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|
val negb : bool -> bool
type nat =
| O
| S of nat
val app : 'a1 list -> 'a1 list -> 'a1 list
type comparison =
| Eq
| Lt
| Gt
val compOpp : comparison -> comparison
val add : nat -> nat -> nat
type positive =
| XI of positive
| XO of positive
| XH
type n =
| N0
| Npos of positive
type z =
| Z0
| Zpos of positive
| Zneg of positive
module Pos :
sig
type mask =
| IsNul
| IsPos of positive
| IsNeg
end
module Coq_Pos :
sig
val succ : positive -> positive
val add : positive -> positive -> positive
val add_carry : positive -> positive -> positive
val pred_double : positive -> positive
type mask = Pos.mask =
| IsNul
| IsPos of positive
| IsNeg
val succ_double_mask : mask -> mask
val double_mask : mask -> mask
val double_pred_mask : positive -> 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 size_nat : positive -> nat
val compare_cont : comparison -> positive -> positive -> comparison
val compare : positive -> positive -> comparison
val gcdn : nat -> positive -> positive -> positive
val gcd : positive -> positive -> positive
val of_succ_nat : nat -> positive
end
module N :
sig
val of_nat : nat -> n
end
val pow_pos : ('a1 -> 'a1 -> 'a1) -> 'a1 -> positive -> 'a1
val nth : nat -> 'a1 list -> 'a1 -> 'a1
val map : ('a1 -> 'a2) -> 'a1 list -> 'a2 list
val fold_right : ('a2 -> 'a1 -> 'a1) -> 'a1 -> 'a2 list -> 'a1
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 sub : z -> z -> z
val mul : z -> z -> z
val compare : z -> z -> comparison
val leb : z -> z -> bool
val ltb : z -> z -> bool
val gtb : z -> z -> bool
val max : z -> z -> z
val abs : z -> z
val to_N : z -> n
val pos_div_eucl : positive -> z -> z * z
val div_eucl : z -> z -> z * z
val div : z -> z -> z
val gcd : z -> z -> z
end
val zeq_bool : z -> z -> bool
type 'c pol =
| Pc of 'c
| Pinj of positive * 'c pol
| PX of 'c pol * positive * 'c pol
val p0 : 'a1 -> 'a1 pol
val p1 : 'a1 -> 'a1 pol
val peq : ('a1 -> 'a1 -> bool) -> 'a1 pol -> 'a1 pol -> bool
val mkPinj : positive -> 'a1 pol -> 'a1 pol
val mkPinj_pred : positive -> 'a1 pol -> 'a1 pol
val mkPX :
'a1 -> ('a1 -> 'a1 -> bool) -> 'a1 pol -> positive -> 'a1 pol -> 'a1 pol
val mkXi : 'a1 -> 'a1 -> positive -> 'a1 pol
val mkX : 'a1 -> 'a1 -> 'a1 pol
val popp : ('a1 -> 'a1) -> 'a1 pol -> 'a1 pol
val paddC : ('a1 -> 'a1 -> 'a1) -> 'a1 pol -> 'a1 -> 'a1 pol
val psubC : ('a1 -> 'a1 -> 'a1) -> 'a1 pol -> 'a1 -> 'a1 pol
val paddI :
('a1 -> 'a1 -> 'a1) -> ('a1 pol -> 'a1 pol -> 'a1 pol) -> 'a1 pol ->
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
val paddX :
'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
val padd :
'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
val pmulC_aux :
'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
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
val psquare :
'a1 -> 'a1 -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1 -> 'a1) -> ('a1 -> 'a1
-> bool) -> 'a1 pol -> 'a1 pol
type 'c pExpr =
| PEc of 'c
| PEX of positive
| PEadd of 'c pExpr * 'c pExpr
| PEsub of 'c pExpr * 'c pExpr
| PEmul of 'c pExpr * 'c pExpr
| PEopp of 'c pExpr
| PEpow of 'c pExpr * n
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
val ppow_N :
'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
type 'a bFormula =
| TT
| FF
| X
| A of 'a
| Cj of 'a bFormula * 'a bFormula
| D of 'a bFormula * 'a bFormula
| N of 'a bFormula
| I of 'a bFormula * 'a bFormula
val map_bformula : ('a1 -> 'a2) -> 'a1 bFormula -> 'a2 bFormula
type 'x clause = 'x list
type 'x cnf = 'x clause list
val tt : 'a1 cnf
val ff : 'a1 cnf
val add_term :
('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 -> 'a1 clause -> 'a1
clause option
val or_clause :
('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
val or_cnf :
('a1 -> bool) -> ('a1 -> 'a1 -> 'a1 option) -> 'a1 cnf -> 'a1 cnf -> 'a1
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
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
val cneqb : ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool
val cltb :
('a1 -> 'a1 -> bool) -> ('a1 -> 'a1 -> bool) -> 'a1 -> 'a1 -> bool
type 'c polC = 'c pol
type op1 =
| Equal
| NonEqual
| Strict
| NonStrict
type 'c nFormula = 'c polC * op1
val opMult : op1 -> op1 -> op1 option
val opAdd : op1 -> op1 -> op1 option
type 'c psatz =
| PsatzIn of nat
| PsatzSquare of 'c polC
| PsatzMulC of 'c polC * 'c psatz
| PsatzMulE of 'c psatz * 'c psatz
| PsatzAdd of 'c psatz * 'c psatz
| PsatzC of 'c
| PsatzZ
val map_option : ('a1 -> 'a2 option) -> 'a1 option -> 'a2 option
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
val nformula_times_nformula :
'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
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
val check_inconsistent :
'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
type op2 =
| OpEq
| OpNEq
| OpLe
| OpGe
| OpLt
| OpGt
type 't formula = { flhs : 't pExpr; fop : op2; frhs : 't pExpr }
val norm :
'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
val padd0 :
'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
val cnf_normalise :
'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
val cnf_negate :
'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
val denorm : 'a1 pol -> 'a1 pExpr
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
type q = { qnum : z; qden : positive }
val qnum : q -> z
val qden : q -> positive
val qeq_bool : q -> q -> bool
val qle_bool : q -> q -> bool
val qplus : q -> q -> q
val qmult : q -> q -> q
val qopp : q -> q
val qminus : q -> q -> q
val qinv : q -> q
val qpower_positive : q -> positive -> q
val qpower : q -> z -> q
type 'a t =
| Empty
| Leaf of 'a
| Node of 'a t * 'a * 'a t
val find : 'a1 -> 'a1 t -> positive -> 'a1
val singleton : 'a1 -> positive -> 'a1 -> 'a1 t
val vm_add : 'a1 -> positive -> 'a1 -> 'a1 t -> 'a1 t
type zWitness = z psatz
val zWeakChecker : z nFormula list -> z psatz -> bool
val psub1 : z pol -> z pol -> z pol
val padd1 : z pol -> z pol -> z pol
val norm0 : z pExpr -> z pol
val xnormalise0 : z formula -> z nFormula list
val normalise : z formula -> z nFormula cnf
val xnegate0 : z formula -> z nFormula list
val negate : z formula -> z nFormula cnf
val zunsat : z nFormula -> bool
val zdeduce : z nFormula -> z nFormula -> z nFormula option
val ceiling : z -> z -> z
type zArithProof =
| DoneProof
| RatProof of zWitness * zArithProof
| CutProof of zWitness * zArithProof
| EnumProof of zWitness * zWitness * zArithProof list
val zgcdM : z -> z -> z
val zgcd_pol : z polC -> z * z
val zdiv_pol : z polC -> z -> z polC
val makeCuttingPlane : z polC -> z polC * z
val genCuttingPlane : z nFormula -> ((z polC * z) * op1) option
val nformula_of_cutting_plane : ((z polC * z) * op1) -> z nFormula
val is_pol_Z0 : z polC -> bool
val eval_Psatz0 : z nFormula list -> zWitness -> z nFormula option
val valid_cut_sign : op1 -> bool
val zChecker : z nFormula list -> zArithProof -> bool
val zTautoChecker : z formula bFormula -> zArithProof list -> bool
type qWitness = q psatz
val qWeakChecker : q nFormula list -> q psatz -> bool
val qnormalise : q formula -> q nFormula cnf
val qnegate : q formula -> q nFormula cnf
val qunsat : q nFormula -> bool
val qdeduce : q nFormula -> q nFormula -> q nFormula option
val qTautoChecker : q formula bFormula -> qWitness list -> 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
type rWitness = q psatz
val rWeakChecker : q nFormula list -> q psatz -> bool
val rnormalise : q formula -> q nFormula cnf
val rnegate : q formula -> q nFormula cnf
val runsat : q nFormula -> bool
val rdeduce : q nFormula -> q nFormula -> q nFormula option
val rTautoChecker : rcst formula bFormula -> rWitness list -> bool
|
