diff options
Diffstat (limited to 'plugins/micromega/micromega.mli')
| -rw-r--r-- | plugins/micromega/micromega.mli | 950 |
1 files changed, 124 insertions, 826 deletions
diff --git a/plugins/micromega/micromega.mli b/plugins/micromega/micromega.mli index bcd61f39..beb042f4 100644 --- a/plugins/micromega/micromega.mli +++ b/plugins/micromega/micromega.mli @@ -1,15 +1,9 @@ -type __ = Obj.t - val negb : bool -> bool type nat = | O | S of nat -val fst : ('a1 * 'a2) -> 'a1 - -val snd : ('a1 * 'a2) -> 'a2 - val app : 'a1 list -> 'a1 list -> 'a1 list type comparison = @@ -19,24 +13,7 @@ type comparison = val compOpp : comparison -> comparison -type compareSpecT = -| CompEqT -| CompLtT -| CompGtT - -val compareSpec2Type : comparison -> compareSpecT - -type 'a compSpecT = compareSpecT - -val compSpec2Type : 'a1 -> 'a1 -> comparison -> 'a1 compSpecT - -type 'a sig0 = - 'a - (* singleton inductive, whose constructor was exist *) - -val plus : nat -> nat -> nat - -val nat_iter : nat -> ('a1 -> 'a1) -> 'a1 -> 'a1 +val add : nat -> nat -> nat type positive = | XI of positive @@ -52,560 +29,59 @@ type z = | Zpos of positive | Zneg of positive -module type TotalOrder' = - sig - type t - end - -module MakeOrderTac : - functor (O:TotalOrder') -> - sig - - end - -module MaxLogicalProperties : - functor (O:TotalOrder') -> - functor (M:sig - val max : O.t -> O.t -> O.t - end) -> - sig - module T : - sig - - end - end - -module Pos : - sig - type t = positive - - val succ : positive -> positive - - val add : positive -> positive -> positive - - val add_carry : positive -> positive -> positive - - val pred_double : positive -> positive - - val pred : positive -> positive - - val pred_N : positive -> n - +module Pos : + sig type mask = | IsNul | IsPos of positive | IsNeg - - val mask_rect : 'a1 -> (positive -> 'a1) -> 'a1 -> mask -> 'a1 - - val mask_rec : 'a1 -> (positive -> 'a1) -> 'a1 -> mask -> 'a1 - - val succ_double_mask : mask -> mask - - val double_mask : mask -> mask - - val double_pred_mask : positive -> mask - - val pred_mask : mask -> mask - - val sub_mask : positive -> positive -> mask - - val sub_mask_carry : positive -> positive -> mask - - val sub : positive -> positive -> positive - - val mul : positive -> positive -> positive - - val iter : positive -> ('a1 -> 'a1) -> 'a1 -> 'a1 - - val pow : positive -> positive -> positive - - val div2 : positive -> positive - - val div2_up : positive -> positive - - val size_nat : positive -> nat - - val size : positive -> positive - - val compare_cont : positive -> positive -> comparison -> comparison - - val compare : positive -> positive -> comparison - - val min : positive -> positive -> positive - - val max : positive -> positive -> positive - - val eqb : positive -> positive -> bool - - val leb : positive -> positive -> bool - - val ltb : positive -> positive -> bool - - val sqrtrem_step : - (positive -> positive) -> (positive -> positive) -> (positive * mask) -> - positive * mask - - val sqrtrem : positive -> positive * mask - - val sqrt : positive -> positive - - val gcdn : nat -> positive -> positive -> positive - - val gcd : positive -> positive -> positive - - val ggcdn : nat -> positive -> positive -> positive * (positive * positive) - - val ggcd : positive -> positive -> positive * (positive * positive) - - val coq_Nsucc_double : n -> n - - val coq_Ndouble : n -> n - - val coq_lor : positive -> positive -> positive - - val coq_land : positive -> positive -> n - - val ldiff : positive -> positive -> n - - val coq_lxor : positive -> positive -> n - - val shiftl_nat : positive -> nat -> positive - - val shiftr_nat : positive -> nat -> positive - - val shiftl : positive -> n -> positive - - val shiftr : positive -> n -> positive - - val testbit_nat : positive -> nat -> bool - - val testbit : positive -> n -> bool - - val iter_op : ('a1 -> 'a1 -> 'a1) -> positive -> 'a1 -> 'a1 - - val to_nat : positive -> nat - - val of_nat : nat -> positive - - val of_succ_nat : nat -> positive end -module Coq_Pos : - sig - module Coq__1 : sig - type t = positive - end - type t = Coq__1.t - +module Coq_Pos : + sig val succ : positive -> positive - + val add : positive -> positive -> positive - + val add_carry : positive -> positive -> positive - + val pred_double : positive -> positive - - val pred : positive -> positive - - val pred_N : positive -> n - + type mask = Pos.mask = | IsNul | IsPos of positive | IsNeg - - val mask_rect : 'a1 -> (positive -> 'a1) -> 'a1 -> mask -> 'a1 - - val mask_rec : 'a1 -> (positive -> 'a1) -> 'a1 -> mask -> 'a1 - + val succ_double_mask : mask -> mask - + val double_mask : mask -> mask - + val double_pred_mask : positive -> mask - - val pred_mask : mask -> mask - + val sub_mask : positive -> positive -> mask - + val sub_mask_carry : positive -> positive -> mask - + val sub : positive -> positive -> positive - + val mul : positive -> positive -> positive - - val iter : positive -> ('a1 -> 'a1) -> 'a1 -> 'a1 - - val pow : positive -> positive -> positive - - val div2 : positive -> positive - - val div2_up : positive -> positive - + val size_nat : positive -> nat - - val size : positive -> positive - - val compare_cont : positive -> positive -> comparison -> comparison - + + val compare_cont : comparison -> positive -> positive -> comparison + val compare : positive -> positive -> comparison - - val min : positive -> positive -> positive - - val max : positive -> positive -> positive - - val eqb : positive -> positive -> bool - - val leb : positive -> positive -> bool - - val ltb : positive -> positive -> bool - - val sqrtrem_step : - (positive -> positive) -> (positive -> positive) -> (positive * mask) -> - positive * mask - - val sqrtrem : positive -> positive * mask - - val sqrt : positive -> positive - + val gcdn : nat -> positive -> positive -> positive - + val gcd : positive -> positive -> positive - - val ggcdn : nat -> positive -> positive -> positive * (positive * positive) - - val ggcd : positive -> positive -> positive * (positive * positive) - - val coq_Nsucc_double : n -> n - - val coq_Ndouble : n -> n - - val coq_lor : positive -> positive -> positive - - val coq_land : positive -> positive -> n - - val ldiff : positive -> positive -> n - - val coq_lxor : positive -> positive -> n - - val shiftl_nat : positive -> nat -> positive - - val shiftr_nat : positive -> nat -> positive - - val shiftl : positive -> n -> positive - - val shiftr : positive -> n -> positive - - val testbit_nat : positive -> nat -> bool - - val testbit : positive -> n -> bool - - val iter_op : ('a1 -> 'a1 -> 'a1) -> positive -> 'a1 -> 'a1 - - val to_nat : positive -> nat - - val of_nat : nat -> positive - + val of_succ_nat : nat -> positive - - val eq_dec : positive -> positive -> bool - - val peano_rect : 'a1 -> (positive -> 'a1 -> 'a1) -> positive -> 'a1 - - val peano_rec : 'a1 -> (positive -> 'a1 -> 'a1) -> positive -> 'a1 - - type coq_PeanoView = - | PeanoOne - | PeanoSucc of positive * coq_PeanoView - - val coq_PeanoView_rect : - 'a1 -> (positive -> coq_PeanoView -> 'a1 -> 'a1) -> positive -> - coq_PeanoView -> 'a1 - - val coq_PeanoView_rec : - 'a1 -> (positive -> coq_PeanoView -> 'a1 -> 'a1) -> positive -> - coq_PeanoView -> 'a1 - - val peanoView_xO : positive -> coq_PeanoView -> coq_PeanoView - - val peanoView_xI : positive -> coq_PeanoView -> coq_PeanoView - - val peanoView : positive -> coq_PeanoView - - val coq_PeanoView_iter : - 'a1 -> (positive -> 'a1 -> 'a1) -> positive -> coq_PeanoView -> 'a1 - - val switch_Eq : comparison -> comparison -> comparison - - val mask2cmp : mask -> comparison - - module T : - sig - - end - - module ORev : - sig - type t = Coq__1.t - end - - module MRev : - sig - val max : t -> t -> t - end - - module MPRev : - sig - module T : - sig - - end - end - - module P : - sig - val max_case_strong : - t -> t -> (t -> t -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> - 'a1 - - val max_case : - t -> t -> (t -> t -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 - - val max_dec : t -> t -> bool - - val min_case_strong : - t -> t -> (t -> t -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> - 'a1 - - val min_case : - t -> t -> (t -> t -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 - - val min_dec : t -> t -> bool - end - - val max_case_strong : t -> t -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 - - val max_case : t -> t -> 'a1 -> 'a1 -> 'a1 - - val max_dec : t -> t -> bool - - val min_case_strong : t -> t -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 - - val min_case : t -> t -> 'a1 -> 'a1 -> 'a1 - - val min_dec : t -> t -> bool end -module N : - sig - type t = n - - val zero : n - - val one : n - - val two : n - - val succ_double : n -> n - - val double : n -> n - - val succ : n -> n - - val pred : n -> n - - val succ_pos : n -> positive - - val add : n -> n -> n - - val sub : n -> n -> n - - val mul : n -> n -> n - - val compare : n -> n -> comparison - - val eqb : n -> n -> bool - - val leb : n -> n -> bool - - val ltb : n -> n -> bool - - val min : n -> n -> n - - val max : n -> n -> n - - val div2 : n -> n - - val even : n -> bool - - val odd : n -> bool - - val pow : n -> n -> n - - val log2 : n -> n - - val size : n -> n - - val size_nat : n -> nat - - val pos_div_eucl : positive -> n -> n * n - - val div_eucl : n -> n -> n * n - - val div : n -> n -> n - - val modulo : n -> n -> n - - val gcd : n -> n -> n - - val ggcd : n -> n -> n * (n * n) - - val sqrtrem : n -> n * n - - val sqrt : n -> n - - val coq_lor : n -> n -> n - - val coq_land : n -> n -> n - - val ldiff : n -> n -> n - - val coq_lxor : n -> n -> n - - val shiftl_nat : n -> nat -> n - - val shiftr_nat : n -> nat -> n - - val shiftl : n -> n -> n - - val shiftr : n -> n -> n - - val testbit_nat : n -> nat -> bool - - val testbit : n -> n -> bool - - val to_nat : n -> nat - +module N : + sig val of_nat : nat -> n - - val iter : n -> ('a1 -> 'a1) -> 'a1 -> 'a1 - - val eq_dec : n -> n -> bool - - val discr : n -> positive option - - val binary_rect : 'a1 -> (n -> 'a1 -> 'a1) -> (n -> 'a1 -> 'a1) -> n -> 'a1 - - val binary_rec : 'a1 -> (n -> 'a1 -> 'a1) -> (n -> 'a1 -> 'a1) -> n -> 'a1 - - val peano_rect : 'a1 -> (n -> 'a1 -> 'a1) -> n -> 'a1 - - val peano_rec : 'a1 -> (n -> 'a1 -> 'a1) -> n -> 'a1 - - module BootStrap : - sig - - end - - val recursion : 'a1 -> (n -> 'a1 -> 'a1) -> n -> 'a1 - - module OrderElts : - sig - type t = n - end - - module OrderTac : - sig - - end - - module NZPowP : - sig - - end - - module NZSqrtP : - sig - - end - - val sqrt_up : n -> n - - val log2_up : n -> n - - module NZDivP : - sig - - end - - val lcm : n -> n -> n - - val b2n : bool -> n - - val setbit : n -> n -> n - - val clearbit : n -> n -> n - - val ones : n -> n - - val lnot : n -> n -> n - - module T : - sig - - end - - module ORev : - sig - type t = n - end - - module MRev : - sig - val max : n -> n -> n - end - - module MPRev : - sig - module T : - sig - - end - end - - module P : - sig - val max_case_strong : - n -> n -> (n -> n -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> - 'a1 - - val max_case : - n -> n -> (n -> n -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 - - val max_dec : n -> n -> bool - - val min_case_strong : - n -> n -> (n -> n -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> - 'a1 - - val min_case : - n -> n -> (n -> n -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 - - val min_dec : n -> n -> bool - end - - val max_case_strong : n -> n -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 - - val max_case : n -> n -> 'a1 -> 'a1 -> 'a1 - - val max_dec : n -> n -> bool - - val min_case_strong : n -> n -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 - - val min_case : n -> n -> 'a1 -> 'a1 -> 'a1 - - val min_dec : n -> n -> bool end val pow_pos : ('a1 -> 'a1 -> 'a1) -> 'a1 -> positive -> 'a1 @@ -616,225 +92,45 @@ val map : ('a1 -> 'a2) -> 'a1 list -> 'a2 list val fold_right : ('a2 -> 'a1 -> 'a1) -> 'a1 -> 'a2 list -> 'a1 -module Z : - sig - type t = z - - val zero : z - - val one : z - - val two : z - +module Z : + sig val double : z -> z - + val succ_double : z -> z - + val pred_double : z -> z - + val pos_sub : positive -> positive -> z - + val add : z -> z -> z - + val opp : z -> z - - val succ : z -> z - - val pred : z -> z - + val sub : z -> z -> z - + val mul : z -> z -> z - - val pow_pos : z -> positive -> z - - val pow : z -> z -> z - + val compare : z -> z -> comparison - - val sgn : z -> z - + val leb : z -> z -> bool - - val geb : z -> z -> bool - + val ltb : z -> z -> bool - + val gtb : z -> z -> bool - - val eqb : z -> z -> bool - + val max : z -> z -> z - - val min : z -> z -> z - + val abs : z -> z - - val abs_nat : z -> nat - - val abs_N : z -> n - - val to_nat : z -> nat - + val to_N : z -> n - - val of_nat : nat -> z - - val of_N : n -> z - - val iter : z -> ('a1 -> 'a1) -> 'a1 -> 'a1 - + val pos_div_eucl : positive -> z -> z * z - + val div_eucl : z -> z -> z * z - + val div : z -> z -> z - - val modulo : z -> z -> z - - val quotrem : z -> z -> z * z - - val quot : z -> z -> z - - val rem : z -> z -> z - - val even : z -> bool - - val odd : z -> bool - - val div2 : z -> z - - val quot2 : z -> z - - val log2 : z -> z - - val sqrtrem : z -> z * z - - val sqrt : z -> z - + val gcd : z -> z -> z - - val ggcd : z -> z -> z * (z * z) - - val testbit : z -> z -> bool - - val shiftl : z -> z -> z - - val shiftr : z -> z -> z - - val coq_lor : z -> z -> z - - val coq_land : z -> z -> z - - val ldiff : z -> z -> z - - val coq_lxor : z -> z -> z - - val eq_dec : z -> z -> bool - - module BootStrap : - sig - - end - - module OrderElts : - sig - type t = z - end - - module OrderTac : - sig - - end - - val sqrt_up : z -> z - - val log2_up : z -> z - - module NZDivP : - sig - - end - - module Quot2Div : - sig - val div : z -> z -> z - - val modulo : z -> z -> z - end - - module NZQuot : - sig - - end - - val lcm : z -> z -> z - - val b2z : bool -> z - - val setbit : z -> z -> z - - val clearbit : z -> z -> z - - val lnot : z -> z - - val ones : z -> z - - module T : - sig - - end - - module ORev : - sig - type t = z - end - - module MRev : - sig - val max : z -> z -> z - end - - module MPRev : - sig - module T : - sig - - end - end - - module P : - sig - val max_case_strong : - z -> z -> (z -> z -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> - 'a1 - - val max_case : - z -> z -> (z -> z -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 - - val max_dec : z -> z -> bool - - val min_case_strong : - z -> z -> (z -> z -> __ -> 'a1 -> 'a1) -> (__ -> 'a1) -> (__ -> 'a1) -> - 'a1 - - val min_case : - z -> z -> (z -> z -> __ -> 'a1 -> 'a1) -> 'a1 -> 'a1 -> 'a1 - - val min_dec : z -> z -> bool - end - - val max_case_strong : z -> z -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 - - val max_case : z -> z -> 'a1 -> 'a1 -> 'a1 - - val max_dec : z -> z -> bool - - val min_case_strong : z -> z -> (__ -> 'a1) -> (__ -> 'a1) -> 'a1 - - val min_case : z -> z -> 'a1 -> 'a1 -> 'a1 - - val min_dec : z -> z -> bool end val zeq_bool : z -> z -> bool @@ -872,44 +168,44 @@ val paddI : positive -> 'a1 pol -> 'a1 pol val psubI : - ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> - 'a1 pol -> positive -> 'a1 pol -> 'a1 pol + ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) + -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol val paddX : - 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol - -> positive -> 'a1 pol -> 'a1 pol + 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 + pol -> positive -> 'a1 pol -> 'a1 pol val psubX : - 'a1 -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 - pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol + 'a1 -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> + 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol val padd : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> - 'a1 pol + 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol + -> 'a1 pol val psub : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 - -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol + 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> + ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol val pmulC_aux : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 -> 'a1 - pol + 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 -> + 'a1 pol val pmulC : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 - -> 'a1 pol + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> + 'a1 -> 'a1 pol val pmulI : 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol val pmul : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol val psquare : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - bool) -> 'a1 pol -> 'a1 pol + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> bool) -> 'a1 pol -> 'a1 pol type 'c pExpr = | PEc of 'c @@ -923,16 +219,17 @@ type 'c pExpr = val mk_X : 'a1 -> 'a1 -> positive -> 'a1 pol val ppow_pos : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> 'a1 pol -> positive -> 'a1 pol + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> 'a1 pol -> positive -> + 'a1 pol val ppow_N : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> n -> 'a1 pol + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> bool) -> ('a1 pol -> 'a1 pol) -> 'a1 pol -> n -> 'a1 pol val norm_aux : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> 'a1 pol + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> 'a1 pol type 'a bFormula = | TT @@ -946,9 +243,9 @@ type 'a bFormula = val map_bformula : ('a1 -> 'a2) -> 'a1 bFormula -> 'a2 bFormula -type 'term' clause = 'term' list +type 'x clause = 'x list -type 'term' cnf = 'term' clause list +type 'x cnf = 'x clause list val tt : 'a1 cnf @@ -959,12 +256,12 @@ val add_term : clause option val or_clause : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 clause -> - 'a1 clause option + ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 clause + -> 'a1 clause option val or_clause_cnf : - ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 cnf -> 'a1 - cnf + ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 clause -> 'a1 cnf -> + 'a1 cnf val or_cnf : ('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 cnf -> 'a1 cnf -> 'a1 @@ -973,18 +270,20 @@ val or_cnf : val and_cnf : 'a1 cnf -> 'a1 cnf -> 'a1 cnf val xcnf : - ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a2 cnf) -> ('a1 -> - 'a2 cnf) -> bool -> 'a1 bFormula -> 'a2 cnf + ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a2 cnf) -> ('a1 + -> 'a2 cnf) -> bool -> 'a1 bFormula -> 'a2 cnf val cnf_checker : ('a1 list -> 'a2 -> bool) -> 'a1 cnf -> 'a2 list -> bool val tauto_checker : - ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a2 cnf) -> ('a1 -> - 'a2 cnf) -> ('a2 list -> 'a3 -> bool) -> 'a1 bFormula -> 'a3 list -> bool + ('a2 -> bool) -> ('a2 -> 'a2 -> 'a2 option) -> ('a1 -> 'a2 cnf) -> ('a1 + -> 'a2 cnf) -> ('a2 list -> 'a3 -> bool) -> 'a1 bFormula -> 'a3 list -> + bool val cneqb : ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool -val cltb : ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool +val cltb : + ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool type 'c polC = 'c pol @@ -1015,28 +314,30 @@ val map_option2 : ('a1 -> 'a2 -> 'a3 option) -> 'a1 option -> 'a2 option -> 'a3 option val pexpr_times_nformula : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - bool) -> 'a1 polC -> 'a1 nFormula -> 'a1 nFormula option + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> bool) -> 'a1 polC -> 'a1 nFormula -> 'a1 nFormula option val nformula_times_nformula : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - bool) -> 'a1 nFormula -> 'a1 nFormula -> 'a1 nFormula option + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> bool) -> 'a1 nFormula -> 'a1 nFormula -> 'a1 nFormula option val nformula_plus_nformula : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> 'a1 - nFormula -> 'a1 nFormula option + 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> + 'a1 nFormula -> 'a1 nFormula option val eval_Psatz : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz -> 'a1 - nFormula option + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz -> + 'a1 nFormula option val check_inconsistent : - 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> bool + 'a1 -> ('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula -> + bool val check_normalised_formulas : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz -> bool + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 nFormula list -> 'a1 psatz -> + bool type op2 = | OpEq @@ -1048,43 +349,37 @@ type op2 = type 't formula = { flhs : 't pExpr; fop : op2; frhs : 't pExpr } -val flhs : 'a1 formula -> 'a1 pExpr - -val fop : 'a1 formula -> op2 - -val frhs : 'a1 formula -> 'a1 pExpr - val norm : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> 'a1 pol + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pExpr -> 'a1 pol val psub0 : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> ('a1 - -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol + 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1) -> + ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> 'a1 pol val padd0 : - 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> - 'a1 pol + 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol + -> 'a1 pol val xnormalise : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 nFormula - list + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 + nFormula list val cnf_normalise : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 nFormula - cnf + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 + nFormula cnf val xnegate : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 nFormula - list + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 + nFormula list val cnf_negate : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> - 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 nFormula - cnf + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 + -> 'a1) -> ('a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 formula -> 'a1 + nFormula cnf val xdenorm : positive -> 'a1 pol -> 'a1 pExpr @@ -1095,8 +390,8 @@ val map_PExpr : ('a2 -> 'a1) -> 'a2 pExpr -> 'a1 pExpr val map_Formula : ('a2 -> 'a1) -> 'a2 formula -> 'a1 formula val simpl_cone : - 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 psatz -> - 'a1 psatz + 'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> bool) -> 'a1 psatz + -> 'a1 psatz type q = { qnum : z; qden : positive } @@ -1122,12 +417,16 @@ val qpower_positive : q -> positive -> q val qpower : q -> z -> q -type 'a t0 = +type 'a t = | Empty | Leaf of 'a -| Node of 'a t0 * 'a * 'a t0 +| Node of 'a t * 'a * 'a t + +val find : 'a1 -> 'a1 t -> positive -> 'a1 -val find : 'a1 -> 'a1 t0 -> positive -> 'a1 +val singleton : 'a1 -> positive -> 'a1 -> 'a1 t + +val vm_add : 'a1 -> positive -> 'a1 -> 'a1 t -> 'a1 t type zWitness = z psatz @@ -1221,4 +520,3 @@ val runsat : q nFormula -> bool val rdeduce : q nFormula -> q nFormula -> q nFormula option val rTautoChecker : rcst formula bFormula -> rWitness list -> bool - |