Source file eConstr.ml
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open CErrors
open Util
open Names
open Constr
open Context
module ESorts = struct
include Evd.MiniEConstr.ESorts
let equal sigma s1 s2 =
Sorts.equal (kind sigma s1) (kind sigma s2)
end
module EInstance = struct
include Evd.MiniEConstr.EInstance
let equal sigma i1 i2 =
Univ.Instance.equal (kind sigma i1) (kind sigma i2)
end
include (Evd.MiniEConstr : module type of Evd.MiniEConstr
with module ESorts := ESorts
and module EInstance := EInstance)
type types = t
type constr = t
type existential = t pexistential
type case_return = t pcase_return
type case_branch = t pcase_branch
type case_invert = t pcase_invert
type case = (t, t, EInstance.t) pcase
type fixpoint = (t, t) pfixpoint
type cofixpoint = (t, t) pcofixpoint
type unsafe_judgment = (constr, types) Environ.punsafe_judgment
type unsafe_type_judgment = types Environ.punsafe_type_judgment
type named_declaration = (constr, types) Context.Named.Declaration.pt
type rel_declaration = (constr, types) Context.Rel.Declaration.pt
type named_context = (constr, types) Context.Named.pt
type rel_context = (constr, types) Context.Rel.pt
type 'a puniverses = 'a * EInstance.t
let in_punivs a = (a, EInstance.empty)
let mkSProp = of_kind (Sort (ESorts.make Sorts.sprop))
let mkProp = of_kind (Sort (ESorts.make Sorts.prop))
let mkSet = of_kind (Sort (ESorts.make Sorts.set))
let mkType u = of_kind (Sort (ESorts.make (Sorts.sort_of_univ u)))
let mkRel n = of_kind (Rel n)
let mkVar id = of_kind (Var id)
let mkMeta n = of_kind (Meta n)
let mkEvar e = of_kind (Evar e)
let mkSort s = of_kind (Sort (ESorts.make s))
let mkCast (b, k, t) = of_kind (Cast (b, k, t))
let mkProd (na, t, u) = of_kind (Prod (na, t, u))
let mkLambda (na, t, c) = of_kind (Lambda (na, t, c))
let mkLetIn (na, b, t, c) = of_kind (LetIn (na, b, t, c))
let mkApp (f, arg) = of_kind (App (f, arg))
let mkConstU pc = of_kind (Const pc)
let mkConst c = of_kind (Const (in_punivs c))
let mkIndU pi = of_kind (Ind pi)
let mkInd i = of_kind (Ind (in_punivs i))
let mkConstructU pc = of_kind (Construct pc)
let mkConstruct c = of_kind (Construct (in_punivs c))
let mkConstructUi ((ind,u),i) = of_kind (Construct ((ind,i),u))
let mkCase (ci, u, pms, c, iv, r, p) = of_kind (Case (ci, u, pms, c, iv, r, p))
let mkFix f = of_kind (Fix f)
let mkCoFix f = of_kind (CoFix f)
let mkProj (p, c) = of_kind (Proj (p, c))
let mkArrow t1 r t2 = of_kind (Prod (make_annot Anonymous r, t1, t2))
let mkArrowR t1 t2 = mkArrow t1 Sorts.Relevant t2
let mkInt i = of_kind (Int i)
let mkFloat f = of_kind (Float f)
let mkArray (u,t,def,ty) = of_kind (Array (u,t,def,ty))
let mkRef (gr,u) = let open GlobRef in match gr with
| ConstRef c -> mkConstU (c,u)
| IndRef ind -> mkIndU (ind,u)
| ConstructRef c -> mkConstructU (c,u)
| VarRef x -> mkVar x
let type1 = mkSort Sorts.type1
let applist (f, arg) = mkApp (f, Array.of_list arg)
let applistc f arg = mkApp (f, Array.of_list arg)
let isRel sigma c = match kind sigma c with Rel _ -> true | _ -> false
let isVar sigma c = match kind sigma c with Var _ -> true | _ -> false
let isInd sigma c = match kind sigma c with Ind _ -> true | _ -> false
let isEvar sigma c = match kind sigma c with Evar _ -> true | _ -> false
let isMeta sigma c = match kind sigma c with Meta _ -> true | _ -> false
let isSort sigma c = match kind sigma c with Sort _ -> true | _ -> false
let isCast sigma c = match kind sigma c with Cast _ -> true | _ -> false
let isApp sigma c = match kind sigma c with App _ -> true | _ -> false
let isLambda sigma c = match kind sigma c with Lambda _ -> true | _ -> false
let isLetIn sigma c = match kind sigma c with LetIn _ -> true | _ -> false
let isProd sigma c = match kind sigma c with Prod _ -> true | _ -> false
let isConst sigma c = match kind sigma c with Const _ -> true | _ -> false
let isConstruct sigma c = match kind sigma c with Construct _ -> true | _ -> false
let isFix sigma c = match kind sigma c with Fix _ -> true | _ -> false
let isCoFix sigma c = match kind sigma c with CoFix _ -> true | _ -> false
let isCase sigma c = match kind sigma c with Case _ -> true | _ -> false
let isProj sigma c = match kind sigma c with Proj _ -> true | _ -> false
let rec isType sigma c = match kind sigma c with
| Sort s -> (match ESorts.kind sigma s with
| Sorts.Type _ -> true
| _ -> false )
| Cast (c,_,_) -> isType sigma c
| _ -> false
let isVarId sigma id c =
match kind sigma c with Var id' -> Id.equal id id' | _ -> false
let isRelN sigma n c =
match kind sigma c with Rel n' -> Int.equal n n' | _ -> false
let isRef sigma c = match kind sigma c with
| Const _ | Ind _ | Construct _ | Var _ -> true
| _ -> false
let isRefX sigma x c =
let open GlobRef in
match x, kind sigma c with
| ConstRef c, Const (c', _) -> Constant.CanOrd.equal c c'
| IndRef i, Ind (i', _) -> Ind.CanOrd.equal i i'
| ConstructRef i, Construct (i', _) -> Construct.CanOrd.equal i i'
| VarRef id, Var id' -> Id.equal id id'
| _ -> false
let destRel sigma c = match kind sigma c with
| Rel p -> p
| _ -> raise DestKO
let destVar sigma c = match kind sigma c with
| Var p -> p
| _ -> raise DestKO
let destInd sigma c = match kind sigma c with
| Ind p -> p
| _ -> raise DestKO
let destEvar sigma c = match kind sigma c with
| Evar p -> p
| _ -> raise DestKO
let destMeta sigma c = match kind sigma c with
| Meta p -> p
| _ -> raise DestKO
let destSort sigma c = match kind sigma c with
| Sort p -> p
| _ -> raise DestKO
let destCast sigma c = match kind sigma c with
| Cast (c, k, t) -> (c, k, t)
| _ -> raise DestKO
let destApp sigma c = match kind sigma c with
| App (f, a) -> (f, a)
| _ -> raise DestKO
let destLambda sigma c = match kind sigma c with
| Lambda (na, t, c) -> (na, t, c)
| _ -> raise DestKO
let destLetIn sigma c = match kind sigma c with
| LetIn (na, b, t, c) -> (na, b, t, c)
| _ -> raise DestKO
let destProd sigma c = match kind sigma c with
| Prod (na, t, c) -> (na, t, c)
| _ -> raise DestKO
let destConst sigma c = match kind sigma c with
| Const p -> p
| _ -> raise DestKO
let destConstruct sigma c = match kind sigma c with
| Construct p -> p
| _ -> raise DestKO
let destFix sigma c = match kind sigma c with
| Fix p -> p
| _ -> raise DestKO
let destCoFix sigma c = match kind sigma c with
| CoFix p -> p
| _ -> raise DestKO
let destCase sigma c = match kind sigma c with
| Case (ci, u, pms, t, iv, c, p) -> (ci, u, pms, t, iv, c, p)
| _ -> raise DestKO
let destProj sigma c = match kind sigma c with
| Proj (p, c) -> (p, c)
| _ -> raise DestKO
let destRef sigma c = let open GlobRef in match kind sigma c with
| Var x -> VarRef x, EInstance.empty
| Const (c,u) -> ConstRef c, u
| Ind (ind,u) -> IndRef ind, u
| Construct (c,u) -> ConstructRef c, u
| _ -> raise DestKO
let decompose_app sigma c =
match kind sigma c with
| App (f,cl) -> (f, Array.to_list cl)
| _ -> (c,[])
let decompose_lam sigma c =
let rec lamdec_rec l c = match kind sigma c with
| Lambda (x,t,c) -> lamdec_rec ((x,t)::l) c
| Cast (c,_,_) -> lamdec_rec l c
| _ -> l,c
in
lamdec_rec [] c
let decompose_lam_assum sigma c =
let open Rel.Declaration in
let rec lamdec_rec l c =
match kind sigma c with
| Lambda (x,t,c) -> lamdec_rec (Context.Rel.add (LocalAssum (x,t)) l) c
| LetIn (x,b,t,c) -> lamdec_rec (Context.Rel.add (LocalDef (x,b,t)) l) c
| Cast (c,_,_) -> lamdec_rec l c
| _ -> l,c
in
lamdec_rec Context.Rel.empty c
let decompose_lam_n_assum sigma n c =
let open Rel.Declaration in
if n < 0 then
anomaly Pp.(str "decompose_lam_n_assum: integer parameter must be positive.");
let rec lamdec_rec l n c =
if Int.equal n 0 then l,c
else
match kind sigma c with
| Lambda (x,t,c) -> lamdec_rec (Context.Rel.add (LocalAssum (x,t)) l) (n-1) c
| LetIn (x,b,t,c) -> lamdec_rec (Context.Rel.add (LocalDef (x,b,t)) l) n c
| Cast (c,_,_) -> lamdec_rec l n c
| c -> anomaly Pp.(str "decompose_lam_n_assum: not enough abstractions.")
in
lamdec_rec Context.Rel.empty n c
let decompose_lam_n_decls sigma n =
let open Rel.Declaration in
if n < 0 then
anomaly Pp.(str "decompose_lam_n_decls: integer parameter must be positive.");
let rec lamdec_rec l n c =
if Int.equal n 0 then l,c
else
match kind sigma c with
| Lambda (x,t,c) -> lamdec_rec (Context.Rel.add (LocalAssum (x,t)) l) (n-1) c
| LetIn (x,b,t,c) -> lamdec_rec (Context.Rel.add (LocalDef (x,b,t)) l) (n-1) c
| Cast (c,_,_) -> lamdec_rec l n c
| c -> anomaly Pp.(str "decompose_lam_n_decls: not enough abstractions.")
in
lamdec_rec Context.Rel.empty n
let lamn n env b =
let rec lamrec = function
| (0, env, b) -> b
| (n, ((v,t)::l), b) -> lamrec (n-1, l, mkLambda (v,t,b))
| _ -> assert false
in
lamrec (n,env,b)
let compose_lam l b = lamn (List.length l) l b
let rec to_lambda sigma n prod =
if Int.equal n 0 then
prod
else
match kind sigma prod with
| Prod (na,ty,bd) -> mkLambda (na,ty,to_lambda sigma (n-1) bd)
| Cast (c,_,_) -> to_lambda sigma n c
| _ -> anomaly Pp.(str "Not enough products.")
let decompose_prod sigma c =
let rec proddec_rec l c = match kind sigma c with
| Prod (x,t,c) -> proddec_rec ((x,t)::l) c
| Cast (c,_,_) -> proddec_rec l c
| _ -> l,c
in
proddec_rec [] c
let decompose_prod_assum sigma c =
let open Rel.Declaration in
let rec proddec_rec l c =
match kind sigma c with
| Prod (x,t,c) -> proddec_rec (Context.Rel.add (LocalAssum (x,t)) l) c
| LetIn (x,b,t,c) -> proddec_rec (Context.Rel.add (LocalDef (x,b,t)) l) c
| Cast (c,_,_) -> proddec_rec l c
| _ -> l,c
in
proddec_rec Context.Rel.empty c
let decompose_prod_n_assum sigma n c =
let open Rel.Declaration in
if n < 0 then
anomaly Pp.(str "decompose_prod_n_assum: integer parameter must be positive.");
let rec prodec_rec l n c =
if Int.equal n 0 then l,c
else
match kind sigma c with
| Prod (x,t,c) -> prodec_rec (Context.Rel.add (LocalAssum (x,t)) l) (n-1) c
| LetIn (x,b,t,c) -> prodec_rec (Context.Rel.add (LocalDef (x,b,t)) l) (n-1) c
| Cast (c,_,_) -> prodec_rec l n c
| c -> anomaly Pp.(str "decompose_prod_n_assum: not enough declarations.")
in
prodec_rec Context.Rel.empty n c
let existential_type = Evd.existential_type
let lift n c = of_constr (Vars.lift n (unsafe_to_constr c))
let of_branches : Constr.case_branch array -> case_branch array =
match Evd.MiniEConstr.unsafe_eq with
| Refl -> fun x -> x
let unsafe_to_branches : case_branch array -> Constr.case_branch array =
match Evd.MiniEConstr.unsafe_eq with
| Refl -> fun x -> x
let of_return : Constr.case_return -> case_return =
match Evd.MiniEConstr.unsafe_eq with
| Refl -> fun x -> x
let unsafe_to_return : case_return -> Constr.case_return =
match Evd.MiniEConstr.unsafe_eq with
| Refl -> fun x -> x
let map_branches f br =
let f c = unsafe_to_constr (f (of_constr c)) in
of_branches (Constr.map_branches f (unsafe_to_branches br))
let map_return_predicate f p =
let f c = unsafe_to_constr (f (of_constr c)) in
of_return (Constr.map_return_predicate f (unsafe_to_return p))
let map sigma f c =
let f c = unsafe_to_constr (f (of_constr c)) in
of_constr (Constr.map f (unsafe_to_constr (whd_evar sigma c)))
let map_with_binders sigma g f l c =
let f l c = unsafe_to_constr (f l (of_constr c)) in
of_constr (Constr.map_with_binders g f l (unsafe_to_constr (whd_evar sigma c)))
let iter sigma f c =
let f c = f (of_constr c) in
Constr.iter f (unsafe_to_constr (whd_evar sigma c))
let expand_case env _sigma (ci, u, pms, p, iv, c, bl) =
let u = EInstance.unsafe_to_instance u in
let pms = unsafe_to_constr_array pms in
let p = unsafe_to_return p in
let iv = unsafe_to_case_invert iv in
let c = unsafe_to_constr c in
let bl = unsafe_to_branches bl in
let (ci, p, iv, c, bl) = Inductive.expand_case env (ci, u, pms, p, iv, c, bl) in
let p = of_constr p in
let c = of_constr c in
let iv = of_case_invert iv in
let bl = of_constr_array bl in
(ci, p, iv, c, bl)
let annotate_case env sigma (ci, u, pms, p, iv, c, bl as case) =
let (_, p, _, _, bl) = expand_case env sigma case in
let p =
let (_, mip) = Inductive.lookup_mind_specif env ci.ci_ind in
decompose_lam_n_decls sigma (mip.Declarations.mind_nrealdecls + 1) p
in
let mk_br c n = decompose_lam_n_decls sigma n c in
let bl = Array.map2 mk_br bl ci.ci_cstr_ndecls in
(ci, u, pms, p, iv, c, bl)
let expand_branch env _sigma u pms (ind, i) (nas, _br) =
let open Declarations in
let u = EInstance.unsafe_to_instance u in
let pms = unsafe_to_constr_array pms in
let (mib, mip) = Inductive.lookup_mind_specif env ind in
let paramdecl = Vars.subst_instance_context u mib.mind_params_ctxt in
let paramsubst = Vars.subst_of_rel_context_instance paramdecl pms in
let (ctx, _) = mip.mind_nf_lc.(i - 1) in
let (ctx, _) = List.chop mip.mind_consnrealdecls.(i - 1) ctx in
let ans = Inductive.instantiate_context u paramsubst nas ctx in
let ans : rel_context = match Evd.MiniEConstr.unsafe_eq with Refl -> ans in
ans
let contract_case env _sigma (ci, p, iv, c, bl) =
let p = unsafe_to_constr p in
let iv = unsafe_to_case_invert iv in
let c = unsafe_to_constr c in
let bl = unsafe_to_constr_array bl in
let (ci, u, pms, p, iv, c, bl) = Inductive.contract_case env (ci, p, iv, c, bl) in
let u = EInstance.make u in
let pms = of_constr_array pms in
let p = of_return p in
let iv = of_case_invert iv in
let c = of_constr c in
let bl = of_branches bl in
(ci, u, pms, p, iv, c, bl)
let iter_with_full_binders env sigma g f n c =
let open Context.Rel.Declaration in
match kind sigma c with
| (Rel _ | Meta _ | Var _ | Sort _ | Const _ | Ind _
| Construct _ | Int _ | Float _) -> ()
| Cast (c,_,t) -> f n c; f n t
| Prod (na,t,c) -> f n t; f (g (LocalAssum (na, t)) n) c
| Lambda (na,t,c) -> f n t; f (g (LocalAssum (na, t)) n) c
| LetIn (na,b,t,c) -> f n b; f n t; f (g (LocalDef (na, b, t)) n) c
| App (c,l) -> f n c; Array.Fun1.iter f n l
| Evar (_,l) -> List.iter (fun c -> f n c) l
| Case (ci,u,pms,p,iv,c,bl) ->
let (ci, _, pms, p, iv, c, bl) = annotate_case env sigma (ci, u, pms, p, iv, c, bl) in
let f_ctx (ctx, c) = f (List.fold_right g ctx n) c in
Array.Fun1.iter f n pms; f_ctx p; iter_invert (f n) iv; f n c; Array.iter f_ctx bl
| Proj (p,c) -> f n c
| Fix (_,(lna,tl,bl)) ->
Array.iter (f n) tl;
let n' = Array.fold_left2_i (fun i n na t -> g (LocalAssum (na, lift i t)) n) n lna tl in
Array.iter (f n') bl
| CoFix (_,(lna,tl,bl)) ->
Array.iter (f n) tl;
let n' = Array.fold_left2_i (fun i n na t -> g (LocalAssum (na,lift i t)) n) n lna tl in
Array.iter (f n') bl
| Array (_u,t,def,ty) -> Array.Fun1.iter f n t; f n def; f n ty
let iter_with_binders sigma g f n c =
let f l c = f l (of_constr c) in
Constr.iter_with_binders g f n (unsafe_to_constr (whd_evar sigma c))
let fold sigma f acc c =
let f acc c = f acc (of_constr c) in
Constr.fold f acc (unsafe_to_constr (whd_evar sigma c))
let fold_with_binders sigma g f acc e c =
let f e acc c = f e acc (of_constr c) in
Constr.fold_constr_with_binders g f acc e (unsafe_to_constr (whd_evar sigma c))
let compare_gen k eq_inst eq_sort eq_constr nargs c1 c2 =
(c1 == c2) || Constr.compare_head_gen_with k k eq_inst eq_sort eq_constr nargs c1 c2
let eq_constr sigma c1 c2 =
let kind c = kind sigma c in
let eq_inst _ i1 i2 = EInstance.equal sigma i1 i2 in
let eq_sorts s1 s2 = ESorts.equal sigma s1 s2 in
let rec eq_constr nargs c1 c2 =
compare_gen kind eq_inst eq_sorts eq_constr nargs c1 c2
in
eq_constr 0 c1 c2
let eq_constr_nounivs sigma c1 c2 =
let kind c = kind sigma c in
let rec eq_constr nargs c1 c2 =
compare_gen kind (fun _ _ _ -> true) (fun _ _ -> true) eq_constr nargs c1 c2
in
eq_constr 0 c1 c2
let compare_constr sigma cmp c1 c2 =
let kind c = kind sigma c in
let eq_inst _ i1 i2 = EInstance.equal sigma i1 i2 in
let eq_sorts s1 s2 = ESorts.equal sigma s1 s2 in
let cmp nargs c1 c2 = cmp c1 c2 in
compare_gen kind eq_inst eq_sorts cmp 0 c1 c2
let compare_cumulative_instances cv_pb nargs_ok variances u u' cstrs =
let open UnivProblem in
if not nargs_ok then enforce_eq_instances_univs false u u' cstrs
else
let make u = Sorts.sort_of_univ @@ Univ.Universe.make u in
CArray.fold_left3
(fun cstrs v u u' ->
let open Univ.Variance in
match v with
| Irrelevant -> Set.add (UWeak (u,u')) cstrs
| Covariant ->
(match cv_pb with
| Reduction.CONV -> Set.add (UEq (make u, make u')) cstrs
| Reduction.CUMUL -> Set.add (ULe (make u, make u')) cstrs)
| Invariant ->
Set.add (UEq (make u, make u')) cstrs)
cstrs variances (Univ.Instance.to_array u) (Univ.Instance.to_array u')
let cmp_inductives cv_pb (mind,ind as spec) nargs u1 u2 cstrs =
let open UnivProblem in
match mind.Declarations.mind_variance with
| None -> enforce_eq_instances_univs false u1 u2 cstrs
| Some variances ->
let num_param_arity = Reduction.inductive_cumulativity_arguments spec in
compare_cumulative_instances cv_pb (Int.equal num_param_arity nargs) variances u1 u2 cstrs
let cmp_constructors (mind, ind, cns as spec) nargs u1 u2 cstrs =
let open UnivProblem in
match mind.Declarations.mind_variance with
| None -> enforce_eq_instances_univs false u1 u2 cstrs
| Some _ ->
let num_cnstr_args = Reduction.constructor_cumulativity_arguments spec in
if not (Int.equal num_cnstr_args nargs)
then enforce_eq_instances_univs false u1 u2 cstrs
else
Array.fold_left2 (fun cstrs u1 u2 -> UnivProblem.(Set.add (UWeak (u1,u2)) cstrs))
cstrs (Univ.Instance.to_array u1) (Univ.Instance.to_array u2)
let eq_universes env sigma cstrs cv_pb refargs l l' =
if EInstance.is_empty l then (assert (EInstance.is_empty l'); true)
else
let l = EInstance.kind sigma l
and l' = EInstance.kind sigma l' in
let open GlobRef in
let open UnivProblem in
match refargs with
| Some (ConstRef c, 1) when Environ.is_array_type env c ->
cstrs := compare_cumulative_instances cv_pb true [|Univ.Variance.Irrelevant|] l l' !cstrs;
true
| None | Some (ConstRef _, _) ->
cstrs := enforce_eq_instances_univs true l l' !cstrs; true
| Some (VarRef _, _) -> assert false
| Some (IndRef ind, nargs) ->
let mind = Environ.lookup_mind (fst ind) env in
cstrs := cmp_inductives cv_pb (mind,snd ind) nargs l l' !cstrs;
true
| Some (ConstructRef ((mi,ind),ctor), nargs) ->
let mind = Environ.lookup_mind mi env in
cstrs := cmp_constructors (mind,ind,ctor) nargs l l' !cstrs;
true
let test_constr_universes env sigma leq ?(nargs=0) m n =
let open UnivProblem in
let kind c = kind sigma c in
if m == n then Some Set.empty
else
let cstrs = ref Set.empty in
let cv_pb = if leq then Reduction.CUMUL else Reduction.CONV in
let eq_universes refargs l l' = eq_universes env sigma cstrs Reduction.CONV refargs l l'
and leq_universes refargs l l' = eq_universes env sigma cstrs cv_pb refargs l l' in
let eq_sorts s1 s2 =
let s1 = ESorts.kind sigma s1 in
let s2 = ESorts.kind sigma s2 in
if Sorts.equal s1 s2 then true
else (cstrs := Set.add
(UEq (s1, s2)) !cstrs;
true)
in
let leq_sorts s1 s2 =
let s1 = ESorts.kind sigma s1 in
let s2 = ESorts.kind sigma s2 in
if Sorts.equal s1 s2 then true
else
(cstrs := Set.add
(ULe (s1, s2)) !cstrs;
true)
in
let rec eq_constr' nargs m n = compare_gen kind eq_universes eq_sorts eq_constr' nargs m n in
let res =
if leq then
let rec compare_leq nargs m n =
Constr.compare_head_gen_leq_with kind kind leq_universes leq_sorts
eq_constr' leq_constr' nargs m n
and leq_constr' nargs m n = m == n || compare_leq nargs m n in
compare_leq nargs m n
else
Constr.compare_head_gen_with kind kind eq_universes eq_sorts eq_constr' nargs m n
in
if res then Some !cstrs else None
let eq_constr_universes env sigma ?nargs m n =
test_constr_universes env sigma false ?nargs m n
let leq_constr_universes env sigma ?nargs m n =
test_constr_universes env sigma true ?nargs m n
let compare_head_gen_proj env sigma equ eqs eqc' nargs m n =
let kind c = kind sigma c in
match kind m, kind n with
| Proj (p, c), App (f, args)
| App (f, args), Proj (p, c) ->
(match kind f with
| Const (p', u) when Environ.QConstant.equal env (Projection.constant p) p' ->
let npars = Projection.npars p in
if Array.length args == npars + 1 then
eqc' 0 c args.(npars)
else false
| _ -> false)
| _ -> Constr.compare_head_gen_with kind kind equ eqs eqc' nargs m n
let eq_constr_universes_proj env sigma m n =
let open UnivProblem in
if m == n then Some Set.empty
else
let cstrs = ref Set.empty in
let eq_universes ref l l' = eq_universes env sigma cstrs Reduction.CONV ref l l' in
let eq_sorts s1 s2 =
let s1 = ESorts.kind sigma s1 in
let s2 = ESorts.kind sigma s2 in
if Sorts.equal s1 s2 then true
else
(cstrs := Set.add
(UEq (s1, s2)) !cstrs;
true)
in
let rec eq_constr' nargs m n =
m == n || compare_head_gen_proj env sigma eq_universes eq_sorts eq_constr' nargs m n
in
let res = eq_constr' 0 m n in
if res then Some !cstrs else None
let universes_of_constr sigma c =
let open Univ in
let rec aux s c =
match kind sigma c with
| Const (c, u) ->
Level.Set.fold Level.Set.add (Instance.levels (EInstance.kind sigma u)) s
| Ind ((mind,_), u) | Construct (((mind,_),_), u) ->
Level.Set.fold Level.Set.add (Instance.levels (EInstance.kind sigma u)) s
| Sort u ->
let sort = ESorts.kind sigma u in
if Sorts.is_small sort then s
else
Level.Set.fold Level.Set.add (Sorts.levels sort) s
| Evar (k, args) ->
let concl = Evd.evar_concl (Evd.find sigma k) in
fold sigma aux (aux s concl) c
| Array (u,_,_,_) ->
let s = Level.Set.fold Level.Set.add (Instance.levels (EInstance.kind sigma u)) s in
fold sigma aux s c
| Case (_,u,_,_,_,_,_) ->
let s = Level.Set.fold Level.Set.add (Instance.levels (EInstance.kind sigma u)) s in
fold sigma aux s c
| _ -> fold sigma aux s c
in aux Level.Set.empty c
open Context
open Environ
let cast_list : type a b. (a,b) eq -> a list -> b list =
fun Refl x -> x
let cast_list_snd : type a b. (a,b) eq -> ('c * a) list -> ('c * b) list =
fun Refl x -> x
let cast_vect : type a b. (a,b) eq -> a array -> b array =
fun Refl x -> x
let cast_rel_decl :
type a b. (a,b) eq -> (a, a) Rel.Declaration.pt -> (b, b) Rel.Declaration.pt =
fun Refl x -> x
let cast_rel_context :
type a b. (a,b) eq -> (a, a) Rel.pt -> (b, b) Rel.pt =
fun Refl x -> x
let cast_rec_decl :
type a b. (a,b) eq -> (a, a) Constr.prec_declaration -> (b, b) Constr.prec_declaration =
fun Refl x -> x
let cast_named_decl :
type a b. (a,b) eq -> (a, a) Named.Declaration.pt -> (b, b) Named.Declaration.pt =
fun Refl x -> x
let cast_named_context :
type a b. (a,b) eq -> (a, a) Named.pt -> (b, b) Named.pt =
fun Refl x -> x
module Vars =
struct
exception LocalOccur
let to_constr = unsafe_to_constr
let to_rel_decl = unsafe_to_rel_decl
type instance = t array
type instance_list = t list
type substl = t list
(** Operations that commute with evar-normalization *)
let lift = lift
let liftn n m c = of_constr (Vars.liftn n m (to_constr c))
let substnl subst n c = of_constr (Vars.substnl (cast_list unsafe_eq subst) n (to_constr c))
let substl subst c = of_constr (Vars.substl (cast_list unsafe_eq subst) (to_constr c))
let subst1 c r = of_constr (Vars.subst1 (to_constr c) (to_constr r))
let substnl_decl subst n d = of_rel_decl (Vars.substnl_decl (cast_list unsafe_eq subst) n (to_rel_decl d))
let substl_decl subst d = of_rel_decl (Vars.substl_decl (cast_list unsafe_eq subst) (to_rel_decl d))
let subst1_decl c d = of_rel_decl (Vars.subst1_decl (to_constr c) (to_rel_decl d))
let replace_vars subst c =
of_constr (Vars.replace_vars (cast_list_snd unsafe_eq subst) (to_constr c))
let substn_vars n subst c = of_constr (Vars.substn_vars n subst (to_constr c))
let subst_vars subst c = of_constr (Vars.subst_vars subst (to_constr c))
let subst_var subst c = of_constr (Vars.subst_var subst (to_constr c))
let subst_univs_level_constr subst c =
of_constr (Vars.subst_univs_level_constr subst (to_constr c))
let subst_instance_context subst ctx =
cast_rel_context (sym unsafe_eq) (Vars.subst_instance_context subst (cast_rel_context unsafe_eq ctx))
let subst_instance_constr subst c =
of_constr (Vars.subst_instance_constr subst (to_constr c))
(** Operations that dot NOT commute with evar-normalization *)
let noccurn sigma n term =
let rec occur_rec n c = match kind sigma c with
| Rel m -> if Int.equal m n then raise LocalOccur
| _ -> iter_with_binders sigma succ occur_rec n c
in
try occur_rec n term; true with LocalOccur -> false
let noccur_between sigma n m term =
let rec occur_rec n c = match kind sigma c with
| Rel p -> if n<=p && p<n+m then raise LocalOccur
| _ -> iter_with_binders sigma succ occur_rec n c
in
try occur_rec n term; true with LocalOccur -> false
let closedn sigma n c =
let rec closed_rec n c = match kind sigma c with
| Rel m -> if m>n then raise LocalOccur
| _ -> iter_with_binders sigma succ closed_rec n c
in
try closed_rec n c; true with LocalOccur -> false
let closed0 sigma c = closedn sigma 0 c
let subst_of_rel_context_instance ctx subst =
cast_list (sym unsafe_eq)
(Vars.subst_of_rel_context_instance (cast_rel_context unsafe_eq ctx) (cast_vect unsafe_eq subst))
let subst_of_rel_context_instance_list ctx subst =
cast_list (sym unsafe_eq)
(Vars.subst_of_rel_context_instance_list (cast_rel_context unsafe_eq ctx) (cast_list unsafe_eq subst))
let liftn_rel_context n k ctx =
cast_rel_context (sym unsafe_eq)
(Vars.liftn_rel_context n k (cast_rel_context unsafe_eq ctx))
let lift_rel_context n ctx =
cast_rel_context (sym unsafe_eq)
(Vars.lift_rel_context n (cast_rel_context unsafe_eq ctx))
let substnl_rel_context subst n ctx =
cast_rel_context (sym unsafe_eq)
(Vars.substnl_rel_context (cast_list unsafe_eq subst) n (cast_rel_context unsafe_eq ctx))
let substl_rel_context subst ctx =
cast_rel_context (sym unsafe_eq)
(Vars.substl_rel_context (cast_list unsafe_eq subst) (cast_rel_context unsafe_eq ctx))
let smash_rel_context ctx =
cast_rel_context (sym unsafe_eq)
(Vars.smash_rel_context (cast_rel_context unsafe_eq ctx))
let esubst : (int -> 'a -> t) -> 'a Esubst.subs -> t -> t =
match unsafe_eq with
| Refl -> Vars.esubst
type substituend = Vars.substituend
let make_substituend c = Vars.make_substituend (unsafe_to_constr c)
let lift_substituend n s = of_constr (Vars.lift_substituend n s)
end
let rec isArity sigma c =
match kind sigma c with
| Prod (_,_,c) -> isArity sigma c
| LetIn (_,b,_,c) -> isArity sigma (Vars.subst1 b c)
| Cast (c,_,_) -> isArity sigma c
| Sort _ -> true
| _ -> false
type arity = rel_context * ESorts.t
let destArity sigma =
let open Context.Rel.Declaration in
let rec prodec_rec l c =
match kind sigma c with
| Prod (x,t,c) -> prodec_rec (LocalAssum (x,t) :: l) c
| LetIn (x,b,t,c) -> prodec_rec (LocalDef (x,b,t) :: l) c
| Cast (c,_,_) -> prodec_rec l c
| Sort s -> l,s
| _ -> anomaly ~label:"destArity" (Pp.str "not an arity.")
in
prodec_rec []
let mkProd_or_LetIn decl c =
let open Context.Rel.Declaration in
match decl with
| LocalAssum (na,t) -> mkProd (na, t, c)
| LocalDef (na,b,t) -> mkLetIn (na, b, t, c)
let mkLambda_or_LetIn decl c =
let open Context.Rel.Declaration in
match decl with
| LocalAssum (na,t) -> mkLambda (na, t, c)
| LocalDef (na,b,t) -> mkLetIn (na, b, t, c)
let mkNamedProd id typ c = mkProd (map_annot Name.mk_name id, typ, Vars.subst_var id.binder_name c)
let mkNamedLambda id typ c = mkLambda (map_annot Name.mk_name id, typ, Vars.subst_var id.binder_name c)
let mkNamedLetIn id c1 t c2 = mkLetIn (map_annot Name.mk_name id, c1, t, Vars.subst_var id.binder_name c2)
let mkNamedProd_or_LetIn decl c =
let open Context.Named.Declaration in
match decl with
| LocalAssum (id,t) -> mkNamedProd id t c
| LocalDef (id,b,t) -> mkNamedLetIn id b t c
let mkNamedLambda_or_LetIn decl c =
let open Context.Named.Declaration in
match decl with
| LocalAssum (id,t) -> mkNamedLambda id t c
| LocalDef (id,b,t) -> mkNamedLetIn id b t c
let it_mkProd_or_LetIn t ctx = List.fold_left (fun c d -> mkProd_or_LetIn d c) t ctx
let it_mkLambda_or_LetIn t ctx = List.fold_left (fun c d -> mkLambda_or_LetIn d c) t ctx
let push_rel d e = push_rel (cast_rel_decl unsafe_eq d) e
let push_rel_context d e = push_rel_context (cast_rel_context unsafe_eq d) e
let push_rec_types d e = push_rec_types (cast_rec_decl unsafe_eq d) e
let push_named d e = push_named (cast_named_decl unsafe_eq d) e
let push_named_context d e = push_named_context (cast_named_context unsafe_eq d) e
let push_named_context_val d e = push_named_context_val (cast_named_decl unsafe_eq d) e
let rel_context e = cast_rel_context (sym unsafe_eq) (rel_context e)
let named_context e = cast_named_context (sym unsafe_eq) (named_context e)
let val_of_named_context e = val_of_named_context (cast_named_context unsafe_eq e)
let named_context_of_val e = cast_named_context (sym unsafe_eq) (named_context_of_val e)
let of_existential : Constr.existential -> existential =
let gen : type a b. (a,b) eq -> 'c * b list -> 'c * a list = fun Refl x -> x in
gen unsafe_eq
let lookup_rel i e = cast_rel_decl (sym unsafe_eq) (lookup_rel i e)
let lookup_named n e = cast_named_decl (sym unsafe_eq) (lookup_named n e)
let lookup_named_val n e = cast_named_decl (sym unsafe_eq) (lookup_named_ctxt n e)
let map_rel_context_in_env f env sign =
let rec aux env acc = function
| d::sign ->
aux (push_rel d env) (Context.Rel.Declaration.map_constr (f env) d :: acc) sign
| [] ->
acc
in
aux env [] (List.rev sign)
let match_named_context_val :
named_context_val -> (named_declaration * lazy_val * named_context_val) option =
match unsafe_eq with
| Refl -> match_named_context_val
let identity_subst_val : named_context_val -> t list =
match unsafe_eq with Refl -> fun ctx -> ctx.env_named_var
let fresh_global ?loc ?rigid ?names env sigma reference =
let (evd,t) = Evd.fresh_global ?loc ?rigid ?names env sigma reference in
evd, t
let is_global = isRefX
(** Kind of type *)
type kind_of_type =
| SortType of ESorts.t
| CastType of types * t
| ProdType of Name.t Context.binder_annot * t * t
| LetInType of Name.t Context.binder_annot * t * t * t
| AtomicType of t * t array
let kind_of_type sigma t = match kind sigma t with
| Sort s -> SortType s
| Cast (c,_,t) -> CastType (c, t)
| Prod (na,t,c) -> ProdType (na, t, c)
| LetIn (na,b,t,c) -> LetInType (na, b, t, c)
| App (c,l) -> AtomicType (c, l)
| (Rel _ | Meta _ | Var _ | Evar _ | Const _
| Proj _ | Case _ | Fix _ | CoFix _ | Ind _)
-> AtomicType (t,[||])
| (Lambda _ | Construct _ | Int _ | Float _ | Array _) -> failwith "Not a type"
module Unsafe =
struct
let to_sorts = ESorts.unsafe_to_sorts
let to_instance = EInstance.unsafe_to_instance
let to_constr = unsafe_to_constr
let to_constr_array = unsafe_to_constr_array
let to_rel_decl = unsafe_to_rel_decl
let to_named_decl = unsafe_to_named_decl
let to_named_context =
let gen : type a b. (a, b) eq -> (a,a) Context.Named.pt -> (b,b) Context.Named.pt
= fun Refl x -> x
in
gen unsafe_eq
let to_rel_context =
let gen : type a b. (a, b) eq -> (a,a) Context.Rel.pt -> (b,b) Context.Rel.pt
= fun Refl x -> x
in
gen unsafe_eq
let to_case_invert = unsafe_to_case_invert
let eq = unsafe_eq
end