Source file coq_micromega.ml
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open Pp
open Names
open Goptions
open Mutils
open Constr
open Context
open Tactypes
open McPrinter
(**
* Debug flag
*)
let debug = false
let max_depth = max_int
let lra_proof_depth =
declare_int_option_and_ref ~depr:true ~key:["Lra"; "Depth"] ~value:max_depth
let lia_enum =
declare_bool_option_and_ref ~depr:true ~key:["Lia"; "Enum"] ~value:true
let lia_proof_depth =
declare_int_option_and_ref ~depr:true ~key:["Lia"; "Depth"] ~value:max_depth
let get_lia_option () =
(true, lia_enum (), lia_proof_depth ())
let use_lia_cache =
declare_bool_option_and_ref ~depr:false ~key:["Lia"; "Cache"] ~value:true
let use_nia_cache =
declare_bool_option_and_ref ~depr:false ~key:["Nia"; "Cache"] ~value:true
let use_nra_cache =
declare_bool_option_and_ref ~depr:false ~key:["Nra"; "Cache"] ~value:true
let use_csdp_cache () = true
(**
* Initialize a tag type to the Tag module declaration (see Mutils).
*)
type tag = Tag.t
module Mc = Micromega
(**
* An atom is of the form:
* pExpr1 \{<,>,=,<>,<=,>=\} pExpr2
* where pExpr1, pExpr2 are polynomial expressions (see Micromega). pExprs are
* parametrized by 'cst, which is used as the type of constants.
*)
type 'cst atom = 'cst Mc.formula
type 'cst formula =
('cst atom, EConstr.constr, tag * EConstr.constr, Names.Id.t) Mc.gFormula
type 'cst clause = ('cst Mc.nFormula, tag * EConstr.constr) Mc.clause
type 'cst cnf = ('cst Mc.nFormula, tag * EConstr.constr) Mc.cnf
let pp_kind o = function
| Mc.IsProp -> output_string o "Prop"
| Mc.IsBool -> output_string o "bool"
let kind_is_prop = function Mc.IsProp -> true | Mc.IsBool -> false
let rec pp_formula o (f : 'cst formula) =
Mc.(
match f with
| TT k -> output_string o (if kind_is_prop k then "True" else "true")
| FF k -> output_string o (if kind_is_prop k then "False" else "false")
| X (k, c) -> Printf.fprintf o "X %a" pp_kind k
| A (_, _, (t, _)) -> Printf.fprintf o "A(%a)" Tag.pp t
| AND (_, f1, f2) ->
Printf.fprintf o "AND(%a,%a)" pp_formula f1 pp_formula f2
| OR (_, f1, f2) -> Printf.fprintf o "OR(%a,%a)" pp_formula f1 pp_formula f2
| IMPL (_, f1, n, f2) ->
Printf.fprintf o "IMPL(%a,%s,%a)" pp_formula f1
(match n with Some id -> Names.Id.to_string id | None -> "")
pp_formula f2
| NOT (_, f) -> Printf.fprintf o "NOT(%a)" pp_formula f
| IFF (_, f1, f2) ->
Printf.fprintf o "IFF(%a,%a)" pp_formula f1 pp_formula f2
| EQ (f1, f2) -> Printf.fprintf o "EQ(%a,%a)" pp_formula f1 pp_formula f2)
(**
* Given a set of integers s=\{i0,...,iN\} and a list m, return the list of
* elements of m that are at position i0,...,iN.
*)
let selecti s m =
let rec xselecti i m =
match m with
| [] -> []
| e :: m ->
if ISet.mem i s then e :: xselecti (i + 1) m else xselecti (i + 1) m
in
xselecti 0 m
(**
* MODULE: Mapping of the Coq data-strustures into Caml and Caml extracted
* code. This includes initializing Caml variables based on Coq terms, parsing
* various Coq expressions into Caml, and dumping Caml expressions into Coq.
*
* Opened here and in csdpcert.ml.
*)
(**
* Initialization : a large amount of Caml symbols are derived from
* ZMicromega.v
*)
let constr_of_ref str =
EConstr.of_constr (UnivGen.constr_of_monomorphic_global (Global.env ()) (Coqlib.lib_ref str))
let coq_and = lazy (constr_of_ref "core.and.type")
let coq_or = lazy (constr_of_ref "core.or.type")
let coq_not = lazy (constr_of_ref "core.not.type")
let coq_iff = lazy (constr_of_ref "core.iff.type")
let coq_True = lazy (constr_of_ref "core.True.type")
let coq_False = lazy (constr_of_ref "core.False.type")
let coq_bool = lazy (constr_of_ref "core.bool.type")
let coq_true = lazy (constr_of_ref "core.bool.true")
let coq_false = lazy (constr_of_ref "core.bool.false")
let coq_andb = lazy (constr_of_ref "core.bool.andb")
let coq_orb = lazy (constr_of_ref "core.bool.orb")
let coq_implb = lazy (constr_of_ref "core.bool.implb")
let coq_eqb = lazy (constr_of_ref "core.bool.eqb")
let coq_negb = lazy (constr_of_ref "core.bool.negb")
let coq_cons = lazy (constr_of_ref "core.list.cons")
let coq_nil = lazy (constr_of_ref "core.list.nil")
let coq_list = lazy (constr_of_ref "core.list.type")
let coq_O = lazy (constr_of_ref "num.nat.O")
let coq_S = lazy (constr_of_ref "num.nat.S")
let coq_nat = lazy (constr_of_ref "num.nat.type")
let coq_unit = lazy (constr_of_ref "core.unit.type")
let coq_None = lazy (constr_of_ref "core.option.None")
let coq_tt = lazy (constr_of_ref "core.unit.tt")
let coq_Inl = lazy (constr_of_ref "core.sum.inl")
let coq_Inr = lazy (constr_of_ref "core.sum.inr")
let coq_N0 = lazy (constr_of_ref "num.N.N0")
let coq_Npos = lazy (constr_of_ref "num.N.Npos")
let coq_xH = lazy (constr_of_ref "num.pos.xH")
let coq_xO = lazy (constr_of_ref "num.pos.xO")
let coq_xI = lazy (constr_of_ref "num.pos.xI")
let coq_Z = lazy (constr_of_ref "num.Z.type")
let coq_ZERO = lazy (constr_of_ref "num.Z.Z0")
let coq_POS = lazy (constr_of_ref "num.Z.Zpos")
let coq_NEG = lazy (constr_of_ref "num.Z.Zneg")
let coq_Q = lazy (constr_of_ref "rat.Q.type")
let coq_Qmake = lazy (constr_of_ref "rat.Q.Qmake")
let coq_R = lazy (constr_of_ref "reals.R.type")
let coq_Rcst = lazy (constr_of_ref "micromega.Rcst.type")
let coq_C0 = lazy (constr_of_ref "micromega.Rcst.C0")
let coq_C1 = lazy (constr_of_ref "micromega.Rcst.C1")
let coq_CQ = lazy (constr_of_ref "micromega.Rcst.CQ")
let coq_CZ = lazy (constr_of_ref "micromega.Rcst.CZ")
let coq_CPlus = lazy (constr_of_ref "micromega.Rcst.CPlus")
let coq_CMinus = lazy (constr_of_ref "micromega.Rcst.CMinus")
let coq_CMult = lazy (constr_of_ref "micromega.Rcst.CMult")
let coq_CPow = lazy (constr_of_ref "micromega.Rcst.CPow")
let coq_CInv = lazy (constr_of_ref "micromega.Rcst.CInv")
let coq_COpp = lazy (constr_of_ref "micromega.Rcst.COpp")
let coq_R0 = lazy (constr_of_ref "reals.R.R0")
let coq_R1 = lazy (constr_of_ref "reals.R.R1")
let coq_proofTerm = lazy (constr_of_ref "micromega.ZArithProof.type")
let coq_doneProof = lazy (constr_of_ref "micromega.ZArithProof.DoneProof")
let coq_ratProof = lazy (constr_of_ref "micromega.ZArithProof.RatProof")
let coq_cutProof = lazy (constr_of_ref "micromega.ZArithProof.CutProof")
let coq_splitProof = lazy (constr_of_ref "micromega.ZArithProof.SplitProof")
let coq_enumProof = lazy (constr_of_ref "micromega.ZArithProof.EnumProof")
let coq_ExProof = lazy (constr_of_ref "micromega.ZArithProof.ExProof")
let coq_IsProp = lazy (constr_of_ref "micromega.kind.isProp")
let coq_IsBool = lazy (constr_of_ref "micromega.kind.isBool")
let coq_Zgt = lazy (constr_of_ref "num.Z.gt")
let coq_Zge = lazy (constr_of_ref "num.Z.ge")
let coq_Zle = lazy (constr_of_ref "num.Z.le")
let coq_Zlt = lazy (constr_of_ref "num.Z.lt")
let coq_Zgtb = lazy (constr_of_ref "num.Z.gtb")
let coq_Zgeb = lazy (constr_of_ref "num.Z.geb")
let coq_Zleb = lazy (constr_of_ref "num.Z.leb")
let coq_Zltb = lazy (constr_of_ref "num.Z.ltb")
let coq_Zeqb = lazy (constr_of_ref "num.Z.eqb")
let coq_eq = lazy (constr_of_ref "core.eq.type")
let coq_Zplus = lazy (constr_of_ref "num.Z.add")
let coq_Zminus = lazy (constr_of_ref "num.Z.sub")
let coq_Zopp = lazy (constr_of_ref "num.Z.opp")
let coq_Zmult = lazy (constr_of_ref "num.Z.mul")
let coq_Zpower = lazy (constr_of_ref "num.Z.pow")
let coq_Qle = lazy (constr_of_ref "rat.Q.Qle")
let coq_Qlt = lazy (constr_of_ref "rat.Q.Qlt")
let coq_Qeq = lazy (constr_of_ref "rat.Q.Qeq")
let coq_Qplus = lazy (constr_of_ref "rat.Q.Qplus")
let coq_Qminus = lazy (constr_of_ref "rat.Q.Qminus")
let coq_Qopp = lazy (constr_of_ref "rat.Q.Qopp")
let coq_Qmult = lazy (constr_of_ref "rat.Q.Qmult")
let coq_Qpower = lazy (constr_of_ref "rat.Q.Qpower")
let coq_Rgt = lazy (constr_of_ref "reals.R.Rgt")
let coq_Rge = lazy (constr_of_ref "reals.R.Rge")
let coq_Rle = lazy (constr_of_ref "reals.R.Rle")
let coq_Rlt = lazy (constr_of_ref "reals.R.Rlt")
let coq_Rplus = lazy (constr_of_ref "reals.R.Rplus")
let coq_Rminus = lazy (constr_of_ref "reals.R.Rminus")
let coq_Ropp = lazy (constr_of_ref "reals.R.Ropp")
let coq_Rmult = lazy (constr_of_ref "reals.R.Rmult")
let coq_Rinv = lazy (constr_of_ref "reals.R.Rinv")
let coq_Rpower = lazy (constr_of_ref "reals.R.pow")
let coq_powerZR = lazy (constr_of_ref "reals.R.powerRZ")
let coq_IZR = lazy (constr_of_ref "reals.R.IZR")
let coq_IQR = lazy (constr_of_ref "reals.R.Q2R")
let coq_PEX = lazy (constr_of_ref "micromega.PExpr.PEX")
let coq_PEc = lazy (constr_of_ref "micromega.PExpr.PEc")
let coq_PEadd = lazy (constr_of_ref "micromega.PExpr.PEadd")
let coq_PEopp = lazy (constr_of_ref "micromega.PExpr.PEopp")
let coq_PEmul = lazy (constr_of_ref "micromega.PExpr.PEmul")
let coq_PEsub = lazy (constr_of_ref "micromega.PExpr.PEsub")
let coq_PEpow = lazy (constr_of_ref "micromega.PExpr.PEpow")
let coq_PX = lazy (constr_of_ref "micromega.Pol.PX")
let coq_Pc = lazy (constr_of_ref "micromega.Pol.Pc")
let coq_Pinj = lazy (constr_of_ref "micromega.Pol.Pinj")
let coq_OpEq = lazy (constr_of_ref "micromega.Op2.OpEq")
let coq_OpNEq = lazy (constr_of_ref "micromega.Op2.OpNEq")
let coq_OpLe = lazy (constr_of_ref "micromega.Op2.OpLe")
let coq_OpLt = lazy (constr_of_ref "micromega.Op2.OpLt")
let coq_OpGe = lazy (constr_of_ref "micromega.Op2.OpGe")
let coq_OpGt = lazy (constr_of_ref "micromega.Op2.OpGt")
let coq_PsatzLet = lazy (constr_of_ref "micromega.Psatz.PsatzLet")
let coq_PsatzIn = lazy (constr_of_ref "micromega.Psatz.PsatzIn")
let coq_PsatzSquare = lazy (constr_of_ref "micromega.Psatz.PsatzSquare")
let coq_PsatzMulE = lazy (constr_of_ref "micromega.Psatz.PsatzMulE")
let coq_PsatzMultC = lazy (constr_of_ref "micromega.Psatz.PsatzMulC")
let coq_PsatzAdd = lazy (constr_of_ref "micromega.Psatz.PsatzAdd")
let coq_PsatzC = lazy (constr_of_ref "micromega.Psatz.PsatzC")
let coq_PsatzZ = lazy (constr_of_ref "micromega.Psatz.PsatzZ")
let coq_DeclaredConstant =
lazy (constr_of_ref "micromega.DeclaredConstant.type")
let coq_TT = lazy (constr_of_ref "micromega.GFormula.TT")
let coq_FF = lazy (constr_of_ref "micromega.GFormula.FF")
let coq_AND = lazy (constr_of_ref "micromega.GFormula.AND")
let coq_OR = lazy (constr_of_ref "micromega.GFormula.OR")
let coq_NOT = lazy (constr_of_ref "micromega.GFormula.NOT")
let coq_Atom = lazy (constr_of_ref "micromega.GFormula.A")
let coq_X = lazy (constr_of_ref "micromega.GFormula.X")
let coq_IMPL = lazy (constr_of_ref "micromega.GFormula.IMPL")
let coq_IFF = lazy (constr_of_ref "micromega.GFormula.IFF")
let coq_EQ = lazy (constr_of_ref "micromega.GFormula.EQ")
let coq_Formula = lazy (constr_of_ref "micromega.BFormula.type")
let coq_eKind = lazy (constr_of_ref "micromega.eKind")
(**
* Initialization : a few Caml symbols are derived from other libraries;
* QMicromega, ZArithRing, RingMicromega.
*)
let coq_QWitness = lazy (constr_of_ref "micromega.QWitness.type")
let coq_Build = lazy (constr_of_ref "micromega.Formula.Build_Formula")
let coq_Cstr = lazy (constr_of_ref "micromega.Formula.type")
(**
* Parsing and dumping : transformation functions between Caml and Coq
* data-structures.
*
* dump_* functions go from Micromega to Coq terms
* undump_* functions go from Coq to Micromega terms (reverse of dump_)
* parse_* functions go from Coq to Micromega terms
* pp_* functions pretty-print Coq terms.
*)
exception ParseError
let get_left_construct sigma term =
match EConstr.kind sigma term with
| Construct ((_, i), _) -> (i, [||])
| App (l, rst) -> (
match EConstr.kind sigma l with
| Construct ((_, i), _) -> (i, rst)
| _ -> raise ParseError )
| _ -> raise ParseError
let rec parse_nat sigma term =
let i, c = get_left_construct sigma term in
match i with
| 1 -> Mc.O
| 2 -> Mc.S (parse_nat sigma c.(0))
| i -> raise ParseError
let rec dump_nat x =
match x with
| Mc.O -> Lazy.force coq_O
| Mc.S p -> EConstr.mkApp (Lazy.force coq_S, [|dump_nat p|])
let rec parse_positive sigma term =
let i, c = get_left_construct sigma term in
match i with
| 1 -> Mc.XI (parse_positive sigma c.(0))
| 2 -> Mc.XO (parse_positive sigma c.(0))
| 3 -> Mc.XH
| i -> raise ParseError
let rec dump_positive x =
match x with
| Mc.XH -> Lazy.force coq_xH
| Mc.XO p -> EConstr.mkApp (Lazy.force coq_xO, [|dump_positive p|])
| Mc.XI p -> EConstr.mkApp (Lazy.force coq_xI, [|dump_positive p|])
let parse_n sigma term =
let i, c = get_left_construct sigma term in
match i with
| 1 -> Mc.N0
| 2 -> Mc.Npos (parse_positive sigma c.(0))
| i -> raise ParseError
let dump_n x =
match x with
| Mc.N0 -> Lazy.force coq_N0
| Mc.Npos p -> EConstr.mkApp (Lazy.force coq_Npos, [|dump_positive p|])
(** [is_ground_term env sigma term] holds if the term [term]
is an instance of the typeclass [DeclConstant.GT term]
i.e. built from user-defined constants and functions.
NB: This mechanism can be used to customise the reification process to decide
what to consider as a constant (see [parse_constant])
*)
let is_declared_term env evd t =
match EConstr.kind evd t with
| Const _ | Construct _ -> (
let typ = Retyping.get_type_of env evd t in
try
ignore
(Typeclasses.resolve_one_typeclass env evd
(EConstr.mkApp (Lazy.force coq_DeclaredConstant, [|typ; t|])));
true
with Not_found -> false )
| _ -> false
let rec is_ground_term env evd term =
match EConstr.kind evd term with
| App (c, args) ->
is_declared_term env evd c && Array.for_all (is_ground_term env evd) args
| Const _ | Construct _ -> is_declared_term env evd term
| _ -> false
let parse_z sigma term =
let i, c = get_left_construct sigma term in
match i with
| 1 -> Mc.Z0
| 2 -> Mc.Zpos (parse_positive sigma c.(0))
| 3 -> Mc.Zneg (parse_positive sigma c.(0))
| i -> raise ParseError
let dump_z x =
match x with
| Mc.Z0 -> Lazy.force coq_ZERO
| Mc.Zpos p -> EConstr.mkApp (Lazy.force coq_POS, [|dump_positive p|])
| Mc.Zneg p -> EConstr.mkApp (Lazy.force coq_NEG, [|dump_positive p|])
let dump_q q =
EConstr.mkApp
( Lazy.force coq_Qmake
, [|dump_z q.Micromega.qnum; dump_positive q.Micromega.qden|] )
let parse_q sigma term =
match EConstr.kind sigma term with
| App (c, args) ->
if EConstr.eq_constr sigma c (Lazy.force coq_Qmake) then
{Mc.qnum = parse_z sigma args.(0); Mc.qden = parse_positive sigma args.(1)}
else raise ParseError
| _ -> raise ParseError
let rec pp_Rcst o cst =
match cst with
| Mc.C0 -> output_string o "C0"
| Mc.C1 -> output_string o "C1"
| Mc.CQ q -> output_string o "CQ _"
| Mc.CZ z -> pp_z o z
| Mc.CPlus (x, y) -> Printf.fprintf o "(%a + %a)" pp_Rcst x pp_Rcst y
| Mc.CMinus (x, y) -> Printf.fprintf o "(%a - %a)" pp_Rcst x pp_Rcst y
| Mc.CMult (x, y) -> Printf.fprintf o "(%a * %a)" pp_Rcst x pp_Rcst y
| Mc.CPow (x, y) -> Printf.fprintf o "(%a ^ _)" pp_Rcst x
| Mc.CInv t -> Printf.fprintf o "(/ %a)" pp_Rcst t
| Mc.COpp t -> Printf.fprintf o "(- %a)" pp_Rcst t
let rec dump_Rcst cst =
match cst with
| Mc.C0 -> Lazy.force coq_C0
| Mc.C1 -> Lazy.force coq_C1
| Mc.CQ q -> EConstr.mkApp (Lazy.force coq_CQ, [|dump_q q|])
| Mc.CZ z -> EConstr.mkApp (Lazy.force coq_CZ, [|dump_z z|])
| Mc.CPlus (x, y) ->
EConstr.mkApp (Lazy.force coq_CPlus, [|dump_Rcst x; dump_Rcst y|])
| Mc.CMinus (x, y) ->
EConstr.mkApp (Lazy.force coq_CMinus, [|dump_Rcst x; dump_Rcst y|])
| Mc.CMult (x, y) ->
EConstr.mkApp (Lazy.force coq_CMult, [|dump_Rcst x; dump_Rcst y|])
| Mc.CPow (x, y) ->
EConstr.mkApp
( Lazy.force coq_CPow
, [| dump_Rcst x
; ( match y with
| Mc.Inl z ->
EConstr.mkApp
( Lazy.force coq_Inl
, [|Lazy.force coq_Z; Lazy.force coq_nat; dump_z z|] )
| Mc.Inr n ->
EConstr.mkApp
( Lazy.force coq_Inr
, [|Lazy.force coq_Z; Lazy.force coq_nat; dump_nat n|] ) ) |] )
| Mc.CInv t -> EConstr.mkApp (Lazy.force coq_CInv, [|dump_Rcst t|])
| Mc.COpp t -> EConstr.mkApp (Lazy.force coq_COpp, [|dump_Rcst t|])
let rec dump_list typ dump_elt l =
match l with
| [] -> EConstr.mkApp (Lazy.force coq_nil, [|typ|])
| e :: l ->
EConstr.mkApp
(Lazy.force coq_cons, [|typ; dump_elt e; dump_list typ dump_elt l|])
let undump_var = parse_positive
let dump_var = dump_positive
let undump_expr undump_constant sigma e =
let is c c' = EConstr.eq_constr sigma c (Lazy.force c') in
let rec xundump e =
match EConstr.kind sigma e with
| App (c, [|_; n|]) when is c coq_PEX -> Mc.PEX (undump_var sigma n)
| App (c, [|_; z|]) when is c coq_PEc -> Mc.PEc (undump_constant sigma z)
| App (c, [|_; e1; e2|]) when is c coq_PEadd ->
Mc.PEadd (xundump e1, xundump e2)
| App (c, [|_; e1; e2|]) when is c coq_PEsub ->
Mc.PEsub (xundump e1, xundump e2)
| App (c, [|_; e|]) when is c coq_PEopp -> Mc.PEopp (xundump e)
| App (c, [|_; e1; e2|]) when is c coq_PEmul ->
Mc.PEmul (xundump e1, xundump e2)
| App (c, [|_; e; n|]) when is c coq_PEpow ->
Mc.PEpow (xundump e, parse_n sigma n)
| _ -> raise ParseError
in
xundump e
let dump_expr typ dump_z e =
let rec dump_expr e =
match e with
| Mc.PEX n -> EConstr.mkApp (Lazy.force coq_PEX, [|typ; dump_var n|])
| Mc.PEc z -> EConstr.mkApp (Lazy.force coq_PEc, [|typ; dump_z z|])
| Mc.PEadd (e1, e2) ->
EConstr.mkApp (Lazy.force coq_PEadd, [|typ; dump_expr e1; dump_expr e2|])
| Mc.PEsub (e1, e2) ->
EConstr.mkApp (Lazy.force coq_PEsub, [|typ; dump_expr e1; dump_expr e2|])
| Mc.PEopp e -> EConstr.mkApp (Lazy.force coq_PEopp, [|typ; dump_expr e|])
| Mc.PEmul (e1, e2) ->
EConstr.mkApp (Lazy.force coq_PEmul, [|typ; dump_expr e1; dump_expr e2|])
| Mc.PEpow (e, n) ->
EConstr.mkApp (Lazy.force coq_PEpow, [|typ; dump_expr e; dump_n n|])
in
dump_expr e
let dump_pol typ dump_c e =
let rec dump_pol e =
match e with
| Mc.Pc n -> EConstr.mkApp (Lazy.force coq_Pc, [|typ; dump_c n|])
| Mc.Pinj (p, pol) ->
EConstr.mkApp (Lazy.force coq_Pinj, [|typ; dump_positive p; dump_pol pol|])
| Mc.PX (pol1, p, pol2) ->
EConstr.mkApp
( Lazy.force coq_PX
, [|typ; dump_pol pol1; dump_positive p; dump_pol pol2|] )
in
dump_pol e
let pp_clause_tag o (f : 'cst clause) =
List.iter (fun ((p, _), (t, _)) -> Printf.fprintf o "(_ @%a)" Tag.pp t) f
let pp_cnf_tag o (f : 'cst cnf) =
List.iter (fun l -> Printf.fprintf o "[%a]" pp_clause_tag l) f
let dump_psatz typ dump_z e =
let z = Lazy.force typ in
let rec dump_cone e =
match e with
| Mc.PsatzLet (e1, e2) ->
EConstr.mkApp (Lazy.force coq_PsatzLet, [|z; dump_cone e1; dump_cone e2|])
| Mc.PsatzIn n -> EConstr.mkApp (Lazy.force coq_PsatzIn, [|z; dump_nat n|])
| Mc.PsatzMulC (e, c) ->
EConstr.mkApp
(Lazy.force coq_PsatzMultC, [|z; dump_pol z dump_z e; dump_cone c|])
| Mc.PsatzSquare e ->
EConstr.mkApp (Lazy.force coq_PsatzSquare, [|z; dump_pol z dump_z e|])
| Mc.PsatzAdd (e1, e2) ->
EConstr.mkApp (Lazy.force coq_PsatzAdd, [|z; dump_cone e1; dump_cone e2|])
| Mc.PsatzMulE (e1, e2) ->
EConstr.mkApp (Lazy.force coq_PsatzMulE, [|z; dump_cone e1; dump_cone e2|])
| Mc.PsatzC p -> EConstr.mkApp (Lazy.force coq_PsatzC, [|z; dump_z p|])
| Mc.PsatzZ -> EConstr.mkApp (Lazy.force coq_PsatzZ, [|z|])
in
dump_cone e
let undump_op sigma c =
let i, c = get_left_construct sigma c in
match i with
| 1 -> Mc.OpEq
| 2 -> Mc.OpNEq
| 3 -> Mc.OpLe
| 4 -> Mc.OpGe
| 5 -> Mc.OpLt
| 6 -> Mc.OpGt
| _ -> raise ParseError
let dump_op = function
| Mc.OpEq -> Lazy.force coq_OpEq
| Mc.OpNEq -> Lazy.force coq_OpNEq
| Mc.OpLe -> Lazy.force coq_OpLe
| Mc.OpGe -> Lazy.force coq_OpGe
| Mc.OpGt -> Lazy.force coq_OpGt
| Mc.OpLt -> Lazy.force coq_OpLt
let undump_cstr undump_constant sigma c =
let is c c' = EConstr.eq_constr sigma c (Lazy.force c') in
match EConstr.kind sigma c with
| App (c, [|_; e1; o; e2|]) when is c coq_Build ->
{Mc.flhs = undump_expr undump_constant sigma e1;
Mc.fop = undump_op sigma o;
Mc.frhs = undump_expr undump_constant sigma e2}
| _ -> raise ParseError
let dump_cstr typ dump_constant {Mc.flhs = e1; Mc.fop = o; Mc.frhs = e2} =
EConstr.mkApp
( Lazy.force coq_Build
, [| typ
; dump_expr typ dump_constant e1
; dump_op o
; dump_expr typ dump_constant e2 |] )
let assoc_const sigma x l =
try
snd (List.find (fun (x', y) -> EConstr.eq_constr sigma x (Lazy.force x')) l)
with Not_found -> raise ParseError
let zop_table_prop =
[ (coq_Zgt, Mc.OpGt)
; (coq_Zge, Mc.OpGe)
; (coq_Zlt, Mc.OpLt)
; (coq_Zle, Mc.OpLe) ]
let zop_table_bool =
[ (coq_Zgtb, Mc.OpGt)
; (coq_Zgeb, Mc.OpGe)
; (coq_Zltb, Mc.OpLt)
; (coq_Zleb, Mc.OpLe)
; (coq_Zeqb, Mc.OpEq) ]
let rop_table_prop =
[ (coq_Rgt, Mc.OpGt)
; (coq_Rge, Mc.OpGe)
; (coq_Rlt, Mc.OpLt)
; (coq_Rle, Mc.OpLe) ]
let rop_table_bool = []
let qop_table_prop = [(coq_Qlt, Mc.OpLt); (coq_Qle, Mc.OpLe); (coq_Qeq, Mc.OpEq)]
let qop_table_bool = []
type gl = Environ.env * Evd.evar_map
let is_convertible env sigma t1 t2 = Reductionops.is_conv env sigma t1 t2
let parse_operator table_prop table_bool has_equality typ (env, sigma) k
(op, args) =
match args with
| [|a1; a2|] ->
( assoc_const sigma op
(match k with Mc.IsProp -> table_prop | Mc.IsBool -> table_bool)
, a1
, a2 )
| [|ty; a1; a2|] ->
if
has_equality
&& EConstr.eq_constr sigma op (Lazy.force coq_eq)
&& is_convertible env sigma ty (Lazy.force typ)
then (Mc.OpEq, args.(1), args.(2))
else raise ParseError
| _ -> raise ParseError
let parse_zop = parse_operator zop_table_prop zop_table_bool true coq_Z
let parse_rop = parse_operator rop_table_prop [] true coq_R
let parse_qop = parse_operator qop_table_prop [] false coq_R
type 'a op =
| Binop of ('a Mc.pExpr -> 'a Mc.pExpr -> 'a Mc.pExpr)
| Opp
| Power
| Ukn of string
let assoc_ops sigma x l =
try
snd (List.find (fun (x', y) -> EConstr.eq_constr sigma x (Lazy.force x')) l)
with Not_found -> Ukn "Oups"
(**
* MODULE: Env is for environment.
*)
module Env = struct
type t =
{ vars : (EConstr.t * Mc.kind) list
;
gl : gl
}
let empty gl = {vars = []; gl}
(** [eq_constr gl x y] returns an updated [gl] if x and y can be unified *)
let eq_constr (env, sigma) x y =
match EConstr.eq_constr_universes_proj env sigma x y with
| Some csts -> (
let csts = UnivProblem.Set.force csts in
match Evd.add_universe_constraints sigma csts with
| sigma -> Some (env, sigma)
| exception UGraph.UniverseInconsistency _ -> None )
| None -> None
let compute_rank_add env v is_prop =
let rec _add gl vars n v =
match vars with
| [] -> (gl, [(v, is_prop)], n)
| (e, b) :: l -> (
match eq_constr gl e v with
| Some gl' -> (gl', vars, n)
| None ->
let gl, l', n = _add gl l (n + 1) v in
(gl, (e, b) :: l', n) )
in
let gl', vars', n = _add env.gl env.vars 1 v in
({vars = vars'; gl = gl'}, CamlToCoq.positive n)
let get_rank env v =
let gl = env.gl in
let rec _get_rank env n =
match env with
| [] -> raise (Invalid_argument "get_rank")
| (e, _) :: l -> (
match eq_constr gl e v with Some _ -> n | None -> _get_rank l (n + 1) )
in
_get_rank env.vars 1
let elements env = env.vars
let pp (genv, sigma) env =
let ppl =
List.mapi
(fun i (e, _) ->
Pp.str "x"
++ Pp.int (i + 1)
++ Pp.str ":"
++ Printer.pr_econstr_env genv sigma e)
env
in
List.fold_right (fun e p -> e ++ Pp.str " ; " ++ p) ppl (Pp.str "\n")
end
(**
* This is the big generic function for expression parsers.
*)
let parse_expr (genv, sigma) parse_constant parse_exp ops_spec env term =
if debug then
Feedback.msg_debug
(Pp.str "parse_expr: " ++ Printer.pr_leconstr_env genv sigma term);
let parse_variable env term =
let env, n = Env.compute_rank_add env term Mc.IsBool in
(Mc.PEX n, env)
in
let rec parse_expr env term =
let combine env op (t1, t2) =
let expr1, env = parse_expr env t1 in
let expr2, env = parse_expr env t2 in
(op expr1 expr2, env)
in
try (Mc.PEc (parse_constant (genv, sigma) term), env)
with ParseError -> (
match EConstr.kind sigma term with
| App (t, args) -> (
match EConstr.kind sigma t with
| Const c -> (
match assoc_ops sigma t ops_spec with
| Binop f -> combine env f (args.(0), args.(1))
| Opp ->
let expr, env = parse_expr env args.(0) in
(Mc.PEopp expr, env)
| Power -> (
try
let expr, env = parse_expr env args.(0) in
let power = parse_exp expr args.(1) in
(power, env)
with ParseError ->
let env, n = Env.compute_rank_add env term Mc.IsBool in
(Mc.PEX n, env) )
| Ukn s ->
if debug then (
Printf.printf "unknown op: %s\n" s;
flush stdout );
let env, n = Env.compute_rank_add env term Mc.IsBool in
(Mc.PEX n, env) )
| _ -> parse_variable env term )
| _ -> parse_variable env term )
in
parse_expr env term
let zop_spec =
[ (coq_Zplus, Binop (fun x y -> Mc.PEadd (x, y)))
; (coq_Zminus, Binop (fun x y -> Mc.PEsub (x, y)))
; (coq_Zmult, Binop (fun x y -> Mc.PEmul (x, y)))
; (coq_Zopp, Opp)
; (coq_Zpower, Power) ]
let qop_spec =
[ (coq_Qplus, Binop (fun x y -> Mc.PEadd (x, y)))
; (coq_Qminus, Binop (fun x y -> Mc.PEsub (x, y)))
; (coq_Qmult, Binop (fun x y -> Mc.PEmul (x, y)))
; (coq_Qopp, Opp)
; (coq_Qpower, Power) ]
let rop_spec =
[ (coq_Rplus, Binop (fun x y -> Mc.PEadd (x, y)))
; (coq_Rminus, Binop (fun x y -> Mc.PEsub (x, y)))
; (coq_Rmult, Binop (fun x y -> Mc.PEmul (x, y)))
; (coq_Ropp, Opp)
; (coq_Rpower, Power) ]
let parse_constant parse ((genv : Environ.env), sigma) t = parse sigma t
(** [parse_more_constant parse gl t] returns the reification of term [t].
If [t] is a ground term, then it is first reduced to normal form
before using a 'syntactic' parser *)
let parse_more_constant parse (genv, sigma) t =
try parse (genv, sigma) t
with ParseError ->
if debug then Feedback.msg_debug Pp.(str "try harder");
if is_ground_term genv sigma t then
parse (genv, sigma) (Redexpr.cbv_vm genv sigma t)
else raise ParseError
let zconstant = parse_constant parse_z
let qconstant = parse_constant parse_q
let nconstant = parse_constant parse_nat
(** [parse_more_zexpr parse_constant gl] improves the parsing of exponent
which can be arithmetic expressions (without variables).
[parse_constant_expr] returns a constant if the argument is an expression without variables. *)
let rec parse_zexpr gl =
parse_expr gl zconstant
(fun expr (x : EConstr.t) ->
let z = parse_zconstant gl x in
match z with
| Mc.Zneg _ -> Mc.PEc Mc.Z0
| _ -> Mc.PEpow (expr, Mc.Z.to_N z))
zop_spec
and parse_zconstant gl e =
let e, _ = parse_zexpr gl (Env.empty gl) e in
match Mc.zeval_const e with None -> raise ParseError | Some z -> z
let rconst_assoc =
[ (coq_Rplus, fun x y -> Mc.CPlus (x, y))
; (coq_Rminus, fun x y -> Mc.CMinus (x, y))
; (coq_Rmult, fun x y -> Mc.CMult (x, y))
]
let rconstant (genv, sigma) term =
let rec rconstant term =
match EConstr.kind sigma term with
| Const x ->
if EConstr.eq_constr sigma term (Lazy.force coq_R0) then Mc.C0
else if EConstr.eq_constr sigma term (Lazy.force coq_R1) then Mc.C1
else raise ParseError
| App (op, args) -> (
try
let f = assoc_const sigma op rconst_assoc in
let a = rconstant args.(0) in
let b = rconstant args.(1) in
f a b
with ParseError -> (
match op with
| op when EConstr.eq_constr sigma op (Lazy.force coq_Rinv) ->
let arg = rconstant args.(0) in
if Mc.qeq_bool (Mc.q_of_Rcst arg) {Mc.qnum = Mc.Z0; Mc.qden = Mc.XH}
then raise ParseError
else Mc.CInv arg
| op when EConstr.eq_constr sigma op (Lazy.force coq_Rpower) ->
Mc.CPow
( rconstant args.(0)
, Mc.Inr (parse_more_constant nconstant (genv, sigma) args.(1)) )
| op when EConstr.eq_constr sigma op (Lazy.force coq_IQR) ->
Mc.CQ (qconstant (genv, sigma) args.(0))
| op when EConstr.eq_constr sigma op (Lazy.force coq_IZR) ->
Mc.CZ (parse_more_constant zconstant (genv, sigma) args.(0))
| _ -> raise ParseError ) )
| _ -> raise ParseError
in
rconstant term
let rconstant (genv, sigma) term =
if debug then
Feedback.msg_debug
(Pp.str "rconstant: " ++ Printer.pr_leconstr_env genv sigma term ++ fnl ());
let res = rconstant (genv, sigma) term in
if debug then (
Printf.printf "rconstant -> %a\n" pp_Rcst res;
flush stdout );
res
let parse_qexpr gl =
parse_expr gl qconstant
(fun expr x ->
let exp = zconstant gl x in
match exp with
| Mc.Zneg _ -> (
match expr with
| Mc.PEc q -> Mc.PEc (Mc.qpower q exp)
| _ -> raise ParseError )
| _ ->
let exp = Mc.Z.to_N exp in
Mc.PEpow (expr, exp))
qop_spec
let parse_rexpr (genv, sigma) =
parse_expr (genv, sigma) rconstant
(fun expr x ->
let exp = Mc.N.of_nat (parse_nat sigma x) in
Mc.PEpow (expr, exp))
rop_spec
let parse_arith parse_op parse_expr (k : Mc.kind) env cstr (genv, sigma) =
if debug then
Feedback.msg_debug
( Pp.str "parse_arith: "
++ Printer.pr_leconstr_env genv sigma cstr
++ fnl () );
match EConstr.kind sigma cstr with
| App (op, args) ->
let op, lhs, rhs = parse_op (genv, sigma) k (op, args) in
let e1, env = parse_expr (genv, sigma) env lhs in
let e2, env = parse_expr (genv, sigma) env rhs in
({Mc.flhs = e1; Mc.fop = op; Mc.frhs = e2}, env)
| _ -> failwith "error : parse_arith(2)"
let parse_zarith = parse_arith parse_zop parse_zexpr
let parse_qarith = parse_arith parse_qop parse_qexpr
let parse_rarith = parse_arith parse_rop parse_rexpr
let mkAND b f1 f2 = Mc.AND (b, f1, f2)
let mkOR b f1 f2 = Mc.OR (b, f1, f2)
let mkIff b f1 f2 = Mc.IFF (b, f1, f2)
let mkIMPL b f1 f2 = Mc.IMPL (b, f1, None, f2)
let mkEQ f1 f2 = Mc.EQ (f1, f2)
let mkformula_binary b g term f1 f2 =
match (f1, f2) with
| Mc.X (b1, _), Mc.X (b2, _) -> Mc.X (b, term)
| _ -> g f1 f2
(**
* This is the big generic function for formula parsers.
*)
let is_prop env sigma term =
let sort = Retyping.get_sort_of env sigma term in
Sorts.is_prop sort
type formula_op =
{ op_impl : EConstr.t option
; op_and : EConstr.t
; op_or : EConstr.t
; op_iff : EConstr.t
; op_not : EConstr.t
; op_tt : EConstr.t
; op_ff : EConstr.t }
let prop_op =
lazy
{ op_impl = None
; op_and = Lazy.force coq_and
; op_or = Lazy.force coq_or
; op_iff = Lazy.force coq_iff
; op_not = Lazy.force coq_not
; op_tt = Lazy.force coq_True
; op_ff = Lazy.force coq_False }
let bool_op =
lazy
{ op_impl = Some (Lazy.force coq_implb)
; op_and = Lazy.force coq_andb
; op_or = Lazy.force coq_orb
; op_iff = Lazy.force coq_eqb
; op_not = Lazy.force coq_negb
; op_tt = Lazy.force coq_true
; op_ff = Lazy.force coq_false }
let is_implb sigma l o =
match o with None -> false | Some c -> EConstr.eq_constr sigma l c
let parse_formula (genv, sigma) parse_atom env tg term =
let parse_atom b env tg t =
try
let at, env = parse_atom b env t (genv, sigma) in
(Mc.A (b, at, (tg, t)), env, Tag.next tg)
with ParseError -> (Mc.X (b, t), env, tg)
in
let prop_op = Lazy.force prop_op in
let bool_op = Lazy.force bool_op in
let eq = Lazy.force coq_eq in
let bool = Lazy.force coq_bool in
let rec xparse_formula op k env tg term =
match EConstr.kind sigma term with
| App (l, rst) -> (
match rst with
| [|a; b|] when is_implb sigma l op.op_impl ->
let f, env, tg = xparse_formula op k env tg a in
let g, env, tg = xparse_formula op k env tg b in
(mkformula_binary k (mkIMPL k) term f g, env, tg)
| [|a; b|] when EConstr.eq_constr sigma l op.op_and ->
let f, env, tg = xparse_formula op k env tg a in
let g, env, tg = xparse_formula op k env tg b in
(mkformula_binary k (mkAND k) term f g, env, tg)
| [|a; b|] when EConstr.eq_constr sigma l op.op_or ->
let f, env, tg = xparse_formula op k env tg a in
let g, env, tg = xparse_formula op k env tg b in
(mkformula_binary k (mkOR k) term f g, env, tg)
| [|a; b|] when EConstr.eq_constr sigma l op.op_iff ->
let f, env, tg = xparse_formula op k env tg a in
let g, env, tg = xparse_formula op k env tg b in
(mkformula_binary k (mkIff k) term f g, env, tg)
| [|ty; a; b|]
when EConstr.eq_constr sigma l eq && is_convertible genv sigma ty bool
->
let f, env, tg = xparse_formula bool_op Mc.IsBool env tg a in
let g, env, tg = xparse_formula bool_op Mc.IsBool env tg b in
(mkformula_binary Mc.IsProp mkEQ term f g, env, tg)
| [|a|] when EConstr.eq_constr sigma l op.op_not ->
let f, env, tg = xparse_formula op k env tg a in
(Mc.NOT (k, f), env, tg)
| _ -> parse_atom k env tg term )
| Prod (typ, a, b)
when kind_is_prop k
&& (typ.binder_name = Anonymous || EConstr.Vars.noccurn sigma 1 b) ->
let f, env, tg = xparse_formula op k env tg a in
let g, env, tg = xparse_formula op k env tg b in
(mkformula_binary Mc.IsProp (mkIMPL Mc.IsProp) term f g, env, tg)
| _ ->
if EConstr.eq_constr sigma term op.op_tt then (Mc.TT k, env, tg)
else if EConstr.eq_constr sigma term op.op_ff then Mc.(FF k, env, tg)
else (Mc.X (k, term), env, tg)
in
xparse_formula prop_op Mc.IsProp env tg term
let undump_kind sigma k =
if EConstr.eq_constr sigma k (Lazy.force coq_IsProp) then Mc.IsProp
else Mc.IsBool
let dump_kind k =
Lazy.force (match k with Mc.IsProp -> coq_IsProp | Mc.IsBool -> coq_IsBool)
let undump_formula undump_atom tg sigma f =
let is c c' = EConstr.eq_constr sigma c (Lazy.force c') in
let kind k = undump_kind sigma k in
let rec xundump f =
match EConstr.kind sigma f with
| App (c, [|_; _; _; _; k|]) when is c coq_TT -> Mc.TT (kind k)
| App (c, [|_; _; _; _; k|]) when is c coq_FF -> Mc.FF (kind k)
| App (c, [|_; _; _; _; k; f1; f2|]) when is c coq_AND ->
Mc.AND (kind k, xundump f1, xundump f2)
| App (c, [|_; _; _; _; k; f1; f2|]) when is c coq_OR ->
Mc.OR (kind k, xundump f1, xundump f2)
| App (c, [|_; _; _; _; k; f1; _; f2|]) when is c coq_IMPL ->
Mc.IMPL (kind k, xundump f1, None, xundump f2)
| App (c, [|_; _; _; _; k; f|]) when is c coq_NOT ->
Mc.NOT (kind k, xundump f)
| App (c, [|_; _; _; _; k; f1; f2|]) when is c coq_IFF ->
Mc.IFF (kind k, xundump f1, xundump f2)
| App (c, [|_; _; _; _; f1; f2|]) when is c coq_EQ ->
Mc.EQ (xundump f1, xundump f2)
| App (c, [|_; _; _; _; k; x; _|]) when is c coq_Atom ->
Mc.A (kind k, undump_atom sigma x, tg)
| App (c, [|_; _; _; _; k; x|]) when is c coq_X ->
Mc.X (kind k, x)
| _ -> raise ParseError
in
xundump f
let dump_formula typ dump_atom f =
let app_ctor c args =
EConstr.mkApp
( Lazy.force c
, Array.of_list
( typ :: Lazy.force coq_eKind :: Lazy.force coq_unit
:: Lazy.force coq_unit :: args ) )
in
let rec xdump f =
match f with
| Mc.TT k -> app_ctor coq_TT [dump_kind k]
| Mc.FF k -> app_ctor coq_FF [dump_kind k]
| Mc.AND (k, x, y) -> app_ctor coq_AND [dump_kind k; xdump x; xdump y]
| Mc.OR (k, x, y) -> app_ctor coq_OR [dump_kind k; xdump x; xdump y]
| Mc.IMPL (k, x, _, y) ->
app_ctor coq_IMPL
[ dump_kind k
; xdump x
; EConstr.mkApp (Lazy.force coq_None, [|Lazy.force coq_unit|])
; xdump y ]
| Mc.NOT (k, x) -> app_ctor coq_NOT [dump_kind k; xdump x]
| Mc.IFF (k, x, y) -> app_ctor coq_IFF [dump_kind k; xdump x; xdump y]
| Mc.EQ (x, y) -> app_ctor coq_EQ [xdump x; xdump y]
| Mc.A (k, x, _) ->
app_ctor coq_Atom [dump_kind k; dump_atom x; Lazy.force coq_tt]
| Mc.X (k, t) -> app_ctor coq_X [dump_kind k; t]
in
xdump f
let prop_env_of_formula gl form =
Mc.(
let rec doit env = function
| TT _ | FF _ | A (_, _, _) -> env
| X (b, t) -> fst (Env.compute_rank_add env t b)
| AND (b, f1, f2) | OR (b, f1, f2) | IMPL (b, f1, _, f2) | IFF (b, f1, f2)
->
doit (doit env f1) f2
| NOT (b, f) -> doit env f
| EQ (f1, f2) -> doit (doit env f1) f2
in
doit (Env.empty gl) form)
let var_env_of_formula form =
let rec vars_of_expr = function
| Mc.PEX n -> ISet.singleton (CoqToCaml.positive n)
| Mc.PEc z -> ISet.empty
| Mc.PEadd (e1, e2) | Mc.PEmul (e1, e2) | Mc.PEsub (e1, e2) ->
ISet.union (vars_of_expr e1) (vars_of_expr e2)
| Mc.PEopp e | Mc.PEpow (e, _) -> vars_of_expr e
in
let vars_of_atom {Mc.flhs; Mc.fop; Mc.frhs} =
ISet.union (vars_of_expr flhs) (vars_of_expr frhs)
in
Mc.(
let rec doit = function
| TT _ | FF _ | X _ -> ISet.empty
| A (_, a, (t, c)) -> vars_of_atom a
| AND (_, f1, f2)
|OR (_, f1, f2)
|IMPL (_, f1, _, f2)
|IFF (_, f1, f2)
|EQ (f1, f2) ->
ISet.union (doit f1) (doit f2)
| NOT (_, f) -> doit f
in
doit form)
type 'cst dump_expr =
{
interp_typ : EConstr.constr
; dump_cst : 'cst -> EConstr.constr
; dump_add : EConstr.constr
; dump_sub : EConstr.constr
; dump_opp : EConstr.constr
; dump_mul : EConstr.constr
; dump_pow : EConstr.constr
; dump_pow_arg : Mc.n -> EConstr.constr
; dump_op_prop : (Mc.op2 * EConstr.constr) list
; dump_op_bool : (Mc.op2 * EConstr.constr) list }
let dump_zexpr =
lazy
{ interp_typ = Lazy.force coq_Z
; dump_cst = dump_z
; dump_add = Lazy.force coq_Zplus
; dump_sub = Lazy.force coq_Zminus
; dump_opp = Lazy.force coq_Zopp
; dump_mul = Lazy.force coq_Zmult
; dump_pow = Lazy.force coq_Zpower
; dump_pow_arg = (fun n -> dump_z (CamlToCoq.z (CoqToCaml.n n)))
; dump_op_prop = List.map (fun (x, y) -> (y, Lazy.force x)) zop_table_prop
; dump_op_bool = List.map (fun (x, y) -> (y, Lazy.force x)) zop_table_bool
}
let dump_qexpr =
lazy
{ interp_typ = Lazy.force coq_Q
; dump_cst = dump_q
; dump_add = Lazy.force coq_Qplus
; dump_sub = Lazy.force coq_Qminus
; dump_opp = Lazy.force coq_Qopp
; dump_mul = Lazy.force coq_Qmult
; dump_pow = Lazy.force coq_Qpower
; dump_pow_arg = (fun n -> dump_z (CamlToCoq.z (CoqToCaml.n n)))
; dump_op_prop = List.map (fun (x, y) -> (y, Lazy.force x)) qop_table_prop
; dump_op_bool = List.map (fun (x, y) -> (y, Lazy.force x)) qop_table_bool
}
let rec dump_Rcst_as_R cst =
match cst with
| Mc.C0 -> Lazy.force coq_R0
| Mc.C1 -> Lazy.force coq_R1
| Mc.CQ q -> EConstr.mkApp (Lazy.force coq_IQR, [|dump_q q|])
| Mc.CZ z -> EConstr.mkApp (Lazy.force coq_IZR, [|dump_z z|])
| Mc.CPlus (x, y) ->
EConstr.mkApp (Lazy.force coq_Rplus, [|dump_Rcst_as_R x; dump_Rcst_as_R y|])
| Mc.CMinus (x, y) ->
EConstr.mkApp (Lazy.force coq_Rminus, [|dump_Rcst_as_R x; dump_Rcst_as_R y|])
| Mc.CMult (x, y) ->
EConstr.mkApp (Lazy.force coq_Rmult, [|dump_Rcst_as_R x; dump_Rcst_as_R y|])
| Mc.CPow (x, y) -> (
match y with
| Mc.Inl z ->
EConstr.mkApp (Lazy.force coq_powerZR, [|dump_Rcst_as_R x; dump_z z|])
| Mc.Inr n ->
EConstr.mkApp (Lazy.force coq_Rpower, [|dump_Rcst_as_R x; dump_nat n|]) )
| Mc.CInv t -> EConstr.mkApp (Lazy.force coq_Rinv, [|dump_Rcst_as_R t|])
| Mc.COpp t -> EConstr.mkApp (Lazy.force coq_Ropp, [|dump_Rcst_as_R t|])
let dump_rexpr =
lazy
{ interp_typ = Lazy.force coq_R
; dump_cst = dump_Rcst_as_R
; dump_add = Lazy.force coq_Rplus
; dump_sub = Lazy.force coq_Rminus
; dump_opp = Lazy.force coq_Ropp
; dump_mul = Lazy.force coq_Rmult
; dump_pow = Lazy.force coq_Rpower
; dump_pow_arg = (fun n -> dump_nat (CamlToCoq.nat (CoqToCaml.n n)))
; dump_op_prop = List.map (fun (x, y) -> (y, Lazy.force x)) rop_table_prop
; dump_op_bool = List.map (fun (x, y) -> (y, Lazy.force x)) rop_table_bool
}
let prodn n env b =
let rec prodrec = function
| 0, env, b -> b
| n, (v, t) :: l, b ->
prodrec (n - 1, l, EConstr.mkProd (make_annot v Sorts.Relevant, t, b))
| _ -> assert false
in
prodrec (n, env, b)
(** [make_goal_of_formula depxr vars props form] where
- vars is an environment for the arithmetic variables occurring in form
- props is an environment for the propositions occurring in form
@return a goal where all the variables and propositions of the formula are quantified
*)
let eKind = function
| Mc.IsProp -> EConstr.mkProp
| Mc.IsBool -> Lazy.force coq_bool
let make_goal_of_formula gl dexpr form =
let vars_idx =
List.mapi (fun i v -> (v, i + 1)) (ISet.elements (var_env_of_formula form))
in
let props = prop_env_of_formula gl form in
let fresh_var str i = Names.Id.of_string (str ^ string_of_int i) in
let fresh_prop str i = Names.Id.of_string (str ^ string_of_int i) in
let vars_n =
List.map (fun (_, i) -> (fresh_var "__x" i, dexpr.interp_typ)) vars_idx
in
let props_n =
List.mapi
(fun i (_, k) -> (fresh_prop "__p" (i + 1), eKind k))
(Env.elements props)
in
let var_name_pos =
List.map2 (fun (idx, _) (id, _) -> (id, idx)) vars_idx vars_n
in
let dump_expr i e =
let rec dump_expr = function
| Mc.PEX n ->
EConstr.mkRel (i + List.assoc (CoqToCaml.positive n) vars_idx)
| Mc.PEc z -> dexpr.dump_cst z
| Mc.PEadd (e1, e2) ->
EConstr.mkApp (dexpr.dump_add, [|dump_expr e1; dump_expr e2|])
| Mc.PEsub (e1, e2) ->
EConstr.mkApp (dexpr.dump_sub, [|dump_expr e1; dump_expr e2|])
| Mc.PEopp e -> EConstr.mkApp (dexpr.dump_opp, [|dump_expr e|])
| Mc.PEmul (e1, e2) ->
EConstr.mkApp (dexpr.dump_mul, [|dump_expr e1; dump_expr e2|])
| Mc.PEpow (e, n) ->
EConstr.mkApp (dexpr.dump_pow, [|dump_expr e; dexpr.dump_pow_arg n|])
in
dump_expr e
in
let mkop_prop op e1 e2 =
try EConstr.mkApp (List.assoc op dexpr.dump_op_prop, [|e1; e2|])
with Not_found ->
EConstr.mkApp (Lazy.force coq_eq, [|dexpr.interp_typ; e1; e2|])
in
let dump_cstr_prop i {Mc.flhs; Mc.fop; Mc.frhs} =
mkop_prop fop (dump_expr i flhs) (dump_expr i frhs)
in
let mkop_bool op e1 e2 =
try EConstr.mkApp (List.assoc op dexpr.dump_op_bool, [|e1; e2|])
with Not_found ->
EConstr.mkApp (Lazy.force coq_eq, [|dexpr.interp_typ; e1; e2|])
in
let dump_cstr_bool i {Mc.flhs; Mc.fop; Mc.frhs} =
mkop_bool fop (dump_expr i flhs) (dump_expr i frhs)
in
let rec xdump_prop pi xi f =
match f with
| Mc.TT _ -> Lazy.force coq_True
| Mc.FF _ -> Lazy.force coq_False
| Mc.AND (_, x, y) ->
EConstr.mkApp
(Lazy.force coq_and, [|xdump_prop pi xi x; xdump_prop pi xi y|])
| Mc.OR (_, x, y) ->
EConstr.mkApp
(Lazy.force coq_or, [|xdump_prop pi xi x; xdump_prop pi xi y|])
| Mc.IFF (_, x, y) ->
EConstr.mkApp
(Lazy.force coq_iff, [|xdump_prop pi xi x; xdump_prop pi xi y|])
| Mc.IMPL (_, x, _, y) ->
EConstr.mkArrow (xdump_prop pi xi x) Sorts.Relevant
(xdump_prop (pi + 1) (xi + 1) y)
| Mc.NOT (_, x) ->
EConstr.mkArrow (xdump_prop pi xi x) Sorts.Relevant (Lazy.force coq_False)
| Mc.EQ (x, y) ->
EConstr.mkApp
( Lazy.force coq_eq
, [|Lazy.force coq_bool; xdump_bool pi xi x; xdump_bool pi xi y|] )
| Mc.A (_, x, _) -> dump_cstr_prop xi x
| Mc.X (_, t) ->
let idx = Env.get_rank props t in
EConstr.mkRel (pi + idx)
and xdump_bool pi xi f =
match f with
| Mc.TT _ -> Lazy.force coq_true
| Mc.FF _ -> Lazy.force coq_false
| Mc.AND (_, x, y) ->
EConstr.mkApp
(Lazy.force coq_andb, [|xdump_bool pi xi x; xdump_bool pi xi y|])
| Mc.OR (_, x, y) ->
EConstr.mkApp
(Lazy.force coq_orb, [|xdump_bool pi xi x; xdump_bool pi xi y|])
| Mc.IFF (_, x, y) ->
EConstr.mkApp
(Lazy.force coq_eqb, [|xdump_bool pi xi x; xdump_bool pi xi y|])
| Mc.IMPL (_, x, _, y) ->
EConstr.mkApp
(Lazy.force coq_implb, [|xdump_bool pi xi x; xdump_bool pi xi y|])
| Mc.NOT (_, x) ->
EConstr.mkApp (Lazy.force coq_negb, [|xdump_bool pi xi x|])
| Mc.EQ (x, y) -> assert false
| Mc.A (_, x, _) -> dump_cstr_bool xi x
| Mc.X (_, t) ->
let idx = Env.get_rank props t in
EConstr.mkRel (pi + idx)
in
let nb_vars = List.length vars_n in
let nb_props = List.length props_n in
let subst_prop p =
let idx = Env.get_rank props p in
EConstr.mkVar (Names.Id.of_string (Printf.sprintf "__p%i" idx))
in
let form' = Mc.mapX (fun _ p -> subst_prop p) Mc.IsProp form in
( prodn nb_props
(List.map (fun (x, y) -> (Name.Name x, y)) props_n)
(prodn nb_vars
(List.map (fun (x, y) -> (Name.Name x, y)) vars_n)
(xdump_prop (List.length vars_n) 0 form))
, List.rev props_n
, List.rev var_name_pos
, form' )
(**
* Given a conclusion and a list of affectations, rebuild a term prefixed by
* the appropriate letins.
* TODO: reverse the list of bindings!
*)
let set l concl =
let rec xset acc = function
| [] -> acc
| e :: l ->
let name, expr, typ = e in
xset
(EConstr.mkNamedLetIn
(make_annot (Names.Id.of_string name) Sorts.Relevant)
expr typ acc)
l
in
xset concl l
let coq_Branch = lazy (constr_of_ref "micromega.VarMap.Branch")
let coq_Elt = lazy (constr_of_ref "micromega.VarMap.Elt")
let coq_Empty = lazy (constr_of_ref "micromega.VarMap.Empty")
let coq_VarMap = lazy (constr_of_ref "micromega.VarMap.type")
let rec dump_varmap typ m =
match m with
| Mc.Empty -> EConstr.mkApp (Lazy.force coq_Empty, [|typ|])
| Mc.Elt v -> EConstr.mkApp (Lazy.force coq_Elt, [|typ; v|])
| Mc.Branch (l, o, r) ->
EConstr.mkApp
(Lazy.force coq_Branch, [|typ; dump_varmap typ l; o; dump_varmap typ r|])
let vm_of_list env =
match env with
| [] -> Mc.Empty
| (d, _) :: _ ->
List.fold_left
(fun vm (c, i) -> Mc.vm_add d (CamlToCoq.positive i) c vm)
Mc.Empty env
let rec dump_proof_term = function
| Micromega.DoneProof -> Lazy.force coq_doneProof
| Micromega.RatProof (cone, rst) ->
EConstr.mkApp
( Lazy.force coq_ratProof
, [|dump_psatz coq_Z dump_z cone; dump_proof_term rst|] )
| Micromega.CutProof (cone, prf) ->
EConstr.mkApp
( Lazy.force coq_cutProof
, [|dump_psatz coq_Z dump_z cone; dump_proof_term prf|] )
| Micromega.SplitProof (p, prf1, prf2) ->
EConstr.mkApp
( Lazy.force coq_splitProof
, [| dump_pol (Lazy.force coq_Z) dump_z p
; dump_proof_term prf1
; dump_proof_term prf2 |] )
| Micromega.EnumProof (c1, c2, prfs) ->
EConstr.mkApp
( Lazy.force coq_enumProof
, [| dump_psatz coq_Z dump_z c1
; dump_psatz coq_Z dump_z c2
; dump_list (Lazy.force coq_proofTerm) dump_proof_term prfs |] )
| Micromega.ExProof (p, prf) ->
EConstr.mkApp
(Lazy.force coq_ExProof, [|dump_positive p; dump_proof_term prf|])
let rec size_of_psatz = function
| Micromega.PsatzIn _ -> 1
| Micromega.PsatzSquare _ -> 1
| Micromega.PsatzMulC (_, p) -> 1 + size_of_psatz p
| Micromega.PsatzLet (p1, p2)
|Micromega.PsatzMulE (p1, p2)
|Micromega.PsatzAdd (p1, p2) ->
size_of_psatz p1 + size_of_psatz p2
| Micromega.PsatzC _ -> 1
| Micromega.PsatzZ -> 1
let rec size_of_pf = function
| Micromega.DoneProof -> 1
| Micromega.RatProof (p, a) -> size_of_pf a + size_of_psatz p
| Micromega.CutProof (p, a) -> size_of_pf a + size_of_psatz p
| Micromega.SplitProof (_, p1, p2) -> size_of_pf p1 + size_of_pf p2
| Micromega.EnumProof (p1, p2, l) ->
size_of_psatz p1 + size_of_psatz p2
+ List.fold_left (fun acc p -> size_of_pf p + acc) 0 l
| Micromega.ExProof (_, a) -> size_of_pf a + 1
let dump_proof_term t =
if debug then Printf.printf "dump_proof_term %i\n" (size_of_pf t);
dump_proof_term t
let pp_q o q =
Printf.fprintf o "%a/%a" pp_z q.Micromega.qnum pp_positive q.Micromega.qden
let rec parse_hyps (genv, sigma) parse_arith env tg hyps =
match hyps with
| [] -> ([], env, tg)
| (i, t) :: l ->
let lhyps, env, tg = parse_hyps (genv, sigma) parse_arith env tg l in
if is_prop genv sigma t then
try
let c, env, tg = parse_formula (genv, sigma) parse_arith env tg t in
((i, c) :: lhyps, env, tg)
with ParseError -> (lhyps, env, tg)
else (lhyps, env, tg)
let parse_goal gl parse_arith (env : Env.t) hyps term =
let f, env, tg = parse_formula gl parse_arith env (Tag.from 0) term in
let lhyps, env, tg = parse_hyps gl parse_arith env tg hyps in
(lhyps, f, env)
(**
* The datastructures that aggregate theory-dependent proof values.
*)
type ('synt_c, 'prf) domain_spec =
{ typ : EConstr.constr
;
coeff : EConstr.constr
;
dump_coeff : 'synt_c -> EConstr.constr
; undump_coeff : Evd.evar_map -> EConstr.constr -> 'synt_c
; proof_typ : EConstr.constr
; dump_proof : 'prf -> EConstr.constr
; coeff_eq : 'synt_c -> 'synt_c -> bool }
let zz_domain_spec =
lazy
{ typ = Lazy.force coq_Z
; coeff = Lazy.force coq_Z
; dump_coeff = dump_z
; undump_coeff = parse_z
; proof_typ = Lazy.force coq_proofTerm
; dump_proof = dump_proof_term
; coeff_eq = Mc.zeq_bool }
let qq_domain_spec =
lazy
{ typ = Lazy.force coq_Q
; coeff = Lazy.force coq_Q
; dump_coeff = dump_q
; undump_coeff = parse_q
; proof_typ = Lazy.force coq_QWitness
; dump_proof = dump_psatz coq_Q dump_q
; coeff_eq = Mc.qeq_bool }
let max_tag f =
1
+ Tag.to_int
(Mc.foldA (fun t1 (t2, _) -> Tag.max t1 t2) Mc.IsProp f (Tag.from 0))
(** Naive topological sort of constr according to the subterm-ordering *)
(**
* Instantiate the current Coq goal with a Micromega formula, a varmap, and a
* witness.
*)
let micromega_order_change spec cert cert_typ env ff
=
let formula_typ = EConstr.mkApp (Lazy.force coq_Cstr, [|spec.coeff|]) in
let ff = dump_formula formula_typ (dump_cstr spec.coeff spec.dump_coeff) ff in
let vm = dump_varmap spec.typ (vm_of_list env) in
Proofview.Goal.enter (fun gl ->
Tacticals.tclTHENLIST
[ Tactics.change_concl
(set
[ ( "__ff"
, ff
, EConstr.mkApp
( Lazy.force coq_Formula
, [|formula_typ; Lazy.force coq_IsProp|] ) )
; ( "__varmap"
, vm
, EConstr.mkApp (Lazy.force coq_VarMap, [|spec.typ|]) )
; ("__wit", cert, cert_typ) ]
(Tacmach.pf_concl gl)) ])
(**
* The datastructures that aggregate prover attributes.
*)
open Certificate
type ('option, 'a, 'prf, 'model) prover =
{ name : string
;
get_option : unit -> 'option
;
prover : 'option * 'a list -> ('prf, 'model) Certificate.res
;
hyps : 'prf -> ISet.t
;
compact : 'prf -> (int -> int) -> 'prf
;
pp_prf : out_channel -> 'prf -> unit
;
pp_f : out_channel -> 'a -> unit
}
(**
* Given a prover and a disjunction of atoms, find a proof of any of
* the atoms. Returns an (optional) pair of a proof and a prover
* datastructure.
*)
let find_witness p polys1 =
try
let polys1 = List.map fst polys1 in
p.prover (p.get_option (), polys1)
with e ->
begin
Printf.printf "find_witness %s" (Printexc.to_string e);
raise e
end
(**
* Given a prover and a CNF, find a proof for each of the clauses.
* Return the proofs as a list.
*)
let witness_list prover l =
let rec xwitness_list l =
match l with
| [] -> Prf []
| e :: l -> (
match xwitness_list l with
| Model (m, e) -> Model (m, e)
| Unknown -> Unknown
| Prf l -> (
match find_witness prover e with
| Model m -> Model (m, e)
| Unknown -> Unknown
| Prf w -> Prf (w :: l) ) )
in
xwitness_list l
(**
* Prune the proof object, according to the 'diff' between two cnf formulas.
*)
let compact_proofs prover (eq_cst : 'cst -> 'cst -> bool) (cnf_ff : 'cst cnf) res
(cnf_ff' : 'cst cnf) =
let eq_formula (p1, o1) (p2, o2) =
let open Mutils.Hash in
eq_pol eq_cst p1 p2 && eq_op1 o1 o2
in
let compact_proof (old_cl : 'cst clause) prf (new_cl : 'cst clause)
=
let new_cl = List.mapi (fun i (f, _) -> (f, i)) new_cl in
let remap i =
let formula =
try fst (List.nth old_cl i) with Failure _ -> failwith "bad old index"
in
CList.assoc_f eq_formula formula new_cl
in
let res =
try prover.compact prf remap
with x when CErrors.noncritical x -> (
if debug then
Printf.fprintf stdout "Proof compaction %s" (Printexc.to_string x);
match prover.prover (prover.get_option (), List.map fst new_cl) with
| Unknown | Model _ -> failwith "proof compaction error"
| Prf p -> p )
in
if debug then begin
Printf.printf " -> %a\n" prover.pp_prf res;
flush stdout
end;
res
in
let is_proof_compatible (hyps, (old_cl : 'cst clause), prf) (new_cl : 'cst clause) =
let eq (f1, (t1, e1)) (f2, (t2, e2)) =
Int.equal (Tag.compare t1 t2) 0
&& eq_formula f1 f2
in
is_sublist eq (Lazy.force hyps) new_cl
in
let map cl prf =
let hyps = lazy (selecti (prover.hyps prf) cl) in
hyps, cl, prf
in
let cnf_res = List.map2 map cnf_ff res in
if debug then begin
Printf.printf "CNFRES\n";
flush stdout;
Printf.printf "CNFOLD %a\n" pp_cnf_tag cnf_ff;
List.iter
(fun (lazy hyps, cl, prf) ->
Printf.printf "\nProver %a -> %a\n" pp_clause_tag cl pp_clause_tag hyps;
flush stdout)
cnf_res;
Printf.printf "CNFNEW %a\n" pp_cnf_tag cnf_ff'
end;
List.map
(fun x ->
let _, o, p =
try List.find (fun p -> is_proof_compatible p x) cnf_res
with Not_found ->
Printf.printf "ERROR: no compatible proof";
flush stdout;
failwith "Cannot find compatible proof"
in
compact_proof o p x)
cnf_ff'
(**
* "Hide out" tagged atoms of a formula by transforming them into generic
* variables. See the Tag module in mutils.ml for more.
*)
let abstract_formula : TagSet.t -> 'a formula -> 'a formula =
fun hyps f ->
let to_constr =
Mc.
{ mkTT =
(let coq_True = Lazy.force coq_True in
let coq_true = Lazy.force coq_true in
function Mc.IsProp -> coq_True | Mc.IsBool -> coq_true)
; mkFF =
(let coq_False = Lazy.force coq_False in
let coq_false = Lazy.force coq_false in
function Mc.IsProp -> coq_False | Mc.IsBool -> coq_false)
; mkA = (fun k a (tg, t) -> t)
; mkAND =
(let coq_and = Lazy.force coq_and in
let coq_andb = Lazy.force coq_andb in
fun k x y ->
EConstr.mkApp
( (match k with Mc.IsProp -> coq_and | Mc.IsBool -> coq_andb)
, [|x; y|] ))
; mkOR =
(let coq_or = Lazy.force coq_or in
let coq_orb = Lazy.force coq_orb in
fun k x y ->
EConstr.mkApp
( (match k with Mc.IsProp -> coq_or | Mc.IsBool -> coq_orb)
, [|x; y|] ))
; mkIMPL =
(fun k x y ->
match k with
| Mc.IsProp -> EConstr.mkArrow x Sorts.Relevant y
| Mc.IsBool -> EConstr.mkApp (Lazy.force coq_implb, [|x; y|]))
; mkIFF =
(let coq_iff = Lazy.force coq_iff in
let coq_eqb = Lazy.force coq_eqb in
fun k x y ->
EConstr.mkApp
( (match k with Mc.IsProp -> coq_iff | Mc.IsBool -> coq_eqb)
, [|x; y|] ))
; mkNOT =
(let coq_not = Lazy.force coq_not in
let coq_negb = Lazy.force coq_negb in
fun k x ->
EConstr.mkApp
( (match k with Mc.IsProp -> coq_not | Mc.IsBool -> coq_negb)
, [|x|] ))
; mkEQ =
(let coq_eq = Lazy.force coq_eq in
fun x y -> EConstr.mkApp (coq_eq, [|Lazy.force coq_bool; x; y|])) }
in
Mc.abst_form to_constr (fun (t, _) -> TagSet.mem t hyps) true Mc.IsProp f
let rec abstract_wrt_formula f1 f2 =
Mc.(
match (f1, f2) with
| X (b, c), _ -> X (b, c)
| A _, A _ -> f2
| AND (b, f1, f2), AND (_, f1', f2') ->
AND (b, abstract_wrt_formula f1 f1', abstract_wrt_formula f2 f2')
| OR (b, f1, f2), OR (_, f1', f2') ->
OR (b, abstract_wrt_formula f1 f1', abstract_wrt_formula f2 f2')
| IMPL (b, f1, _, f2), IMPL (_, f1', x, f2') ->
IMPL (b, abstract_wrt_formula f1 f1', x, abstract_wrt_formula f2 f2')
| IFF (b, f1, f2), IFF (_, f1', f2') ->
IFF (b, abstract_wrt_formula f1 f1', abstract_wrt_formula f2 f2')
| EQ (f1, f2), EQ (f1', f2') ->
EQ (abstract_wrt_formula f1 f1', abstract_wrt_formula f2 f2')
| FF b, FF _ -> FF b
| TT b, TT _ -> TT b
| NOT (b, x), NOT (_, y) -> NOT (b, abstract_wrt_formula x y)
| _ -> failwith "abstract_wrt_formula")
(**
* This exception is raised by really_call_csdpcert if Coq's configure didn't
* find a CSDP executable.
*)
exception CsdpNotFound
let fail_csdp_not_found () =
flush stdout;
let s =
"Skipping the rest of this tactic: the complexity of the \
goal requires the use of an external tool called CSDP. \n\n\
However, the \"csdp\" binary is not present in the search path. \n\n\
Some OS distributions include CSDP (package \"coinor-csdp\" on Debian \
for instance). You can download binaries \
and source code from <https://github.com/coin-or/csdp>." in
Tacticals.tclFAIL (Pp.str s)
(**
* This is the core of Micromega: apply the prover, analyze the result and
* prune unused fomulas, and finally modify the proof state.
*)
let formula_hyps_concl hyps concl =
List.fold_right
(fun (id, f) (cc, ids) ->
match f with
| Mc.X _ -> (cc, ids)
| _ -> (Mc.IMPL (Mc.IsProp, f, Some id, cc), id :: ids))
hyps (concl, [])
let rec fold_trace f accu = function
| Micromega.Null -> accu
| Micromega.Merge (t1, t2) -> fold_trace f (fold_trace f accu t1) t2
| Micromega.Push (x, t) -> fold_trace f (f accu x) t
let micromega_tauto ?(abstract=true) pre_process cnf spec prover
(polys1 : (Names.Id.t * 'cst formula) list) (polys2 : 'cst formula) =
let ff, ids = formula_hyps_concl polys1 polys2 in
let mt = CamlToCoq.positive (max_tag ff) in
let pre_ff = pre_process mt (ff : 'a formula) in
let cnf_ff, cnf_ff_tags = cnf Mc.IsProp pre_ff in
match witness_list prover cnf_ff with
| Model m -> Model m
| Unknown -> Unknown
| Prf res ->
let deps =
List.fold_left
(fun s (cl, prf) ->
let tags =
ISet.fold
(fun i s ->
let t = fst (snd (List.nth cl i)) in
if debug then Printf.fprintf stdout "T : %i -> %a" i Tag.pp t;
TagSet.add t s
)
(prover.hyps prf) TagSet.empty
in
TagSet.union s tags)
(fold_trace (fun s (i, _) -> TagSet.add i s) TagSet.empty cnf_ff_tags)
(List.combine cnf_ff res)
in
let ff' = if abstract then abstract_formula deps ff else ff in
let pre_ff' = pre_process mt ff' in
let cnf_ff', _ = cnf Mc.IsProp pre_ff' in
if debug then begin
output_string stdout "\n";
Printf.printf "TForm : %a\n" pp_formula ff;
flush stdout;
Printf.printf "CNF : %a\n" pp_cnf_tag cnf_ff;
flush stdout;
Printf.printf "TFormAbs : %a\n" pp_formula ff';
flush stdout;
Printf.printf "TFormPre : %a\n" pp_formula pre_ff;
flush stdout;
Printf.printf "TFormPreAbs : %a\n" pp_formula pre_ff';
flush stdout;
Printf.printf "CNF : %a\n" pp_cnf_tag cnf_ff';
flush stdout
end;
let res' = compact_proofs prover spec.coeff_eq cnf_ff res cnf_ff' in
let ff', res', ids = (ff', res', Mc.ids_of_formula Mc.IsProp ff') in
let res' = dump_list spec.proof_typ spec.dump_proof res' in
Prf (ids, ff', res')
let micromega_tauto ?abstract pre_process cnf spec prover
(polys1 : (Names.Id.t * 'cst formula) list) (polys2 : 'cst formula) =
try micromega_tauto ?abstract pre_process cnf spec prover polys1 polys2
with Not_found ->
Printexc.print_backtrace stdout;
flush stdout;
Unknown
(**
* Parse the proof environment, and call micromega_tauto
*)
let fresh_id avoid id gl =
Tactics.fresh_id_in_env avoid id (Proofview.Goal.env gl)
let clear_all_no_check =
Proofview.Goal.enter (fun gl ->
let concl = Tacmach.pf_concl gl in
let env =
Environ.reset_with_named_context Environ.empty_named_context_val
(Tacmach.pf_env gl)
in
Refine.refine ~typecheck:false (fun sigma ->
Evarutil.new_evar env sigma ~principal:true concl))
let micromega_gen parse_arith pre_process cnf spec dumpexpr prover tac =
Proofview.Goal.enter (fun gl ->
let sigma = Tacmach.project gl in
let genv = Tacmach.pf_env gl in
let concl = Tacmach.pf_concl gl in
let hyps = Tacmach.pf_hyps_types gl in
try
let hyps, concl, env =
parse_goal (genv, sigma) parse_arith
(Env.empty (genv, sigma))
hyps concl
in
let env = Env.elements env in
let spec = Lazy.force spec in
let dumpexpr = Lazy.force dumpexpr in
if debug then
Feedback.msg_debug (Pp.str "Env " ++ Env.pp (genv, sigma) env);
match
micromega_tauto pre_process cnf spec prover hyps concl
with
| Unknown ->
flush stdout;
Tacticals.tclFAIL (Pp.str " Cannot find witness")
| Model (m, e) ->
Tacticals.tclFAIL (Pp.str " Cannot find witness")
| Prf (ids, ff', res') ->
let arith_goal, props, vars, ff_arith =
make_goal_of_formula (genv, sigma) dumpexpr ff'
in
let intro (id, _) = Tactics.introduction id in
let intro_vars = Tacticals.tclTHENLIST (List.map intro vars) in
let intro_props = Tacticals.tclTHENLIST (List.map intro props) in
let goal_name =
fresh_id Id.Set.empty (Names.Id.of_string "__arith") gl
in
let env' = List.map (fun (id, i) -> (EConstr.mkVar id, i)) vars in
let tac_arith =
Tacticals.tclTHENLIST
[ clear_all_no_check
; intro_props
; intro_vars
; micromega_order_change spec res'
(EConstr.mkApp (Lazy.force coq_list, [|spec.proof_typ|]))
env' ff_arith ]
in
let goal_props =
List.rev
(List.map fst
(Env.elements (prop_env_of_formula (genv, sigma) ff')))
in
let goal_vars =
List.map (fun (_, i) -> fst (List.nth env (i - 1))) vars
in
let arith_args = goal_props @ goal_vars in
let kill_arith = Tacticals.tclTHEN tac_arith tac in
Tacticals.tclTHEN
(Tactics.assert_by (Names.Name goal_name) arith_goal
kill_arith)
(
Tactics.exact_check
(EConstr.applist
( EConstr.mkVar goal_name
, arith_args @ List.map EConstr.mkVar ids )))
with
| CsdpNotFound -> fail_csdp_not_found ()
| x ->
if debug then
Tacticals.tclFAIL (Pp.str (Printexc.get_backtrace ()))
else raise x)
let micromega_wit_gen pre_process cnf spec prover wit_id ff =
Proofview.Goal.enter (fun gl ->
let sigma = Tacmach.project gl in
try
let spec = Lazy.force spec in
let undump_cstr = undump_cstr spec.undump_coeff in
let tg = Tag.from 0, Lazy.force coq_tt in
let ff = undump_formula undump_cstr tg sigma ff in
match
micromega_tauto ~abstract:false pre_process cnf spec prover [] ff
with
| Unknown ->
flush stdout;
Tacticals.tclFAIL (Pp.str " Cannot find witness")
| Model (m, e) ->
Tacticals.tclFAIL (Pp.str " Cannot find witness")
| Prf (_ids, _ff', res') ->
let tres' = EConstr.mkApp (Lazy.force coq_list, [|spec.proof_typ|]) in
Tactics.letin_tac
None (Names.Name wit_id) res' (Some tres') Locusops.nowhere
with
| CsdpNotFound -> fail_csdp_not_found ()
| x ->
if debug then
Tacticals.tclFAIL (Pp.str (Printexc.get_backtrace ()))
else raise x)
let micromega_order_changer cert env ff =
let coeff = Lazy.force coq_Rcst in
let dump_coeff = dump_Rcst in
let typ = Lazy.force coq_R in
let cert_typ =
EConstr.mkApp (Lazy.force coq_list, [|Lazy.force coq_QWitness|])
in
let formula_typ = EConstr.mkApp (Lazy.force coq_Cstr, [|coeff|]) in
let ff = dump_formula formula_typ (dump_cstr coeff dump_coeff) ff in
let vm = dump_varmap typ (vm_of_list env) in
Proofview.Goal.enter (fun gl ->
Tacticals.tclTHENLIST
[ Tactics.change_concl
(set
[ ( "__ff"
, ff
, EConstr.mkApp
( Lazy.force coq_Formula
, [|formula_typ; Lazy.force coq_IsProp|] ) )
; ("__varmap", vm, EConstr.mkApp (Lazy.force coq_VarMap, [|typ|]))
; ("__wit", cert, cert_typ) ]
(Tacmach.pf_concl gl))
])
let micromega_genr prover tac =
let parse_arith = parse_rarith in
let spec =
lazy
{ typ = Lazy.force coq_R
; coeff = Lazy.force coq_Rcst
; dump_coeff = dump_q
; undump_coeff = parse_q
; proof_typ = Lazy.force coq_QWitness
; dump_proof = dump_psatz coq_Q dump_q
; coeff_eq = Mc.qeq_bool }
in
Proofview.Goal.enter (fun gl ->
let sigma = Tacmach.project gl in
let genv = Tacmach.pf_env gl in
let concl = Tacmach.pf_concl gl in
let hyps = Tacmach.pf_hyps_types gl in
try
let hyps, concl, env =
parse_goal (genv, sigma) parse_arith
(Env.empty (genv, sigma))
hyps concl
in
let env = Env.elements env in
let spec = Lazy.force spec in
let hyps' =
List.map
(fun (n, f) ->
( n
, Mc.map_bformula Mc.IsProp
(Micromega.map_Formula Micromega.q_of_Rcst)
f ))
hyps
in
let concl' =
Mc.map_bformula Mc.IsProp
(Micromega.map_Formula Micromega.q_of_Rcst)
concl
in
match
micromega_tauto
(fun _ x -> x)
Mc.cnfQ spec prover hyps' concl'
with
| Unknown | Model _ ->
flush stdout;
Tacticals.tclFAIL (Pp.str " Cannot find witness")
| Prf (ids, ff', res') ->
let ff, ids =
formula_hyps_concl
(List.filter (fun (n, _) -> CList.mem_f Id.equal n ids) hyps)
concl
in
let ff' = abstract_wrt_formula ff' ff in
let arith_goal, props, vars, ff_arith =
make_goal_of_formula (genv, sigma) (Lazy.force dump_rexpr) ff'
in
let intro (id, _) = Tactics.introduction id in
let intro_vars = Tacticals.tclTHENLIST (List.map intro vars) in
let intro_props = Tacticals.tclTHENLIST (List.map intro props) in
let ipat_of_name id =
Some (CAst.make @@ IntroNaming (Namegen.IntroIdentifier id))
in
let goal_name =
fresh_id Id.Set.empty (Names.Id.of_string "__arith") gl
in
let env' = List.map (fun (id, i) -> (EConstr.mkVar id, i)) vars in
let tac_arith =
Tacticals.tclTHENLIST
[ clear_all_no_check
; intro_props
; intro_vars
; micromega_order_changer res' env' ff_arith ]
in
let goal_props =
List.rev
(List.map fst
(Env.elements (prop_env_of_formula (genv, sigma) ff')))
in
let goal_vars =
List.map (fun (_, i) -> fst (List.nth env (i - 1))) vars
in
let arith_args = goal_props @ goal_vars in
let kill_arith = Tacticals.tclTHEN tac_arith tac in
Tacticals.tclTHENS
(Tactics.forward true (Some None) (ipat_of_name goal_name)
arith_goal)
[ kill_arith
; Tacticals.tclTHENLIST
[ Tactics.generalize (List.map EConstr.mkVar ids)
; Tactics.exact_check
(EConstr.applist (EConstr.mkVar goal_name, arith_args)) ] ]
with
| CsdpNotFound -> fail_csdp_not_found ())
let lift_ratproof prover l =
match prover l with
| Unknown | Model _ -> Unknown
| Prf c -> Prf (Mc.RatProof (c, Mc.DoneProof))
type micromega_polys = (Micromega.q Mc.pol * Mc.op1) list
[@@@ocaml.warning "-37"]
type csdp_certificate = S of Sos_types.positivstellensatz option | F of string
type provername = string * int option
(**
* The caching mechanism.
*)
module MakeCache (T : sig
type prover_option
type coeff
val hash_prover_option : int -> prover_option -> int
val hash_coeff : int -> coeff -> int
val eq_prover_option : prover_option -> prover_option -> bool
val eq_coeff : coeff -> coeff -> bool
end) : sig
type key = T.prover_option * (T.coeff Mc.pol * Mc.op1) list
val memo_opt : (unit -> bool) -> string -> (key -> 'a) -> key -> 'a
end = struct
module E = struct
type t = T.prover_option * (T.coeff Mc.pol * Mc.op1) list
let equal =
Hash.(
eq_pair T.eq_prover_option
(CList.equal (eq_pair (eq_pol T.eq_coeff) Hash.eq_op1)))
let hash =
let hash_cstr = Hash.(hash_pair (hash_pol T.hash_coeff) hash_op1) in
Hash.((hash_pair T.hash_prover_option (List.fold_left hash_cstr)) 0)
end
include Persistent_cache.PHashtable (E)
let memo_opt use_cache cache_file f =
let memof = memo cache_file f in
fun x -> if use_cache () then memof x else f x
end
module CacheCsdp = MakeCache (struct
type prover_option = provername
type coeff = Mc.q
let hash_prover_option =
Hash.(hash_pair hash_string (hash_elt (Option.hash (fun x -> x))))
let eq_prover_option = Hash.(eq_pair String.equal (Option.equal Int.equal))
let hash_coeff = Hash.hash_q
let eq_coeff = Hash.eq_q
end)
(**
* Build the command to call csdpcert, and launch it. This in turn will call
* the sos driver to the csdp executable.
* Throw CsdpNotFound if Coq isn't aware of any csdp executable.
*)
let require_csdp =
if System.is_in_system_path "csdp" then lazy () else lazy (raise CsdpNotFound)
let really_call_csdpcert :
provername -> micromega_polys -> Sos_types.positivstellensatz option =
fun provername poly ->
Lazy.force require_csdp;
let cmdname =
let env = Boot.Env.init () in
let plugin_dir = Boot.Env.plugins env |> Boot.Path.to_string in
List.fold_left Filename.concat plugin_dir
["micromega"; "csdpcert" ^ Coq_config.exec_extension]
in
let cmdname = if Sys.file_exists cmdname then cmdname else "csdpcert" in
match (command cmdname [|cmdname|] (provername, poly) : csdp_certificate) with
| F str ->
if debug then Printf.fprintf stdout "really_call_csdpcert : %s\n" str;
raise (failwith str)
| S res -> res
(**
* Check the cache before calling the prover.
*)
let xcall_csdpcert =
CacheCsdp.memo_opt use_csdp_cache ".csdp.cache" (fun (prover, pb) ->
really_call_csdpcert prover pb)
(**
* Prover callback functions.
*)
let call_csdpcert prover pb = xcall_csdpcert (prover, pb)
let rec z_to_q_pol e =
match e with
| Mc.Pc z -> Mc.Pc {Mc.qnum = z; Mc.qden = Mc.XH}
| Mc.Pinj (p, pol) -> Mc.Pinj (p, z_to_q_pol pol)
| Mc.PX (pol1, p, pol2) -> Mc.PX (z_to_q_pol pol1, p, z_to_q_pol pol2)
let call_csdpcert_q provername poly =
match call_csdpcert provername poly with
| None -> Unknown
| Some cert ->
let cert = Certificate.q_cert_of_pos cert in
if Mc.qWeakChecker poly cert then Prf cert
else (
print_string "buggy certificate";
Unknown )
let call_csdpcert_z provername poly =
let l = List.map (fun (e, o) -> (z_to_q_pol e, o)) poly in
match call_csdpcert provername l with
| None -> Unknown
| Some cert ->
let cert = Certificate.z_cert_of_pos cert in
if Mc.zWeakChecker poly cert then Prf cert
else (
print_string "buggy certificate";
flush stdout;
Unknown )
let rec xhyps_of_cone base acc prf =
match prf with
| Mc.PsatzC _ | Mc.PsatzZ | Mc.PsatzSquare _ -> acc
| Mc.PsatzIn n ->
let n = CoqToCaml.nat n in
if n >= base then ISet.add (n - base) acc else acc
| Mc.PsatzLet (e1, e2) ->
xhyps_of_cone (base + 1) (xhyps_of_cone base acc e1) e2
| Mc.PsatzMulC (_, c) -> xhyps_of_cone base acc c
| Mc.PsatzAdd (e1, e2) | Mc.PsatzMulE (e1, e2) ->
xhyps_of_cone base (xhyps_of_cone base acc e2) e1
let hyps_of_cone prf = xhyps_of_cone 0 ISet.empty prf
let hyps_of_pt pt =
let rec xhyps base pt acc =
match pt with
| Mc.DoneProof -> acc
| Mc.RatProof (c, pt) -> xhyps (base + 1) pt (xhyps_of_cone base acc c)
| Mc.CutProof (c, pt) -> xhyps (base + 1) pt (xhyps_of_cone base acc c)
| Mc.SplitProof (p, p1, p2) -> xhyps (base + 1) p1 (xhyps (base + 1) p2 acc)
| Mc.EnumProof (c1, c2, l) ->
let s = xhyps_of_cone base (xhyps_of_cone base acc c2) c1 in
List.fold_left (fun s x -> xhyps (base + 1) x s) s l
| Mc.ExProof (_, pt) -> xhyps (base + 3) pt acc
in
xhyps 0 pt ISet.empty
let compact_cone prf f =
let translate ofset x = if x < ofset then x else f (x - ofset) + ofset in
let np ofset n = CamlToCoq.nat (translate ofset (CoqToCaml.nat n)) in
let rec xinterp ofset prf =
match prf with
| Mc.PsatzC _ | Mc.PsatzZ | Mc.PsatzSquare _ -> prf
| Mc.PsatzIn n -> Mc.PsatzIn (np ofset n)
| Mc.PsatzLet (e1, e2) ->
Mc.PsatzLet (xinterp ofset e1, xinterp (ofset + 1) e2)
| Mc.PsatzMulC (e, c) -> Mc.PsatzMulC (e, xinterp ofset c)
| Mc.PsatzAdd (e1, e2) -> Mc.PsatzAdd (xinterp ofset e1, xinterp ofset e2)
| Mc.PsatzMulE (e1, e2) -> Mc.PsatzMulE (xinterp ofset e1, xinterp ofset e2)
in
xinterp 0 prf
let compact_pt pt f =
let translate ofset x = if x < ofset then x else f (x - ofset) + ofset in
let rec compact_pt ofset pt =
match pt with
| Mc.DoneProof -> Mc.DoneProof
| Mc.RatProof (c, pt) ->
Mc.RatProof (compact_cone c (translate ofset), compact_pt (ofset + 1) pt)
| Mc.CutProof (c, pt) ->
Mc.CutProof (compact_cone c (translate ofset), compact_pt (ofset + 1) pt)
| Mc.SplitProof (p, p1, p2) ->
Mc.SplitProof (p, compact_pt (ofset + 1) p1, compact_pt (ofset + 1) p2)
| Mc.EnumProof (c1, c2, l) ->
Mc.EnumProof
( compact_cone c1 (translate ofset)
, compact_cone c2 (translate ofset)
, Mc.map (fun x -> compact_pt (ofset + 1) x) l )
| Mc.ExProof (x, pt) -> Mc.ExProof (x, compact_pt (ofset + 3) pt)
in
compact_pt 0 pt
(**
* Definition of provers.
* Instantiates the type ('a,'prf) prover defined above.
*)
let lift_pexpr_prover p l = p (List.map (fun (e, o) -> (Mc.denorm e, o)) l)
module CacheZ = MakeCache (struct
type prover_option = bool * bool * int
type coeff = Mc.z
let hash_prover_option : int -> prover_option -> int =
Hash.hash_elt Hashtbl.hash
let eq_prover_option : prover_option -> prover_option -> bool = ( = )
let eq_coeff = Hash.eq_z
let hash_coeff = Hash.hash_z
end)
module CacheQ = MakeCache (struct
type prover_option = int
type coeff = Mc.q
let hash_prover_option : int -> int -> int = Hash.hash_elt Hashtbl.hash
let eq_prover_option = Int.equal
let eq_coeff = Hash.eq_q
let hash_coeff = Hash.hash_q
end)
let memo_lia =
CacheZ.memo_opt use_lia_cache ".lia.cache" (fun ((_, _, b), s) ->
lift_pexpr_prover (Certificate.lia b) s)
let memo_nlia =
CacheZ.memo_opt use_nia_cache ".nia.cache" (fun ((_, _, b), s) ->
lift_pexpr_prover (Certificate.nlia b) s)
let memo_nra =
CacheQ.memo_opt use_nra_cache ".nra.cache" (fun (o, s) ->
lift_pexpr_prover (Certificate.nlinear_prover o) s)
let linear_prover_Q =
{ name = "linear prover"
; get_option = lra_proof_depth
; prover =
(fun (o, l) ->
lift_pexpr_prover (Certificate.linear_prover_with_cert o) l)
; hyps = hyps_of_cone
; compact = compact_cone
; pp_prf = pp_psatz pp_q
; pp_f = (fun o x -> pp_pol pp_q o (fst x)) }
let linear_prover_R =
{ name = "linear prover"
; get_option = lra_proof_depth
; prover =
(fun (o, l) ->
lift_pexpr_prover (Certificate.linear_prover_with_cert o) l)
; hyps = hyps_of_cone
; compact = compact_cone
; pp_prf = pp_psatz pp_q
; pp_f = (fun o x -> pp_pol pp_q o (fst x)) }
let nlinear_prover_R =
{ name = "nra"
; get_option = lra_proof_depth
; prover = memo_nra
; hyps = hyps_of_cone
; compact = compact_cone
; pp_prf = pp_psatz pp_q
; pp_f = (fun o x -> pp_pol pp_q o (fst x)) }
let non_linear_prover_Q str o =
{ name = "real nonlinear prover"
; get_option = (fun () -> (str, o))
; prover = (fun (o, l) -> call_csdpcert_q o l)
; hyps = hyps_of_cone
; compact = compact_cone
; pp_prf = pp_psatz pp_q
; pp_f = (fun o x -> pp_pol pp_q o (fst x)) }
let non_linear_prover_R str o =
{ name = "real nonlinear prover"
; get_option = (fun () -> (str, o))
; prover = (fun (o, l) -> call_csdpcert_q o l)
; hyps = hyps_of_cone
; compact = compact_cone
; pp_prf = pp_psatz pp_q
; pp_f = (fun o x -> pp_pol pp_q o (fst x)) }
let non_linear_prover_Z str o =
{ name = "real nonlinear prover"
; get_option = (fun () -> (str, o))
; prover = (fun (o, l) -> lift_ratproof (call_csdpcert_z o) l)
; hyps = hyps_of_pt
; compact = compact_pt
; pp_prf = pp_proof_term
; pp_f = (fun o x -> pp_pol pp_z o (fst x)) }
let linear_Z =
{ name = "lia"
; get_option = get_lia_option
; prover = memo_lia
; hyps = hyps_of_pt
; compact = compact_pt
; pp_prf = pp_proof_term
; pp_f = (fun o x -> pp_pol pp_z o (fst x)) }
let nlinear_Z =
{ name = "nlia"
; get_option = get_lia_option
; prover = memo_nlia
; hyps = hyps_of_pt
; compact = compact_pt
; pp_prf = pp_proof_term
; pp_f = (fun o x -> pp_pol pp_z o (fst x)) }
(**
* Functions instantiating micromega_gen with the appropriate theories and
* solvers
*)
let exfalso_if_concl_not_Prop =
Proofview.Goal.enter (fun gl ->
Tacmach.(
if is_prop (pf_env gl) (project gl) (pf_concl gl) then
Tacticals.tclIDTAC
else Tactics.elim_type (Lazy.force coq_False)))
let micromega_gen parse_arith pre_process cnf spec dumpexpr prover tac =
Tacticals.tclTHEN exfalso_if_concl_not_Prop
(micromega_gen parse_arith pre_process cnf spec dumpexpr prover tac)
let micromega_genr prover tac =
Tacticals.tclTHEN exfalso_if_concl_not_Prop (micromega_genr prover tac)
let xlra_Q =
micromega_gen parse_qarith
(fun _ x -> x)
Mc.cnfQ qq_domain_spec dump_qexpr linear_prover_Q
let wlra_Q =
micromega_wit_gen
(fun _ x -> x)
Mc.cnfQ qq_domain_spec linear_prover_Q
let xlra_R = micromega_genr linear_prover_R
let xlia =
micromega_gen parse_zarith
(fun _ x -> x)
Mc.cnfZ zz_domain_spec dump_zexpr linear_Z
let wlia =
micromega_wit_gen
(fun _ x -> x)
Mc.cnfZ zz_domain_spec linear_Z
let xnra_Q =
micromega_gen parse_qarith
(fun _ x -> x)
Mc.cnfQ qq_domain_spec dump_qexpr nlinear_prover_R
let wnra_Q =
micromega_wit_gen
(fun _ x -> x)
Mc.cnfQ qq_domain_spec nlinear_prover_R
let xnra_R = micromega_genr nlinear_prover_R
let xnia =
micromega_gen parse_zarith
(fun _ x -> x)
Mc.cnfZ zz_domain_spec dump_zexpr nlinear_Z
let wnia =
micromega_wit_gen
(fun _ x -> x)
Mc.cnfZ zz_domain_spec nlinear_Z
let xsos_Q =
micromega_gen parse_qarith
(fun _ x -> x)
Mc.cnfQ qq_domain_spec dump_qexpr
(non_linear_prover_Q "pure_sos" None)
let wsos_Q =
micromega_wit_gen
(fun _ x -> x)
Mc.cnfQ qq_domain_spec
(non_linear_prover_Q "pure_sos" None)
let xsos_R = micromega_genr (non_linear_prover_R "pure_sos" None)
let xsos_Z =
micromega_gen parse_zarith
(fun _ x -> x)
Mc.cnfZ zz_domain_spec dump_zexpr
(non_linear_prover_Z "pure_sos" None)
let wsos_Z =
micromega_wit_gen
(fun _ x -> x)
Mc.cnfZ zz_domain_spec
(non_linear_prover_Z "pure_sos" None)
let xpsatz_Q i =
micromega_gen parse_qarith
(fun _ x -> x)
Mc.cnfQ qq_domain_spec dump_qexpr
(non_linear_prover_Q "real_nonlinear_prover" (Some i))
let wpsatz_Q i =
micromega_wit_gen
(fun _ x -> x)
Mc.cnfQ qq_domain_spec
(non_linear_prover_Q "real_nonlinear_prover" (Some i))
let xpsatz_R i =
micromega_genr (non_linear_prover_R "real_nonlinear_prover" (Some i))
let xpsatz_Z i =
micromega_gen parse_zarith
(fun _ x -> x)
Mc.cnfZ zz_domain_spec dump_zexpr
(non_linear_prover_Z "real_nonlinear_prover" (Some i))
let wpsatz_Z i =
micromega_wit_gen
(fun _ x -> x)
Mc.cnfZ zz_domain_spec
(non_linear_prover_Z "real_nonlinear_prover" (Some i))
let print_lia_profile () =
Simplex.(
let { number_of_successes
; number_of_failures
; success_pivots
; failure_pivots
; average_pivots
; maximum_pivots } =
Simplex.get_profile_info ()
in
Feedback.msg_notice
Pp.(
str "number of successes: "
++ int number_of_successes ++ fnl ()
++ str "number of success pivots: "
++ int success_pivots ++ fnl ()
++ str "number of failures: "
++ int number_of_failures ++ fnl ()
++ str "number of failure pivots: "
++ int failure_pivots ++ fnl ()
++ str "average number of pivots: "
++ int average_pivots ++ fnl ()
++ str "maximum number of pivots: "
++ int maximum_pivots ++ fnl ()))