cmul ceqb pmul0 q0 j p') i'
- (pmulI cO cI cmul ceqb pmul0 q0 (pdouble_minus_one j') q')
+ (pmulI cO cI cmul ceqb pmul0 q0 (Coq_Pos.pred_double j') q')
| XH ->
mkPX cO ceqb (pmulI cO cI cmul ceqb pmul0 q0 XH p') i' (pmul0 q' q0))
@@ -773,7 +3063,7 @@ let rec pmul cO cI cadd cmul ceqb p p'' = match p'' with
match j with
| XI j0 -> pmul cO cI cadd cmul ceqb (Pinj ((XO j0), q0)) q'
| XO j0 ->
- pmul cO cI cadd cmul ceqb (Pinj ((pdouble_minus_one j0), q0)) q'
+ pmul cO cI cadd cmul ceqb (Pinj ((Coq_Pos.pred_double j0), q0)) q'
| XH -> pmul cO cI cadd cmul ceqb q0 q'
in
mkPX cO ceqb (pmul cO cI cadd cmul ceqb p p') i' qQ'
@@ -883,6 +3173,18 @@ type 'a bFormula =
| N of 'a bFormula
| I of 'a bFormula * 'a bFormula
+(** val map_bformula : ('a1 -> 'a2) -> 'a1 bFormula -> 'a2 bFormula **)
+
+let rec map_bformula fct = function
+| TT -> TT
+| FF -> FF
+| X -> X
+| A a -> A (fct a)
+| Cj (f1, f2) -> Cj ((map_bformula fct f1), (map_bformula fct f2))
+| D (f1, f2) -> D ((map_bformula fct f1), (map_bformula fct f2))
+| N f0 -> N (map_bformula fct f0)
+| I (f1, f2) -> I ((map_bformula fct f1), (map_bformula fct f2))
+
type 'term' clause = 'term' list
type 'term' cnf = 'term' clause list
@@ -901,21 +3203,21 @@ let ff =
('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 -> 'a1 clause -> 'a1
clause option **)
-let rec add_term unsat deduce t0 = function
+let rec add_term unsat deduce t1 = function
| [] ->
- (match deduce t0 t0 with
- | Some u -> if unsat u then None else Some (t0::[])
- | None -> Some (t0::[]))
+ (match deduce t1 t1 with
+ | Some u -> if unsat u then None else Some (t1::[])
+ | None -> Some (t1::[]))
| t'::cl0 ->
- (match deduce t0 t' with
+ (match deduce t1 t' with
| Some u ->
if unsat u
then None
- else (match add_term unsat deduce t0 cl0 with
+ else (match add_term unsat deduce t1 cl0 with
| Some cl' -> Some (t'::cl')
| None -> None)
| None ->
- (match add_term unsat deduce t0 cl0 with
+ (match add_term unsat deduce t1 cl0 with
| Some cl' -> Some (t'::cl')
| None -> None))
@@ -926,8 +3228,8 @@ let rec add_term unsat deduce t0 = function
let rec or_clause unsat deduce cl1 cl2 =
match cl1 with
| [] -> Some cl2
- | t0::cl ->
- (match add_term unsat deduce t0 cl2 with
+ | t1::cl ->
+ (match add_term unsat deduce t1 cl2 with
| Some cl' -> or_clause unsat deduce cl cl'
| None -> None)
@@ -935,9 +3237,9 @@ let rec or_clause unsat deduce cl1 cl2 =
('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 cnf ->
'a1 cnf **)
-let or_clause_cnf unsat deduce t0 f =
+let or_clause_cnf unsat deduce t1 f =
fold_right (fun e acc ->
- match or_clause unsat deduce t0 e with
+ match or_clause unsat deduce t1 e with
| Some cl -> cl::acc
| None -> acc) [] f
@@ -1175,7 +3477,7 @@ type op2 =
| OpLt
| OpGt
-type 'c formula = { flhs : 'c pExpr; fop : op2; frhs : 'c pExpr }
+type 't formula = { flhs : 't pExpr; fop : op2; frhs : 't pExpr }
(** val flhs : 'a1 formula -> 'a1 pExpr **)
@@ -1215,8 +3517,8 @@ let padd0 cO cplus ceqb =
-> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1
nFormula list **)
-let xnormalise cO cI cplus ctimes cminus copp ceqb t0 =
- let { flhs = lhs; fop = o; frhs = rhs } = t0 in
+let xnormalise cO cI cplus ctimes cminus copp ceqb t1 =
+ let { flhs = lhs; fop = o; frhs = rhs } = t1 in
let lhs0 = norm cO cI cplus ctimes cminus copp ceqb lhs in
let rhs0 = norm cO cI cplus ctimes cminus copp ceqb rhs in
(match o with
@@ -1236,16 +3538,16 @@ let xnormalise cO cI cplus ctimes cminus copp ceqb t0 =
-> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1
nFormula cnf **)
-let cnf_normalise cO cI cplus ctimes cminus copp ceqb t0 =
- map (fun x -> x::[]) (xnormalise cO cI cplus ctimes cminus copp ceqb t0)
+let cnf_normalise cO cI cplus ctimes cminus copp ceqb t1 =
+ map (fun x -> x::[]) (xnormalise cO cI cplus ctimes cminus copp ceqb t1)
(** val xnegate :
'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1
-> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1
nFormula list **)
-let xnegate cO cI cplus ctimes cminus copp ceqb t0 =
- let { flhs = lhs; fop = o; frhs = rhs } = t0 in
+let xnegate cO cI cplus ctimes cminus copp ceqb t1 =
+ let { flhs = lhs; fop = o; frhs = rhs } = t1 in
let lhs0 = norm cO cI cplus ctimes cminus copp ceqb lhs in
let rhs0 = norm cO cI cplus ctimes cminus copp ceqb rhs in
(match o with
@@ -1265,32 +3567,49 @@ let xnegate cO cI cplus ctimes cminus copp ceqb t0 =
-> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1
nFormula cnf **)
-let cnf_negate cO cI cplus ctimes cminus copp ceqb t0 =
- map (fun x -> x::[]) (xnegate cO cI cplus ctimes cminus copp ceqb t0)
+let cnf_negate cO cI cplus ctimes cminus copp ceqb t1 =
+ map (fun x -> x::[]) (xnegate cO cI cplus ctimes cminus copp ceqb t1)
(** val xdenorm : positive -> 'a1 pol -> 'a1 pExpr **)
let rec xdenorm jmp = function
| Pc c -> PEc c
-| Pinj (j, p2) -> xdenorm (pplus j jmp) p2
+| Pinj (j, p2) -> xdenorm (Coq_Pos.add j jmp) p2
| PX (p2, j, q0) ->
PEadd ((PEmul ((xdenorm jmp p2), (PEpow ((PEX jmp), (Npos j))))),
- (xdenorm (psucc jmp) q0))
+ (xdenorm (Coq_Pos.succ jmp) q0))
(** val denorm : 'a1 pol -> 'a1 pExpr **)
let denorm p =
xdenorm XH p
+(** val map_PExpr : ('a2 -> 'a1) -> 'a2 pExpr -> 'a1 pExpr **)
+
+let rec map_PExpr c_of_S = function
+| PEc c -> PEc (c_of_S c)
+| PEX p -> PEX p
+| PEadd (e1, e2) -> PEadd ((map_PExpr c_of_S e1), (map_PExpr c_of_S e2))
+| PEsub (e1, e2) -> PEsub ((map_PExpr c_of_S e1), (map_PExpr c_of_S e2))
+| PEmul (e1, e2) -> PEmul ((map_PExpr c_of_S e1), (map_PExpr c_of_S e2))
+| PEopp e0 -> PEopp (map_PExpr c_of_S e0)
+| PEpow (e0, n0) -> PEpow ((map_PExpr c_of_S e0), n0)
+
+(** val map_Formula : ('a2 -> 'a1) -> 'a2 formula -> 'a1 formula **)
+
+let map_Formula c_of_S f =
+ let { flhs = l; fop = o; frhs = r } = f in
+ { flhs = (map_PExpr c_of_S l); fop = o; frhs = (map_PExpr c_of_S r) }
+
(** val simpl_cone :
'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 psatz ->
'a1 psatz **)
let simpl_cone cO cI ctimes ceqb e = match e with
-| PsatzSquare t0 ->
- (match t0 with
+| PsatzSquare t1 ->
+ (match t1 with
| Pc c -> if ceqb cO c then PsatzZ else PsatzC (ctimes c c)
- | _ -> PsatzSquare t0)
+ | _ -> PsatzSquare t1)
| PsatzMulE (t1, t2) ->
(match t1 with
| PsatzMulE (x, x0) ->
@@ -1354,28 +3673,28 @@ let qden x = x.qden
(** val qeq_bool : q -> q -> bool **)
let qeq_bool x y =
- zeq_bool (zmult x.qnum (Zpos y.qden)) (zmult y.qnum (Zpos x.qden))
+ zeq_bool (Z.mul x.qnum (Zpos y.qden)) (Z.mul y.qnum (Zpos x.qden))
(** val qle_bool : q -> q -> bool **)
let qle_bool x y =
- zle_bool (zmult x.qnum (Zpos y.qden)) (zmult y.qnum (Zpos x.qden))
+ Z.leb (Z.mul x.qnum (Zpos y.qden)) (Z.mul y.qnum (Zpos x.qden))
(** val qplus : q -> q -> q **)
let qplus x y =
- { qnum = (zplus (zmult x.qnum (Zpos y.qden)) (zmult y.qnum (Zpos x.qden)));
- qden = (pmult x.qden y.qden) }
+ { qnum = (Z.add (Z.mul x.qnum (Zpos y.qden)) (Z.mul y.qnum (Zpos x.qden)));
+ qden = (Coq_Pos.mul x.qden y.qden) }
(** val qmult : q -> q -> q **)
let qmult x y =
- { qnum = (zmult x.qnum y.qnum); qden = (pmult x.qden y.qden) }
+ { qnum = (Z.mul x.qnum y.qnum); qden = (Coq_Pos.mul x.qden y.qden) }
(** val qopp : q -> q **)
let qopp x =
- { qnum = (zopp x.qnum); qden = x.qden }
+ { qnum = (Z.opp x.qnum); qden = x.qden }
(** val qminus : q -> q -> q **)
@@ -1402,12 +3721,12 @@ let qpower q0 = function
| Zpos p -> qpower_positive q0 p
| Zneg p -> qinv (qpower_positive q0 p)
-type 'a t =
+type 'a t0 =
| Empty
| Leaf of 'a
-| Node of 'a t * 'a * 'a t
+| Node of 'a t0 * 'a * 'a t0
-(** val find : 'a1 -> 'a1 t -> positive -> 'a1 **)
+(** val find : 'a1 -> 'a1 t0 -> positive -> 'a1 **)
let rec find default vm p =
match vm with
@@ -1424,27 +3743,27 @@ type zWitness = z psatz
(** val zWeakChecker : z nFormula list -> z psatz -> bool **)
let zWeakChecker =
- check_normalised_formulas Z0 (Zpos XH) zplus zmult zeq_bool zle_bool
+ check_normalised_formulas Z0 (Zpos XH) Z.add Z.mul zeq_bool Z.leb
(** val psub1 : z pol -> z pol -> z pol **)
let psub1 =
- psub0 Z0 zplus zminus zopp zeq_bool
+ psub0 Z0 Z.add Z.sub Z.opp zeq_bool
(** val padd1 : z pol -> z pol -> z pol **)
let padd1 =
- padd0 Z0 zplus zeq_bool
+ padd0 Z0 Z.add zeq_bool
(** val norm0 : z pExpr -> z pol **)
let norm0 =
- norm Z0 (Zpos XH) zplus zmult zminus zopp zeq_bool
+ norm Z0 (Zpos XH) Z.add Z.mul Z.sub Z.opp zeq_bool
(** val xnormalise0 : z formula -> z nFormula list **)
-let xnormalise0 t0 =
- let { flhs = lhs; fop = o; frhs = rhs } = t0 in
+let xnormalise0 t1 =
+ let { flhs = lhs; fop = o; frhs = rhs } = t1 in
let lhs0 = norm0 lhs in
let rhs0 = norm0 rhs in
(match o with
@@ -1461,13 +3780,13 @@ let xnormalise0 t0 =
(** val normalise : z formula -> z nFormula cnf **)
-let normalise t0 =
- map (fun x -> x::[]) (xnormalise0 t0)
+let normalise t1 =
+ map (fun x -> x::[]) (xnormalise0 t1)
(** val xnegate0 : z formula -> z nFormula list **)
-let xnegate0 t0 =
- let { flhs = lhs; fop = o; frhs = rhs } = t0 in
+let xnegate0 t1 =
+ let { flhs = lhs; fop = o; frhs = rhs } = t1 in
let lhs0 = norm0 lhs in
let rhs0 = norm0 rhs in
(match o with
@@ -1484,26 +3803,26 @@ let xnegate0 t0 =
(** val negate : z formula -> z nFormula cnf **)
-let negate t0 =
- map (fun x -> x::[]) (xnegate0 t0)
+let negate t1 =
+ map (fun x -> x::[]) (xnegate0 t1)
(** val zunsat : z nFormula -> bool **)
let zunsat =
- check_inconsistent Z0 zeq_bool zle_bool
+ check_inconsistent Z0 zeq_bool Z.leb
(** val zdeduce : z nFormula -> z nFormula -> z nFormula option **)
let zdeduce =
- nformula_plus_nformula Z0 zplus zeq_bool
+ nformula_plus_nformula Z0 Z.add zeq_bool
(** val ceiling : z -> z -> z **)
let ceiling a b =
- let q0,r = zdiv_eucl a b in
+ let q0,r = Z.div_eucl a b in
(match r with
| Z0 -> q0
- | _ -> zplus q0 (Zpos XH))
+ | _ -> Z.add q0 (Zpos XH))
type zArithProof =
| DoneProof
@@ -1514,7 +3833,7 @@ type zArithProof =
(** val zgcdM : z -> z -> z **)
let zgcdM x y =
- zmax (zgcd x y) (Zpos XH)
+ Z.max (Z.gcd x y) (Zpos XH)
(** val zgcd_pol : z polC -> z * z **)
@@ -1529,7 +3848,7 @@ let rec zgcd_pol = function
let rec zdiv_pol p x =
match p with
- | Pc c -> Pc (zdiv c x)
+ | Pc c -> Pc (Z.div c x)
| Pinj (j, p2) -> Pinj (j, (zdiv_pol p2 x))
| PX (p2, j, q0) -> PX ((zdiv_pol p2 x), j, (zdiv_pol q0 x))
@@ -1537,8 +3856,8 @@ let rec zdiv_pol p x =
let makeCuttingPlane p =
let g,c = zgcd_pol p in
- if zgt_bool g Z0
- then (zdiv_pol (psubC zminus p c) g),(zopp (ceiling (zopp c) g))
+ if Z.gtb g Z0
+ then (zdiv_pol (psubC Z.sub p c) g),(Z.opp (ceiling (Z.opp c) g))
else p,Z0
(** val genCuttingPlane : z nFormula -> ((z polC * z) * op1) option **)
@@ -1548,12 +3867,12 @@ let genCuttingPlane = function
(match op with
| Equal ->
let g,c = zgcd_pol e in
- if (&&) (zgt_bool g Z0)
- ((&&) (negb (zeq_bool c Z0)) (negb (zeq_bool (zgcd g c) g)))
+ if (&&) (Z.gtb g Z0)
+ ((&&) (negb (zeq_bool c Z0)) (negb (zeq_bool (Z.gcd g c) g)))
then None
else Some ((makeCuttingPlane e),Equal)
| NonEqual -> Some ((e,Z0),op)
- | Strict -> Some ((makeCuttingPlane (psubC zminus e (Zpos XH))),NonStrict)
+ | Strict -> Some ((makeCuttingPlane (psubC Z.sub e (Zpos XH))),NonStrict)
| NonStrict -> Some ((makeCuttingPlane e),NonStrict))
(** val nformula_of_cutting_plane : ((z polC * z) * op1) -> z nFormula **)
@@ -1573,7 +3892,7 @@ let is_pol_Z0 = function
(** val eval_Psatz0 : z nFormula list -> zWitness -> z nFormula option **)
let eval_Psatz0 =
- eval_Psatz Z0 (Zpos XH) zplus zmult zeq_bool zle_bool
+ eval_Psatz Z0 (Zpos XH) Z.add Z.mul zeq_bool Z.leb
(** val valid_cut_sign : op1 -> bool **)
@@ -1614,11 +3933,11 @@ let rec zChecker l = function
(is_pol_Z0 (padd1 e1 e2))
then let rec label pfs lb ub =
match pfs with
- | [] -> zgt_bool lb ub
+ | [] -> Z.gtb lb ub
| pf1::rsr ->
(&&) (zChecker (((psub1 e1 (Pc lb)),Equal)::l) pf1)
- (label rsr (zplus lb (Zpos XH)) ub)
- in label pf0 (zopp z1) z2
+ (label rsr (Z.add lb (Zpos XH)) ub)
+ in label pf0 (Z.opp z1) z2
else false
| None -> true)
| None -> true)
@@ -1630,12 +3949,6 @@ let rec zChecker l = function
let zTautoChecker f w =
tauto_checker zunsat zdeduce normalise negate zChecker f w
-(** val n_of_Z : z -> n **)
-
-let n_of_Z = function
-| Zpos p -> Npos p
-| _ -> N0
-
type qWitness = q psatz
(** val qWeakChecker : q nFormula list -> q psatz -> bool **)
@@ -1671,35 +3984,63 @@ let qdeduce =
let qTautoChecker f w =
tauto_checker qunsat qdeduce qnormalise qnegate qWeakChecker f w
-type rWitness = z psatz
-
-(** val rWeakChecker : z nFormula list -> z psatz -> bool **)
+type rcst =
+| C0
+| C1
+| CQ of q
+| CZ of z
+| CPlus of rcst * rcst
+| CMinus of rcst * rcst
+| CMult of rcst * rcst
+| CInv of rcst
+| COpp of rcst
+
+(** val q_of_Rcst : rcst -> q **)
+
+let rec q_of_Rcst = function
+| C0 -> { qnum = Z0; qden = XH }
+| C1 -> { qnum = (Zpos XH); qden = XH }
+| CQ q0 -> q0
+| CZ z0 -> { qnum = z0; qden = XH }
+| CPlus (r1, r2) -> qplus (q_of_Rcst r1) (q_of_Rcst r2)
+| CMinus (r1, r2) -> qminus (q_of_Rcst r1) (q_of_Rcst r2)
+| CMult (r1, r2) -> qmult (q_of_Rcst r1) (q_of_Rcst r2)
+| CInv r0 -> qinv (q_of_Rcst r0)
+| COpp r0 -> qopp (q_of_Rcst r0)
+
+type rWitness = q psatz
+
+(** val rWeakChecker : q nFormula list -> q psatz -> bool **)
let rWeakChecker =
- check_normalised_formulas Z0 (Zpos XH) zplus zmult zeq_bool zle_bool
+ check_normalised_formulas { qnum = Z0; qden = XH } { qnum = (Zpos XH);
+ qden = XH } qplus qmult qeq_bool qle_bool
-(** val rnormalise : z formula -> z nFormula cnf **)
+(** val rnormalise : q formula -> q nFormula cnf **)
let rnormalise =
- cnf_normalise Z0 (Zpos XH) zplus zmult zminus zopp zeq_bool
+ cnf_normalise { qnum = Z0; qden = XH } { qnum = (Zpos XH); qden = XH }
+ qplus qmult qminus qopp qeq_bool
-(** val rnegate : z formula -> z nFormula cnf **)
+(** val rnegate : q formula -> q nFormula cnf **)
let rnegate =
- cnf_negate Z0 (Zpos XH) zplus zmult zminus zopp zeq_bool
+ cnf_negate { qnum = Z0; qden = XH } { qnum = (Zpos XH); qden = XH } qplus
+ qmult qminus qopp qeq_bool
-(** val runsat : z nFormula -> bool **)
+(** val runsat : q nFormula -> bool **)
let runsat =
- check_inconsistent Z0 zeq_bool zle_bool
+ check_inconsistent { qnum = Z0; qden = XH } qeq_bool qle_bool
-(** val rdeduce : z nFormula -> z nFormula -> z nFormula option **)
+(** val rdeduce : q nFormula -> q nFormula -> q nFormula option **)
let rdeduce =
- nformula_plus_nformula Z0 zplus zeq_bool
+ nformula_plus_nformula { qnum = Z0; qden = XH } qplus qeq_bool
-(** val rTautoChecker : z formula bFormula -> rWitness list -> bool **)
+(** val rTautoChecker : rcst formula bFormula -> rWitness list -> bool **)
let rTautoChecker f w =
- tauto_checker runsat rdeduce rnormalise rnegate rWeakChecker f w
+ tauto_checker runsat rdeduce rnormalise rnegate rWeakChecker
+ (map_bformula (map_Formula q_of_Rcst) f) w
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-23 16:20:35 +0000