Source file cases.ml
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open Pp
open CErrors
open Util
open Names
open Nameops
open Constr
open Context
open Termops
open Environ
open EConstr
open Vars
open Namegen
open Declarations
open Inductiveops
open Reductionops
open Type_errors
open Glob_term
open Glob_ops
open Retyping
open Pretype_errors
open Evarutil
open Evardefine
open Evarsolve
open Evarconv
open Evd
open Context.Rel.Declaration
open GlobEnv
module RelDecl = Context.Rel.Declaration
module NamedDecl = Context.Named.Declaration
type pattern_matching_error =
| BadPattern of constructor * constr
| BadConstructor of constructor * inductive
| WrongNumargConstructor of
{cstr:constructor; expanded:bool; nargs:int; expected_nassums:int; expected_ndecls:int}
| WrongNumargInductive of
{ind:inductive; expanded:bool; nargs:int; expected_nassums:int; expected_ndecls:int}
| UnusedClause of cases_pattern list
| NonExhaustive of cases_pattern list
| CannotInferPredicate of (constr * types) array
exception PatternMatchingError of env * evar_map * pattern_matching_error
let raise_pattern_matching_error ?loc (env,sigma,te) =
Loc.raise ?loc (PatternMatchingError(env,sigma,te))
let error_bad_pattern ?loc env sigma cstr ind =
raise_pattern_matching_error ?loc
(env, sigma, BadPattern (cstr,ind))
let error_bad_constructor ?loc env cstr ind =
raise_pattern_matching_error ?loc
(env, Evd.empty, BadConstructor (cstr,ind))
let error_wrong_numarg_constructor ?loc env ~cstr ~expanded ~nargs ~expected_nassums ~expected_ndecls =
raise_pattern_matching_error ?loc (env, Evd.empty,
WrongNumargConstructor {cstr; expanded; nargs; expected_nassums; expected_ndecls})
let error_wrong_numarg_inductive ?loc env ~ind ~expanded ~nargs ~expected_nassums ~expected_ndecls =
raise_pattern_matching_error ?loc (env, Evd.empty,
WrongNumargInductive {ind; expanded; nargs; expected_nassums; expected_ndecls})
let list_try_compile f l =
let rec aux errors = function
| [] -> if errors = [] then anomaly (str "try_find_f.") else Exninfo.iraise (List.last errors)
| h::t ->
try f h
with UserError _ | TypeError _ | PretypeError _ | PatternMatchingError _ as e ->
let e = Exninfo.capture e in
aux (e::errors) t in
aux [] l
let force_name =
let nx = Name default_dependent_ident in function Anonymous -> nx | na -> na
open Pp
let msg_may_need_inversion () =
strbrk "Found a matching with no clauses on a term unknown to have an empty inductive type."
let make_anonymous_patvars n =
List.make n (DAst.make @@ PatVar Anonymous)
let relocate_rel n1 n2 k j = if Int.equal j (n1 + k) then n2+k else j
let rec relocate_index sigma n1 n2 k t =
match EConstr.kind sigma t with
| Rel j when Int.equal j (n1 + k) -> mkRel (n2+k)
| Rel j when j < n1+k -> t
| Rel j when j > n1+k -> t
| _ -> EConstr.map_with_binders sigma succ (relocate_index sigma n1 n2) k t
let (!!) env = GlobEnv.env env
type 'a rhs =
{ rhs_env : GlobEnv.t;
rhs_vars : Id.Set.t;
avoid_ids : Id.Set.t;
it : 'a option}
type 'a equation =
{ patterns : cases_pattern list;
rhs : 'a rhs;
alias_stack : Name.t list;
eqn_loc : Loc.t option;
orig : int option;
catch_all_vars : Id.t CAst.t list }
type 'a matrix = 'a equation list
type tomatch_type =
| IsInd of types * inductive_type * Name.t list
| NotInd of constr option * types
type tomatch_status =
| Pushed of (bool*((constr * tomatch_type) * int list * Name.t))
| Alias of (bool*(Name.t * constr * (constr * types)))
| NonDepAlias
| Abstract of int * rel_declaration
type tomatch_stack = tomatch_status list
type pattern_history =
| Top
| MakeConstructor of constructor * pattern_continuation
and pattern_continuation =
| Continuation of int * cases_pattern list * pattern_history
| Result of cases_pattern list
let start_history n = Continuation (n, [], Top)
let feed_history arg = function
| Continuation (n, l, h) when n>=1 ->
Continuation (n-1, arg :: l, h)
| Continuation (n, _, _) ->
anomaly (str "Bad number of expected remaining patterns: " ++ int n ++ str ".")
| Result _ ->
anomaly (Pp.str "Exhausted pattern history.")
let rec glob_pattern_of_partial_history args2 = function
| Continuation (n, args1, h) ->
let args3 = make_anonymous_patvars (n - (List.length args2)) in
build_glob_pattern (List.rev_append args1 (args2@args3)) h
| Result pl -> pl
and build_glob_pattern args = function
| Top -> args
| MakeConstructor (pci, rh) ->
glob_pattern_of_partial_history
[DAst.make @@ PatCstr (pci, args, Anonymous)] rh
let complete_history = glob_pattern_of_partial_history []
let pop_history_pattern = function
| Continuation (0, l, Top) ->
Result (List.rev l)
| Continuation (0, l, MakeConstructor (pci, rh)) ->
feed_history (DAst.make @@ PatCstr (pci,List.rev l,Anonymous)) rh
| _ ->
anomaly (Pp.str "Constructor not yet filled with its arguments.")
let pop_history h =
feed_history (DAst.make @@ PatVar Anonymous) h
let push_history_pattern n pci cont =
Continuation (n, [], MakeConstructor (pci, cont))
type 'a pattern_matching_problem =
{ env : GlobEnv.t;
pred : constr;
tomatch : tomatch_stack;
history : pattern_continuation;
mat : 'a matrix;
caseloc : Loc.t option;
casestyle : case_style;
typing_function: type_constraint -> GlobEnv.t -> evar_map -> 'a option -> evar_map * unsafe_judgment }
let rec find_row_ind = function
[] -> None
| p :: l ->
match DAst.get p with
| PatVar _ -> find_row_ind l
| PatCstr(c,_,_) -> Some (p.CAst.loc,c)
let inductive_template env sigma tmloc ind =
let sigma, indu = Evd.fresh_inductive_instance env sigma ind in
let indu = on_snd EInstance.make indu in
let arsign = inductive_alldecls env indu in
let hole_source i = match tmloc with
| Some loc -> Loc.tag ~loc @@ Evar_kinds.TomatchTypeParameter (ind,i)
| None -> Loc.tag @@ Evar_kinds.TomatchTypeParameter (ind,i) in
let (sigma, _, evarl, _) =
List.fold_right
(fun decl (sigma, subst, evarl, n) ->
match decl with
| LocalAssum (na,ty) ->
let ty' = substl subst ty in
let sigma, e =
Evarutil.new_evar env ~src:(hole_source n) sigma ty'
in
(sigma, e::subst,e::evarl,n+1)
| LocalDef (na,b,ty) ->
(sigma, substl subst b::subst,evarl,n+1))
arsign (sigma, [], [], 1) in
sigma, applist (mkIndU indu,List.rev evarl)
let try_find_ind env sigma typ realnames =
let (IndType(indf,realargs) as ind) = find_rectype env sigma typ in
let names =
match realnames with
| Some names -> names
| None ->
let ind = fst (fst (dest_ind_family indf)) in
List.make (inductive_nrealdecls env ind) Anonymous in
IsInd (typ,ind,names)
let inh_coerce_to_ind env sigma0 loc ty tyi =
let sigma, expected_typ = inductive_template env sigma0 loc tyi in
match Evarconv.unify_leq_delay env sigma expected_typ ty with
| sigma -> sigma
| exception Evarconv.UnableToUnify _ -> sigma0
let binding_vars_of_inductive sigma = function
| NotInd _ -> []
| IsInd (_,IndType(_,realargs),_) -> List.filter (isRel sigma) realargs
let set_tomatch_realnames names = function
| NotInd _ as t -> t
| IsInd (typ,ind,_) -> IsInd (typ,ind,names)
let env sigma decl =
match decl with
| LocalAssum (_,t) ->
let tmtyp =
try try_find_ind env sigma t None
with Not_found -> NotInd (None,t) in
let tmtypvars = binding_vars_of_inductive sigma tmtyp in
(tmtyp,tmtypvars)
| LocalDef (_,_,t) ->
(NotInd (None, t), [])
let unify_tomatch_with_patterns env sigma loc typ pats realnames =
match find_row_ind pats with
| None -> sigma, NotInd (None,typ)
| Some (_,(ind,_)) ->
let sigma = inh_coerce_to_ind env sigma loc typ ind in
try sigma, try_find_ind env sigma typ realnames
with Not_found -> sigma, NotInd (None,typ)
let find_tomatch_tycon env sigma loc = function
| Some {CAst.v=(ind,realnal)} ->
let sigma, tycon = inductive_template env sigma loc ind in
sigma, mk_tycon tycon, Some (List.rev realnal)
| None ->
sigma, empty_tycon, None
let make_return_predicate_ltac_lvar env sigma na tm c =
match na, DAst.get tm with
| Name id, (GVar id' | GRef (GlobRef.VarRef id', _)) when Id.equal id id' ->
let expansion = match kind sigma c with
| Var id' -> Name id'
| _ -> Anonymous in
GlobEnv.hide_variable env expansion id
| _ -> env
let is_patvar pat =
match DAst.get pat with
| PatVar _ -> true
| _ -> false
let coerce_row ~program_mode typing_fun env sigma pats (tomatch,(na,indopt)) =
let loc = loc_of_glob_constr tomatch in
let sigma, tycon, realnames = find_tomatch_tycon !!env sigma loc indopt in
let sigma, j = typing_fun tycon env sigma tomatch in
let sigma, j = Coercion.inh_coerce_to_base ?loc:(loc_of_glob_constr tomatch) ~program_mode !!env sigma j in
let typ = nf_evar sigma j.uj_type in
let env = make_return_predicate_ltac_lvar env sigma na tomatch j.uj_val in
let sigma, t =
if realnames = None && pats <> [] && List.for_all is_patvar pats then
sigma, NotInd (None,typ)
else
try sigma, try_find_ind !!env sigma typ realnames
with Not_found ->
unify_tomatch_with_patterns !!env sigma loc typ pats realnames
in
((env, sigma), (j.uj_val,t))
let coerce_to_indtype ~program_mode typing_fun env sigma matx tomatchl =
let pats = List.map (fun r -> r.patterns) matx in
let matx' = match matrix_transpose pats with
| [] -> List.map (fun _ -> []) tomatchl
| m -> m in
let (env, sigma), tms = List.fold_left2_map (fun (env, sigma) -> coerce_row ~program_mode typing_fun env sigma) (env, sigma) matx' tomatchl in
env, sigma, tms
let mkExistential ?(src=(Loc.tag Evar_kinds.InternalHole)) env sigma =
let sigma, (e, u) = Evarutil.new_type_evar env sigma ~src:src univ_flexible_alg in
sigma, e
let adjust_tomatch_to_pattern ~program_mode sigma pb ((current,typ),deps,dep) =
let typ,names =
match typ with IsInd(t,_,names) -> t,Some names | NotInd(_,t) -> t,None in
let tmtyp =
try try_find_ind !!(pb.env) sigma typ names
with Not_found -> NotInd (None,typ) in
match tmtyp with
| NotInd (None,typ) ->
let tm1 = List.map (fun eqn -> List.hd eqn.patterns) pb.mat in
(match find_row_ind tm1 with
| None -> sigma, (current, tmtyp)
| Some (loc,(ind,_)) ->
let sigma, indt = inductive_template !!(pb.env) sigma None ind in
let sigma, current =
if List.is_empty deps && isEvar sigma typ then
match Evarconv.unify_leq_delay !!(pb.env) sigma indt typ with
| exception Evarconv.UnableToUnify _ -> sigma, current
| sigma -> sigma, current
else
let sigma, j, _trace = Coercion.inh_conv_coerce_to ?loc ~program_mode ~resolve_tc:true !!(pb.env) sigma (make_judge current typ) indt in
sigma, j.uj_val
in
sigma, (current, try_find_ind !!(pb.env) sigma indt names))
| _ -> sigma, (current, tmtyp)
let type_of_tomatch = function
| IsInd (t,_,_) -> t
| NotInd (_,t) -> t
let map_tomatch_type f = function
| IsInd (t,ind,names) -> IsInd (f t,map_inductive_type f ind,names)
| NotInd (c,t) -> NotInd (Option.map f c, f t)
let liftn_tomatch_type n depth = map_tomatch_type (Vars.liftn n depth)
let lift_tomatch_type n = liftn_tomatch_type n 1
let current_pattern eqn =
match eqn.patterns with
| pat::_ -> pat
| [] -> anomaly (Pp.str "Empty list of patterns.")
let remove_current_pattern eqn =
match eqn.patterns with
| pat::pats ->
{ eqn with
patterns = pats;
alias_stack = alias_of_pat pat :: eqn.alias_stack }
| [] -> anomaly (Pp.str "Empty list of patterns.")
let push_current_pattern ~program_mode sigma (cur,ty) eqn =
let vars = VarSet.variables (Global.env ()) in
let hypnaming = if program_mode then ProgramNaming vars else RenameExistingBut vars in
match eqn.patterns with
| pat::pats ->
let r = ERelevance.relevant in
let _,rhs_env = push_rel ~hypnaming sigma (LocalDef (make_annot (alias_of_pat pat) r,cur,ty)) eqn.rhs.rhs_env in
{ eqn with
rhs = { eqn.rhs with rhs_env = rhs_env };
patterns = pats }
| [] -> anomaly (Pp.str "Empty list of patterns.")
let push_noalias_current_pattern eqn =
match eqn.patterns with
| _::pats ->
{ eqn with patterns = pats }
| [] -> anomaly (Pp.str "push_noalias_current_pattern: Empty list of patterns.")
let prepend_pattern tms eqn = {eqn with patterns = tms@eqn.patterns }
exception NotAdjustable
let rec adjust_local_defs ?loc = function
| (pat :: pats, LocalAssum _ :: decls) ->
pat :: adjust_local_defs ?loc (pats,decls)
| (pats, LocalDef _ :: decls) ->
(DAst.make ?loc @@ PatVar Anonymous) :: adjust_local_defs ?loc (pats,decls)
| [], [] -> []
| _ -> raise NotAdjustable
let check_and_adjust_constructor env ind cstrs pat = match DAst.get pat with
| PatVar _ -> pat
| PatCstr (((_,i) as cstr),args,alias) ->
let loc = pat.CAst.loc in
let ind' = inductive_of_constructor cstr in
if QInd.equal env ind' ind then
let ci = cstrs.(i-1) in
let nb_args_constr = ci.cs_nargs in
let nargs = List.length args in
if Int.equal nargs nb_args_constr then pat
else
try
let args' = adjust_local_defs ?loc (args, List.rev ci.cs_args)
in DAst.make ?loc @@ PatCstr (cstr, args', alias)
with NotAdjustable ->
let nlet = List.count (function LocalDef _ -> true | _ -> false) ci.cs_args in
error_wrong_numarg_constructor ?loc env ~cstr
~expanded:false ~nargs ~expected_nassums:nb_args_constr
~expected_ndecls:(nb_args_constr + nlet)
else
try
Coercion.inh_pattern_coerce_to ?loc env pat ind' ind
with Not_found ->
error_bad_constructor ?loc env cstr ind
let check_all_variables env sigma typ mat =
List.iter
(fun eqn ->
let pat = current_pattern eqn in
match DAst.get pat with
| PatVar id -> ()
| PatCstr (cstr_sp,_,_) ->
let loc = pat.CAst.loc in
error_bad_pattern ?loc env sigma cstr_sp typ)
mat
let set_pattern_catch_all_var ?loc eqn = function
| Name id when not (Id.Set.mem id eqn.rhs.rhs_vars) ->
{ eqn with catch_all_vars = CAst.make ?loc id :: eqn.catch_all_vars }
| _ ->
eqn
let warn_named_multi_catch_all =
CWarnings.create ~name:"unused-pattern-matching-variable"
(fun id ->
strbrk "Unused variable " ++ Id.print id
++ strbrk " might be a misspelled constructor. Use _ or _"
++ Id.print id ++ strbrk " to silence this warning.")
let wildcard_id = Id.of_string "wildcard'"
let is_wildcard id =
Id.equal (Id.of_string (Nameops.atompart_of_id id)) wildcard_id
let check_unused_pattern_eqn env vars eqn =
match vars with
| [] -> raise_pattern_matching_error ?loc:eqn.eqn_loc (env, Evd.empty, UnusedClause eqn.patterns)
| _ ->
let warn {CAst.v = id; loc} =
if (Id.to_string id).[0] <> '_' && not (is_wildcard id)
then warn_named_multi_catch_all ?loc id in
List.iter warn (List.uniquize (List.flatten vars))
let check_unused_pattern env used matx =
let result = Array.init (List.length matx) (fun _ -> []) in
List.iter (function (Some n,vars) -> result.(n) <- vars :: result.(n) | _ -> ()) used;
List.iter2 (check_unused_pattern_eqn env) (Array.to_list result) matx
let pb =
match pb.mat with
| [] -> user_err (msg_may_need_inversion())
| eqn::_ -> ([eqn.orig,eqn.catch_all_vars], eqn.rhs)
let occur_in_rhs na rhs =
match na with
| Anonymous -> false
| Name id -> Id.Set.mem id rhs.rhs_vars
let is_dep_patt_in eqn pat = match DAst.get pat with
| PatVar name -> occur_in_rhs name eqn.rhs
| PatCstr _ -> true
let mk_dep_patt_row ~program_mode (pats,_,eqn) =
if program_mode then List.map (fun _ -> true) pats
else List.map (is_dep_patt_in eqn) pats
let dependencies_in_pure_rhs ~program_mode nargs eqns =
if List.is_empty eqns then
List.make nargs (not program_mode) else
let deps_rows = List.map (mk_dep_patt_row ~program_mode) eqns in
let deps_columns = matrix_transpose deps_rows in
List.map (List.exists (fun x -> x)) deps_columns
let dependent_decl sigma a =
function
| LocalAssum (na,t) -> dependent sigma a t
| LocalDef (na,c,t) -> dependent sigma a t || dependent sigma a c
let rec dep_in_tomatch sigma n = function
| (Pushed _ | Alias _ | NonDepAlias) :: l -> dep_in_tomatch sigma n l
| Abstract (_,d) :: l -> RelDecl.exists (fun c -> not (noccurn sigma n c)) d || dep_in_tomatch sigma (n+1) l
| [] -> false
let dependencies_in_rhs ~program_mode sigma nargs current tms eqns =
match EConstr.kind sigma current with
| Rel n when dep_in_tomatch sigma n tms -> List.make nargs true
| _ -> dependencies_in_pure_rhs ~program_mode nargs eqns
let rec find_dependency_list sigma tmblock = function
| [] -> []
| (used,tdeps,tm,d)::rest ->
let deps = find_dependency_list sigma tmblock rest in
if used && List.exists (fun x -> dependent_decl sigma x d) tmblock
then
match EConstr.kind sigma tm with
| Rel n -> List.add_set Int.equal n (List.union Int.equal deps tdeps)
| _ -> List.union Int.equal deps tdeps
else deps
let find_dependencies sigma is_dep_or_cstr_in_rhs (tm,(_,tmtypleaves),d) nextlist =
let deps = find_dependency_list sigma (tm::tmtypleaves) nextlist in
if is_dep_or_cstr_in_rhs || not (List.is_empty deps)
then ((true ,deps,tm,d)::nextlist)
else ((false,[] ,tm,d)::nextlist)
let find_dependencies_signature sigma deps_in_rhs typs =
let l = List.fold_right2 (find_dependencies sigma) deps_in_rhs typs [] in
List.map (fun (_,deps,_,_) -> deps) l
let relocate_index_tomatch sigma n1 n2 =
let rec genrec depth = function
| [] ->
[]
| Pushed (b,((c,tm),l,na)) :: rest ->
let c = relocate_index sigma n1 n2 depth c in
let tm = map_tomatch_type (relocate_index sigma n1 n2 depth) tm in
let l = List.map (relocate_rel n1 n2 depth) l in
Pushed (b,((c,tm),l,na)) :: genrec depth rest
| Alias (initial,(na,c,d)) :: rest ->
Alias (initial,(na,c,map_pair (relocate_index sigma n1 n2 depth) d)) :: genrec depth rest
| NonDepAlias :: rest ->
NonDepAlias :: genrec depth rest
| Abstract (i,d) :: rest ->
let i = relocate_rel n1 n2 depth i in
Abstract (i, RelDecl.map_constr (fun c -> relocate_index sigma n1 n2 depth c) d)
:: genrec (depth+1) rest in
genrec 0
let rec replace_term sigma n c k t =
if isRel sigma t && Int.equal (destRel sigma t) (n + k) then Vars.lift k c
else EConstr.map_with_binders sigma succ (replace_term sigma n c) k t
let length_of_tomatch_type_sign na t =
let l = match na with
| Anonymous -> 0
| Name _ -> 1
in
match t with
| NotInd _ -> l
| IsInd (_, _, names) -> List.length names + l
let replace_tomatch sigma n c =
let rec replrec depth = function
| [] -> []
| Pushed (initial,((b,tm),l,na)) :: rest ->
let b = replace_term sigma n c depth b in
let tm = map_tomatch_type (replace_term sigma n c depth) tm in
List.iter (fun i -> if Int.equal i (n + depth) then anomaly (Pp.str "replace_tomatch.")) l;
Pushed (initial,((b,tm),l,na)) :: replrec depth rest
| Alias (initial,(na,b,d)) :: rest ->
Alias (initial,(na,b,map_pair (replace_term sigma n c depth) d)) :: replrec depth rest
| NonDepAlias :: rest ->
NonDepAlias :: replrec depth rest
| Abstract (i,d) :: rest ->
Abstract (i, RelDecl.map_constr (fun t -> replace_term sigma n c depth t) d)
:: replrec (depth+1) rest in
replrec 0
let rec liftn_tomatch_stack n depth = function
| [] -> []
| Pushed (initial,((c,tm),l,na))::rest ->
let c = liftn n depth c in
let tm = liftn_tomatch_type n depth tm in
let l = List.map (fun i -> if i<depth then i else i+n) l in
Pushed (initial,((c,tm),l,na))::(liftn_tomatch_stack n depth rest)
| Alias (initial,(na,c,d))::rest ->
Alias (initial,(na,liftn n depth c,map_pair (liftn n depth) d))
::(liftn_tomatch_stack n depth rest)
| NonDepAlias :: rest ->
NonDepAlias :: liftn_tomatch_stack n depth rest
| Abstract (i,d)::rest ->
let i = if i<depth then i else i+n in
Abstract (i, RelDecl.map_constr (liftn n depth) d)
::(liftn_tomatch_stack n (depth+1) rest)
let lift_tomatch_stack n = liftn_tomatch_stack n 1
let merge_name get_name obj = function
| Anonymous -> get_name obj
| na -> na
let merge_names get_name = List.map2 (merge_name get_name)
let get_names avoid env sigma sign eqns =
let names1 = List.make (Context.Rel.length sign) Anonymous in
let names2,aliasname =
List.fold_right
(fun (pats,pat_alias,eqn) (names,aliasname) ->
(merge_names alias_of_pat pats names,
merge_name (fun x -> x) pat_alias aliasname))
eqns (names1,Anonymous) in
let allvars =
List.fold_left (fun l (_,_,eqn) -> Id.Set.union l eqn.rhs.avoid_ids)
avoid eqns in
let names3,_ =
List.fold_left2
(fun (l,avoid) d na ->
let na =
merge_name
(fun decl ->
let na = get_name decl in
let t = get_type decl in
Name (next_name_away (named_hd env sigma t na) avoid))
d na
in
(na::l,Id.Set.add (Name.get_id na) avoid))
([],allvars) (List.rev sign) names2 in
names3,aliasname
let recover_initial_subpattern_names = List.map2 RelDecl.set_name
let recover_and_adjust_alias_names (_,avoid) names sign =
let rec aux = function
| [],[] ->
[]
| x::names, LocalAssum (x',t)::sign ->
(x, LocalAssum ({x' with binder_name=alias_of_pat x},t)) :: aux (names,sign)
| names, (LocalDef (na,_,_) as decl)::sign ->
(DAst.make @@ PatVar na.binder_name, decl) :: aux (names,sign)
| _ -> assert false
in
List.split (aux (names,sign))
let push_rels_eqn ~hypnaming sigma sign eqn =
{eqn with
rhs = {eqn.rhs with rhs_env = snd (push_rel_context ~hypnaming sigma sign eqn.rhs.rhs_env) } }
let push_rels_eqn_with_names sigma sign eqn =
let subpats = List.rev (List.firstn (List.length sign) eqn.patterns) in
let subpatnames = List.map alias_of_pat subpats in
let sign = recover_initial_subpattern_names subpatnames sign in
push_rels_eqn sigma sign eqn
let push_generalized_decl_eqn ~hypnaming env sigma n decl eqn =
match RelDecl.get_name decl with
| Anonymous ->
push_rels_eqn ~hypnaming sigma [decl] eqn
| Name _ ->
push_rels_eqn ~hypnaming sigma [RelDecl.set_name (RelDecl.get_name (Environ.lookup_rel n !!(eqn.rhs.rhs_env))) decl] eqn
let drop_alias_eqn eqn =
{ eqn with alias_stack = List.tl eqn.alias_stack }
let push_alias_eqn sigma alias eqn =
let aliasname = List.hd eqn.alias_stack in
let eqn = drop_alias_eqn eqn in
let alias = RelDecl.set_name aliasname alias in
push_rels_eqn sigma [alias] eqn
let rec map_predicate f k ccl = function
| [] -> f k ccl
| Pushed (_,((_,tm),_,na)) :: rest ->
let k' = length_of_tomatch_type_sign na tm in
map_predicate f (k+k') ccl rest
| (Alias _ | NonDepAlias) :: rest ->
map_predicate f k ccl rest
| Abstract _ :: rest ->
map_predicate f (k+1) ccl rest
let noccur_predicate_between sigma n = map_predicate (noccur_between sigma n)
let liftn_predicate n = map_predicate (liftn n)
let lift_predicate n = liftn_predicate n 1
let regeneralize_index_predicate sigma n = map_predicate (relocate_index sigma n 1) 0
let substnl_predicate sigma = map_predicate (substnl sigma)
let subst_predicate (subst,copt) ccl tms =
let sigma = match copt with
| None -> subst
| Some c -> c::subst in
substnl_predicate sigma 0 ccl tms
let specialize_predicate_var (cur,typ,dep) env tms ccl =
let c = match dep with
| Anonymous -> None
| Name _ -> Some cur
in
let l =
match typ with
| IsInd (_, IndType (_, _), []) -> []
| IsInd (_, IndType (indf, realargs), names) ->
let arsign = get_arity env indf in
subst_of_rel_context_instance_list arsign realargs
| NotInd _ -> [] in
subst_predicate (l,c) ccl tms
let generalize_predicate sigma (names,na) ny d tms ccl =
let () = match na with
| Anonymous -> anomaly (Pp.str "Undetected dependency.")
| _ -> () in
let p = List.length names + 1 in
let ccl = lift_predicate 1 ccl tms in
regeneralize_index_predicate sigma (ny+p+1) ccl tms
let rec ccl = function
| (Alias _ | NonDepAlias)::tms ->
extract_predicate ccl tms
| Abstract (i,d)::tms ->
mkProd_wo_LetIn d (extract_predicate ccl tms)
| Pushed (_,((cur,NotInd _),_,na))::tms ->
begin match na with
| Anonymous -> extract_predicate ccl tms
| Name _ ->
let tms = lift_tomatch_stack 1 tms in
let pred = extract_predicate ccl tms in
subst1 cur pred
end
| Pushed (_,((cur,IsInd (_,IndType(_,realargs),_)),_,na))::tms ->
let realargs = List.rev realargs in
let k, nrealargs = match na with
| Anonymous -> 0, realargs
| Name _ -> 1, (cur :: realargs)
in
let tms = lift_tomatch_stack (List.length realargs + k) tms in
let pred = extract_predicate ccl tms in
substl nrealargs pred
| [] ->
ccl
let abstract_predicate env sigma indf cur realargs (names,na) tms ccl =
let sign = make_arity_signature !!env sigma true indf in
let n = List.length sign in
let tms = List.fold_right2 (fun par arg tomatch ->
match EConstr.kind sigma par with
| Rel i -> relocate_index_tomatch sigma (i+n) (destRel sigma arg) tomatch
| _ -> tomatch) (realargs@[cur]) (Context.Rel.instance_list EConstr.mkRel 0 sign)
(lift_tomatch_stack n tms) in
let ccl = match na with
| Anonymous -> lift_predicate 1 ccl tms
| Name _ -> ccl
in
let pred = extract_predicate ccl tms in
let sign = List.map2 set_name (na::names) sign in
it_mkLambda_or_LetIn_name !!env sigma pred sign
let expand_arg tms (p,ccl) ((_,t),_,na) =
let k = length_of_tomatch_type_sign na t in
(p+k,liftn_predicate (k-1) (p+1) ccl tms)
let add_assert_false_case pb tomatch =
let pats = List.map (fun _ -> DAst.make @@ PatVar Anonymous) tomatch in
let aliasnames =
List.map_filter (function Alias _ | NonDepAlias -> Some Anonymous | _ -> None) tomatch
in
[ { patterns = pats;
rhs = { rhs_env = pb.env;
rhs_vars = Id.Set.empty;
avoid_ids = Id.Set.empty;
it = None };
alias_stack = Anonymous::aliasnames;
eqn_loc = None;
orig = None;
catch_all_vars = [] } ]
let adjust_impossible_cases sigma pb pred tomatch submat =
match submat with
| [] ->
begin match EConstr.kind sigma pred with
| Evar (evk, _) ->
let evi = Evd.find_undefined sigma evk in
if snd (Evd.evar_source evi) == Evar_kinds.ImpossibleCase then
let sigma, default = coq_unit_judge !!(pb.env) sigma in
let sigma = Evd.define evk default.uj_type sigma in
sigma, add_assert_false_case pb tomatch
else
sigma, submat
| _ ->
let sigma', default = coq_unit_judge !!(pb.env) sigma in
if EConstr.eq_constr_nounivs sigma' pred default.uj_type
then sigma, add_assert_false_case pb tomatch
else sigma, submat
end
| _ ->
sigma, submat
let specialize_predicate env sigma newtomatchs (names,depna) arsign cs tms ccl =
let nrealargs = List.length names in
let l = match depna with Anonymous -> 0 | Name _ -> 1 in
let k = nrealargs + l in
let n = cs.cs_nargs in
let ccl' = liftn_predicate n (k+1) ccl tms in
let realargsi =
if not (Int.equal nrealargs 0) then
Vars.subst_of_rel_context_instance arsign cs.cs_concl_realargs
else
[] in
let copti = match depna with
| Anonymous -> None
| Name _ -> Some (build_dependent_constructor cs)
in
let ccl'' =
whd_betaiota env sigma (subst_predicate (realargsi, copti) ccl' tms) in
let ccl''' = liftn_predicate n (n+1) ccl'' tms in
snd (List.fold_left (expand_arg tms) (1,ccl''') newtomatchs)
let find_predicate loc env sigma p current (IndType (indf,realargs)) dep tms =
let pred = abstract_predicate env sigma indf current realargs dep tms p in
(pred, whd_betaiota !!env sigma
(applist (pred, realargs@[current])))
let adjust_predicate_from_tomatch tomatch (current,typ as ct) pb =
let ((_,oldtyp),deps,na) = tomatch in
match typ, oldtyp with
| IsInd (_,_,names), NotInd _ ->
let k = match na with
| Anonymous -> 1
| Name _ -> 2
in
let n = List.length names in
{ pb with pred = liftn_predicate n k pb.pred pb.tomatch },
(ct,List.map (fun i -> if i >= k then i+n else i) deps,na)
| _ ->
pb, (ct,deps,na)
let rec ungeneralize sigma n ng body =
match EConstr.kind sigma body with
| Lambda (_,_,c) when Int.equal ng 0 ->
subst1 (mkRel n) c
| Lambda (na,t,c) ->
mkLambda (na,t,ungeneralize sigma (n+1) (ng-1) c)
| LetIn (na,b,t,c) ->
mkLetIn (na,b,t,ungeneralize sigma (n+1) ng c)
| Case (ci,u,pms,(p,rp),iv,c,brs) ->
let p =
let (nas, p) = p in
let sign2,p = decompose_prod_n_decls sigma ng p in
let p = prod_applist sigma p [mkRel (n+Array.length nas+ng)] in
nas, it_mkProd_or_LetIn p sign2
in
let map (nas, br) = nas, ungeneralize sigma (n + Array.length nas) ng br in
mkCase (ci, u, pms, (p,rp), iv, c, Array.map map brs)
| App (f,args) ->
assert (isCase sigma f);
mkApp (ungeneralize sigma n (ng+Array.length args) f,args)
| _ -> assert false
let ungeneralize_branch sigma n k (sign,body) cs =
(sign,ungeneralize sigma (n+cs.cs_nargs) k body)
let rec is_dependent_generalization sigma ng body =
match EConstr.kind sigma body with
| Lambda (_,_,c) when Int.equal ng 0 ->
not (noccurn sigma 1 c)
| Lambda (na,t,c) ->
is_dependent_generalization sigma (ng-1) c
| LetIn (na,b,t,c) ->
is_dependent_generalization sigma ng c
| Case (ci,u,pms,p,iv,c,brs) ->
Array.exists (fun (_, b) -> is_dependent_generalization sigma ng b) brs
| App (g,args) ->
assert (isCase sigma g);
is_dependent_generalization sigma (ng+Array.length args) g
| _ -> assert false
let is_dependent_branch sigma k (_,br) =
is_dependent_generalization sigma k br
let postprocess_dependencies evd tocheck brs tomatch pred deps cs =
let rec aux k brs tomatch pred tocheck deps = match deps, tomatch with
| [], _ -> brs,tomatch,pred,[]
| n::deps, Abstract (i,d) :: tomatch ->
let d = map_constr (fun c -> nf_evar evd c) d in
let is_d = match d with LocalAssum _ -> false | LocalDef _ -> true in
if is_d || List.exists (fun c -> dependent_decl evd (lift k c) d) tocheck
&& Array.exists (is_dependent_branch evd k) brs then
let brs,tomatch,pred,inst = aux (k+1) brs tomatch pred (mkRel n::tocheck) deps in
let inst = match d with
| LocalAssum _ -> mkRel n :: inst
| _ -> inst
in
brs, Abstract (i,d) :: tomatch, pred, inst
else
let pred = lift_predicate (-1) pred tomatch in
let tomatch = relocate_index_tomatch evd 1 (n+1) tomatch in
let tomatch = lift_tomatch_stack (-1) tomatch in
let brs = Array.map2 (ungeneralize_branch evd n k) brs cs in
aux k brs tomatch pred tocheck deps
| _ -> assert false
in aux 0 brs tomatch pred tocheck deps
let rec irrefutable env pat = match DAst.get pat with
| PatVar name -> true
| PatCstr (cstr,args,_) ->
let ind = inductive_of_constructor cstr in
let (_,mip) = Inductive.lookup_mind_specif env ind in
let one_constr = Int.equal (Array.length mip.mind_user_lc) 1 in
one_constr && List.for_all (irrefutable env) args
let first_clause_irrefutable env = function
| {patterns=pat::patl}::mat -> (match DAst.get pat with PatVar _ -> List.for_all (irrefutable env) patl | _ -> false)
| _ -> false
let group_equations pb ind current cstrs mat =
let mat =
if first_clause_irrefutable !!(pb.env) mat then [List.hd mat] else mat in
let brs = Array.make (Array.length cstrs) [] in
let only_default = ref None in
let _ =
List.fold_right
(fun eqn () ->
let rest = remove_current_pattern eqn in
let pat = current_pattern eqn in
match DAst.get (check_and_adjust_constructor !!(pb.env) ind cstrs pat) with
| PatVar name ->
let rest = set_pattern_catch_all_var ?loc:pat.CAst.loc rest name in
for i=1 to Array.length cstrs do
let args = make_anonymous_patvars cstrs.(i-1).cs_nargs in
brs.(i-1) <- (args, name, rest) :: brs.(i-1)
done;
if !only_default == None then only_default := Some true
| PatCstr (((_,i)),args,name) ->
only_default := Some false;
brs.(i-1) <- (args, name, rest) :: brs.(i-1)) mat () in
(brs,Option.default false !only_default)
let rec generalize_problem names sigma pb = function
| [] -> pb, []
| i::l ->
let pb',deps = generalize_problem names sigma pb l in
let d = map_constr (lift i) (lookup_rel i !!(pb.env)) in
begin match d with
| LocalDef ({binder_name=Anonymous},_,_) -> pb', deps
| _ ->
let d = RelDecl.map_type (fun c -> whd_betaiota !!(pb.env) sigma c) d in
let tomatch = lift_tomatch_stack 1 pb'.tomatch in
let tomatch = relocate_index_tomatch sigma (i+1) 1 tomatch in
{ pb' with
tomatch = Abstract (i,d) :: tomatch;
pred = generalize_predicate sigma names i d pb'.tomatch pb'.pred },
i::deps
end
let build_leaf sigma pb =
let used, rhs = extract_rhs pb in
let sigma, j = pb.typing_function (mk_tycon pb.pred) rhs.rhs_env sigma rhs.it in
used, sigma, j_nf_evar sigma j
let build_branch ~program_mode initial current realargs deps (realnames,curname) sigma pb arsign eqns const_info =
let history =
push_history_pattern const_info.cs_nargs (fst const_info.cs_cstr) pb.history in
let cs_args = const_info.cs_args in
let names,aliasname = get_names (GlobEnv.vars_of_env pb.env) !!(pb.env) sigma cs_args eqns in
let typs = List.map2 RelDecl.set_name names cs_args
in
let typs = List.map (map_type (nf_betaiota !!(pb.env) sigma)) typs in
let submat = List.map (fun (tms,_,eqn) -> prepend_pattern tms eqn) eqns in
let typs' =
List.map_i (fun i d -> (mkRel i, map_constr (lift i) d)) 1 typs in
let vars = VarSet.variables (Global.env ()) in
let hypnaming = if program_mode then ProgramNaming vars else RenameExistingBut vars in
let typs,extenv = push_rel_context ~hypnaming sigma typs pb.env in
let typs' =
List.map (fun (c,d) ->
(c,extract_inductive_data !!extenv sigma d,d)) typs' in
let dep_sign =
find_dependencies_signature sigma
(dependencies_in_rhs ~program_mode sigma const_info.cs_nargs current pb.tomatch eqns)
(List.rev typs') in
let ci = build_dependent_constructor const_info in
let cirealargs = Array.to_list const_info.cs_concl_realargs in
let tomatch = List.fold_right2 (fun par arg tomatch ->
match EConstr.kind sigma par with
| Rel i -> replace_tomatch sigma (i+const_info.cs_nargs) arg tomatch
| _ -> tomatch) (current::realargs) (ci::cirealargs)
(lift_tomatch_stack const_info.cs_nargs pb.tomatch) in
let pred_is_not_dep =
noccur_predicate_between sigma 1 (List.length realnames + 1) pb.pred tomatch in
let typs' =
List.map2
(fun (tm, (tmtyp,_), decl) deps ->
let na = RelDecl.get_name decl in
let na = match curname, na with
| Name _, Anonymous -> curname
| Name _, Name _ -> na
| Anonymous, _ ->
if List.is_empty deps && pred_is_not_dep then Anonymous else force_name na in
((tm,tmtyp),deps,na))
typs' (List.rev dep_sign) in
let pred =
specialize_predicate !!(pb.env) sigma typs' (realnames,curname) arsign const_info tomatch pb.pred in
let currents = List.map (fun x -> Pushed (false,x)) typs' in
let alias = match aliasname with
| Anonymous ->
NonDepAlias
| Name _ ->
let cur_alias = lift const_info.cs_nargs current in
let ind =
mkApp (
applist (mkIndU (inductive_of_constructor (fst const_info.cs_cstr), snd const_info.cs_cstr),
List.map (lift const_info.cs_nargs) const_info.cs_params),
const_info.cs_concl_realargs) in
Alias (initial,(aliasname,cur_alias,(ci,ind))) in
let tomatch = List.rev_append (alias :: currents) tomatch in
let sigma, submat = adjust_impossible_cases sigma pb pred tomatch submat in
let () = match submat with
| [] ->
raise_pattern_matching_error (!!(pb.env), Evd.empty, NonExhaustive (complete_history history))
| _ -> ()
in
sigma, typs,
{ pb with
env = extenv;
tomatch = tomatch;
pred = pred;
history = history;
mat = List.map (push_rels_eqn_with_names ~hypnaming sigma typs) submat }
let compile ~program_mode sigma pb =
let vars = VarSet.variables (Global.env ()) in
let hypnaming = if program_mode then ProgramNaming vars else RenameExistingBut vars in
let rec compile sigma pb =
match pb.tomatch with
| Pushed cur :: rest -> match_current sigma { pb with tomatch = rest } cur
| Alias (initial,x) :: rest -> compile_alias initial sigma pb x rest
| NonDepAlias :: rest -> compile_non_dep_alias sigma pb rest
| Abstract (i,d) :: rest -> compile_generalization sigma pb i d rest
| [] -> build_leaf sigma pb
and match_current sigma pb (initial,tomatch) =
let sigma, tm = adjust_tomatch_to_pattern ~program_mode sigma pb tomatch in
let pb,tomatch = adjust_predicate_from_tomatch tomatch tm pb in
let ((current,typ),deps,dep) = tomatch in
match typ with
| NotInd (_,typ) ->
check_all_variables !!(pb.env) sigma typ pb.mat;
compile_all_variables initial tomatch sigma pb
| IsInd (_,(IndType(indf,realargs) as indt),names) ->
let mind,_ = dest_ind_family indf in
let () = Tacred.check_privacy !!(pb.env) (fst mind) in
let cstrs = get_constructors !!(pb.env) indf in
let arsign = get_arity !!(pb.env) indf in
let eqns,onlydflt = group_equations pb (fst mind) current cstrs pb.mat in
let no_cstr = Int.equal (Array.length cstrs) 0 in
if (not no_cstr || not (List.is_empty pb.mat)) && onlydflt then
compile_all_variables initial tomatch sigma pb
else
let pb,deps = generalize_problem (names,dep) sigma pb deps in
let fold_br sigma eqn cstr =
let used, sigma, j = compile_branch initial current realargs (names,dep) deps sigma pb arsign eqn cstr in
sigma, (used, j)
in
let sigma, brvals = Array.fold_left2_map fold_br sigma eqns cstrs in
let used, brvals = Array.split brvals in
let depstocheck = current::binding_vars_of_inductive sigma typ in
let brvals,tomatch,pred,inst =
postprocess_dependencies sigma depstocheck
brvals pb.tomatch pb.pred deps cstrs in
let brvals = Array.map (fun (sign,body) ->
it_mkLambda_or_LetIn body sign) brvals in
let (pred,typ) =
find_predicate pb.caseloc pb.env sigma
pred current indt (names,dep) tomatch
in
let rci = Typing.check_allowed_sort !!(pb.env) sigma mind current pred in
let ci = make_case_info !!(pb.env) (fst mind) pb.casestyle in
let pred = nf_betaiota !!(pb.env) sigma pred in
let case = make_case_or_project !!(pb.env) sigma indt ci (pred,rci) current brvals in
let sigma, _ = Typing.type_of !!(pb.env) sigma pred in
let used = List.flatten (Array.to_list used) in
used, sigma, { uj_val = applist (case, inst);
uj_type = prod_applist sigma typ inst }
and shift_problem ((current,t),_,na) sigma pb =
let ty = type_of_tomatch t in
let tomatch = lift_tomatch_stack 1 pb.tomatch in
let pred = specialize_predicate_var (current,t,na) !!(pb.env) pb.tomatch pb.pred in
let env = Name.fold_left (fun env id -> hide_variable env Anonymous id) pb.env na in
let pb =
{ pb with
env = snd (push_rel ~hypnaming sigma (LocalDef (annotR na,current,ty)) env);
tomatch = tomatch;
pred = lift_predicate 1 pred tomatch;
history = pop_history pb.history;
mat = List.map (push_current_pattern ~program_mode sigma (current,ty)) pb.mat } in
let used, sigma, j = compile sigma pb in
used, sigma, { uj_val = subst1 current j.uj_val;
uj_type = subst1 current j.uj_type }
and pop_problem ((current,t),_,na) sigma pb =
let pred = specialize_predicate_var (current,t,na) !!(pb.env) pb.tomatch pb.pred in
let pb =
{ pb with
pred = pred;
history = pop_history pb.history;
mat = List.map push_noalias_current_pattern pb.mat } in
compile sigma pb
and compile_all_variables initial cur sigma pb =
if initial then shift_problem cur sigma pb
else pop_problem cur sigma pb
and compile_branch initial current realargs names deps sigma pb arsign eqns cstr =
let sigma, sign, pb = build_branch ~program_mode initial current realargs deps names sigma pb arsign eqns cstr in
let used, sigma, j = compile sigma pb in
used, sigma, (sign, j.uj_val)
and compile_generalization sigma pb i d rest =
let pb =
{ pb with
env = snd (push_rel ~hypnaming sigma d pb.env);
tomatch = rest;
mat = List.map (push_generalized_decl_eqn ~hypnaming pb.env sigma i d) pb.mat } in
let used, sigma, j = compile sigma pb in
used, sigma, { uj_val = mkLambda_or_LetIn d j.uj_val;
uj_type = mkProd_wo_LetIn d j.uj_type }
and compile_alias initial sigma pb (na,orig,(expanded,expanded_typ)) rest =
let f c t =
let r = Retyping.relevance_of_type !!(pb.env) sigma t in
let alias = LocalDef (make_annot na r,c,t) in
let pb =
{ pb with
env = snd (push_rel ~hypnaming sigma alias pb.env);
tomatch = lift_tomatch_stack 1 rest;
pred = lift_predicate 1 pb.pred pb.tomatch;
history = pop_history_pattern pb.history;
mat = List.map (push_alias_eqn ~hypnaming sigma alias) pb.mat } in
let used, sigma, j = compile sigma pb in
used, sigma, { uj_val =
if isRel sigma c || isVar sigma c || count_occurrences sigma (mkRel 1) j.uj_val <= 1 then
subst1 c j.uj_val
else
mkLetIn (make_annot na r,c,t,j.uj_val);
uj_type = subst1 c j.uj_type } in
let just_pop sigma =
let pb =
{ pb with
tomatch = rest;
history = pop_history_pattern pb.history;
mat = List.map drop_alias_eqn pb.mat } in
compile sigma pb
in
if not program_mode && (isRel sigma orig || isVar sigma orig) then
try
if initial then f orig (Retyping.get_type_of !!(pb.env) sigma orig)
else just_pop sigma
with e when precatchable_exception e ->
f expanded expanded_typ
else
try f expanded expanded_typ
with e when precatchable_exception e ->
if initial then f orig (Retyping.get_type_of !!(pb.env) sigma orig)
else just_pop sigma
and compile_non_dep_alias sigma pb rest =
let pb =
{ pb with
tomatch = rest;
history = pop_history_pattern pb.history;
mat = List.map drop_alias_eqn pb.mat } in
compile sigma pb
in
compile sigma pb
let matx_of_eqns env eqns =
let build_eqn i {CAst.loc;v=(ids,initial_lpat,initial_rhs)} =
let avoid = ids_of_named_context_val (named_context_val !!env) in
let avoid = List.fold_left (fun accu id -> Id.Set.add id accu) avoid ids in
let rhs =
{ rhs_env = env;
rhs_vars = free_glob_vars initial_rhs;
avoid_ids = avoid;
it = Some initial_rhs } in
{ patterns = initial_lpat;
alias_stack = [];
eqn_loc = loc;
orig = Some i;
catch_all_vars = [];
rhs = rhs }
in List.map_i build_eqn 0 eqns
let adjust_to_extended_env_and_remove_deps env extenv sigma subst t =
let n = Context.Rel.length (rel_context !!env) in
let n' = Context.Rel.length (rel_context !!extenv) in
let map (x, u) =
let (p, _, _) = lookup_rel_id x (rel_context !!extenv) in
let rec traverse_local_defs p =
match lookup_rel p !!extenv with
| LocalDef (_,c,_) -> assert (isRel sigma c); traverse_local_defs (p + destRel sigma c)
| LocalAssum _ -> p in
let p = traverse_local_defs p in
let u = lift (n' - n) u in
try Some (p, u, expand_vars_in_term !!extenv sigma u)
with Failure _ -> None in
let subst0 = List.map_filter map subst in
let t0 = lift (n' - n) t in
(subst0, t0)
let push_binder sigma d (k,env,subst) =
let hypnaming = RenameExistingBut (VarSet.variables (Global.env ())) in
(k+1,snd (push_rel ~hypnaming sigma d env),List.map (fun (na,u,d) -> (na,lift 1 u,d)) subst)
let rec list_assoc_in_triple x = function
[] -> raise Not_found
| (a, b, _)::l -> if Int.equal a x then b else list_assoc_in_triple x l
let abstract_tycon ?loc env sigma subst tycon extenv t =
let t = nf_betaiota !!env sigma t in
let src = match EConstr.kind sigma t with
| Evar (evk,_) -> (Loc.tag ?loc @@ Evar_kinds.SubEvar (None,evk))
| _ -> (Loc.tag ?loc @@ Evar_kinds.CasesType true) in
let subst0,t0 = adjust_to_extended_env_and_remove_deps env extenv sigma subst t in
let evdref = ref sigma in
let rec aux (k,env,subst as x) t =
let sigma = !evdref in
match EConstr.kind sigma t with
| Rel n when is_local_def (lookup_rel n !!env) -> t
| Evar ev ->
let ty = get_type_of !!env sigma t in
let sigma, ty = refresh_universes (Some false) !!env sigma ty in
let inst =
List.map_i
(fun i _ ->
try list_assoc_in_triple i subst0 with Not_found -> mkRel i)
1 (rel_context !!env) in
let sigma, ev' = Evarutil.new_evar ~src ~typeclass_candidate:false !!env sigma ty in
begin
let flags = (default_flags_of TransparentState.full) in
match solve_simple_eqn evar_unify flags !!env sigma (None,ev,substl inst ev') with
| Success evd -> evdref := evd
| UnifFailure _ -> evdref := add_conv_pb (Conversion.CONV,!!env,substl inst ev',t) sigma
end;
ev'
| _ ->
let good = List.filter (fun (_,u,_) -> is_conv_leq !!env sigma t u) subst in
match good with
| [] ->
map_constr_with_full_binders !!env sigma (push_binder sigma) aux x t
| (_, _, u) :: _ ->
let vl = List.map pi1 good in
let ty =
let ty = get_type_of !!env sigma t in
let sigma, res = refresh_universes (Some false) !!env !evdref ty in
evdref := sigma; res
in
let dummy_subst = List.init k (fun _ -> mkProp) in
let ty = substl dummy_subst (aux x ty) in
let sigma = !evdref in
let depvl = free_rels sigma ty in
let inst =
List.map_i
(fun i _ -> if Int.List.mem i vl then u else mkRel i) 1
(rel_context !!extenv) in
let map a = match EConstr.kind sigma a with
| Rel n -> not (noccurn sigma n u) || Int.Set.mem n depvl
| _ -> true
in
let rel_filter = List.map map inst in
let named_filter =
List.map (fun d -> local_occur_var sigma (NamedDecl.get_id d) u)
(named_context !!extenv) in
let filter = Filter.make (rel_filter @ named_filter) in
let candidates = List.rev (u :: List.map mkRel vl) in
let sigma, ev = Evarutil.new_evar !!extenv ~src ~filter ~candidates ~typeclass_candidate:false sigma ty in
let () = evdref := sigma in
lift k ev
in
let ans = aux (0,extenv,subst0) t0 in
!evdref, ans
let build_tycon ?loc env tycon_env s subst tycon extenv sigma t =
let s = mkSort s in
match t with
| None ->
let n = Context.Rel.length (rel_context !!env) in
let n' = Context.Rel.length (rel_context !!tycon_env) in
let src = Loc.tag ?loc Evar_kinds.ImpossibleCase in
let sigma, impossible_case_type =
Evarutil.new_evar (reset_context !!env) sigma ~src ~typeclass_candidate:false s in
(sigma, { uj_val = lift (n'-n) impossible_case_type; uj_type = s })
| Some t ->
let sigma, t = abstract_tycon ?loc tycon_env sigma subst tycon extenv t in
let sigma, tt = Typing.type_of !!extenv sigma t in
match unify_leq_delay !!env sigma tt s with
| exception Evarconv.UnableToUnify _ -> anomaly (Pp.str "Build_tycon: should be a type.");
| sigma -> (sigma, { uj_val = t; uj_type = tt })
let build_inversion_problem ~program_mode loc env sigma tms t =
let hypnaming = RenameExistingBut (VarSet.variables (Global.env ())) in
let make_patvar t (subst,avoid) =
let id = next_name_away (named_hd !!env sigma t Anonymous) avoid in
DAst.make @@ PatVar (Name id), ((id,t)::subst, Id.Set.add id avoid) in
let rec reveal_pattern t (subst,avoid as acc) =
match EConstr.kind sigma (whd_all !!env sigma t) with
| Construct (cstr,u) -> DAst.make (PatCstr (cstr,[],Anonymous)), acc
| App (f,v) when isConstruct sigma f ->
let cstr,u = destConstruct sigma f in
let n = constructor_nrealargs !!env cstr in
let l = List.lastn n (Array.to_list v) in
let l,acc = List.fold_right_map reveal_pattern l acc in
DAst.make (PatCstr (cstr,l,Anonymous)), acc
| _ -> make_patvar t acc in
let rec aux n env acc_sign tms acc =
match tms with
| [] -> [], acc_sign, acc
| (t, IsInd (_,IndType(indf,realargs),_)) :: tms ->
let patl,acc = List.fold_right_map reveal_pattern realargs acc in
let pat,acc = make_patvar t acc in
let indf' = lift_inductive_family n indf in
let sign = make_arity_signature !!env sigma true indf' in
let patl = pat :: List.rev patl in
let patl,sign = recover_and_adjust_alias_names acc patl sign in
let p = List.length patl in
let _,env' = push_rel_context ~hypnaming sigma sign env in
let patl',acc_sign,acc = aux (n+p) env' (sign@acc_sign) tms acc in
List.rev_append patl patl',acc_sign,acc
| (t, NotInd (bo,typ)) :: tms ->
let pat,acc = make_patvar t acc in
let typ = lift n typ in
let d = LocalAssum (annotR (alias_of_pat pat),typ) in
let patl,acc_sign,acc = aux (n+1) (snd (push_rel ~hypnaming sigma d env)) (d::acc_sign) tms acc in
pat::patl,acc_sign,acc in
let avoid0 = GlobEnv.vars_of_env env in
let patl,sign,(subst,avoid) = aux 0 env [] tms ([],avoid0) in
let n = List.length sign in
let decls =
List.map_i (fun i d -> (mkRel i, map_constr (lift i) d)) 1 sign in
let _,pb_env = push_rel_context ~hypnaming sigma sign env in
let decls =
List.map (fun (c,d) -> (c,extract_inductive_data !!(pb_env) sigma d,d)) decls in
let decls = List.rev decls in
let dep_sign = find_dependencies_signature sigma (List.make n true) decls in
let sub_tms =
List.map2 (fun deps (tm, (tmtyp,_), decl) ->
let na = if List.is_empty deps then Anonymous else force_name (RelDecl.get_name decl) in
Pushed (true,((tm,tmtyp),deps,na)))
dep_sign decls in
let subst = List.map (fun (na,t) -> (na,lift n t)) subst in
let main_eqn =
{ patterns = patl;
alias_stack = [];
eqn_loc = None;
orig = None;
catch_all_vars = [];
rhs = { rhs_env = pb_env;
rhs_vars = List.fold_left (fun accu (id, _) -> Id.Set.add id accu) Id.Set.empty subst;
avoid_ids = avoid;
it = Some (lift n t) } } in
let catch_all_eqn =
if List.for_all (irrefutable !!env) patl then
[]
else
[ { patterns = List.map (fun _ -> DAst.make @@ PatVar Anonymous) patl;
alias_stack = [];
eqn_loc = None;
orig = None;
catch_all_vars = [];
rhs = { rhs_env = pb_env;
rhs_vars = Id.Set.empty;
avoid_ids = avoid0;
it = None } } ] in
let s = Retyping.get_sort_of !!env sigma t in
let sigma, s = Sorts.(match ESorts.kind sigma s with
| SProp | Prop | Set ->
sigma, s
| Type _ | QSort _ ->
let sigma, s' = Evd.new_sort_variable univ_flexible sigma in
let sigma = Evd.set_leq_sort !!env sigma s s' in
sigma, s') in
let pb =
{ env = pb_env;
pred = mkSort s;
tomatch = sub_tms;
history = start_history n;
mat = main_eqn :: catch_all_eqn;
caseloc = loc;
casestyle = RegularStyle;
typing_function = build_tycon ?loc env pb_env s subst} in
let _used, sigma, j = compile ~program_mode sigma pb in
(sigma, j.uj_val)
let build_initial_predicate arsign pred =
let rec buildrec pred tmnames = function
| [] -> List.rev tmnames,pred
| (decl::realdecls)::lnames ->
let na = RelDecl.get_name decl in
let realnames = List.map RelDecl.get_name realdecls in
buildrec pred ((force_name na,realnames)::tmnames) lnames
| _ -> assert false
in buildrec pred [] (List.rev arsign)
let ?(dolift=true) env0 tomatchl tmsign =
let lift = if dolift then lift else fun n t -> t in
let get_one_sign n tm (na,t) =
match tm with
| NotInd (bo,typ) ->
(match t with
| None ->
let r = ERelevance.relevant in
let sign = match bo with
| None -> [LocalAssum (make_annot na r, lift n typ)]
| Some b -> [LocalDef (make_annot na r, lift n b, lift n typ)] in sign
| Some {CAst.loc} ->
user_err ?loc
(str"Unexpected type annotation for a term of non inductive type."))
| IsInd (term,IndType(indf,realargs),_) ->
let indf' = if dolift then lift_inductive_family n indf else indf in
let ((ind,_ as indu),_) = dest_ind_family indf' in
let nrealargs_ctxt = inductive_nrealdecls env0 ind in
let arsign = get_arity env0 indf' in
let realnal =
match t with
| Some {CAst.loc;v=(ind',realnal)} ->
if not (QInd.equal env0 ind ind') then
user_err ?loc (str "Wrong inductive type.");
if not (Int.equal nrealargs_ctxt (List.length realnal)) then
anomaly (Pp.str "Ill-formed 'in' clause in cases.");
List.rev realnal
| None ->
List.make nrealargs_ctxt Anonymous in
let r = Inductiveops.relevance_of_inductive env0 indu in
let t = build_dependent_inductive env0 indf' in
LocalAssum (make_annot na r, t) :: List.map2 RelDecl.set_name realnal arsign in
let rec buildrec n = function
| [],[] -> []
| (_,tm)::ltm, (_,x)::tmsign ->
let l = get_one_sign n tm x in
l :: buildrec (n + List.length l) (ltm,tmsign)
| _ -> assert false
in List.rev (buildrec 0 (tomatchl,tmsign))
let inh_conv_coerce_to_tycon ?loc ~program_mode env sigma j tycon =
match tycon with
| Some p ->
let (evd,v,_trace) =
Coercion.inh_conv_coerce_to ?loc ~program_mode ~resolve_tc:true env sigma
~flags:(default_flags_of TransparentState.full) j p
in
(evd,v)
| None -> sigma, j
let add_subst sigma c len (rel_subst,var_subst) =
match EConstr.kind sigma c with
| Rel n -> (n,len) :: rel_subst, var_subst
| Var id -> rel_subst, (id,len) :: var_subst
| _ -> assert false
let dependent_rel_or_var sigma tm c =
match EConstr.kind sigma tm with
| Rel n -> not (noccurn sigma n c)
| Var id -> Termops.local_occur_var sigma id c
| _ -> assert false
let prepare_predicate_from_arsign_tycon ~program_mode env sigma loc tomatchs arsign c =
let nar = List.fold_left (fun n sign -> Context.Rel.nhyps sign + n) 0 arsign in
let (rel_subst,var_subst), len =
List.fold_right2 (fun (tm, tmtype) sign (subst, len) ->
let signlen = Context.Rel.nhyps sign in
match EConstr.kind sigma tm with
| Rel _ | Var _ when Int.equal signlen 1 && dependent_rel_or_var sigma tm c
->
(add_subst sigma tm len subst, len - signlen)
| Rel _ | Var _ when signlen > 1 ->
(match tmtype with
NotInd _ -> (subst, len - signlen)
| IsInd (_, IndType(indf,realargs),_) ->
let subst, len =
List.fold_left
(fun (subst, len) arg ->
match EConstr.kind sigma arg with
| Rel _ | Var _ when dependent_rel_or_var sigma arg c ->
(add_subst sigma arg len subst, pred len)
| _ -> (subst, pred len))
(subst, len) realargs
in
let subst =
if dependent_rel_or_var sigma tm c && List.for_all (fun c -> isRel sigma c || isVar sigma c) realargs
then add_subst sigma tm len subst else subst
in (subst, pred len))
| _ -> (subst, len - signlen))
(List.rev tomatchs) arsign (([],[]), nar)
in
let rec predicate lift c =
match EConstr.kind sigma c with
| Rel n when n > lift ->
(try
let idx = Int.List.assoc (n - lift) rel_subst in
mkRel (idx + lift)
with Not_found ->
mkRel (n + nar))
| Var id ->
(try
let idx = Id.List.assoc id var_subst in
mkRel (idx + lift)
with Not_found ->
c)
| _ ->
EConstr.map_with_binders sigma succ predicate lift c
in
assert (len == 0);
let p = predicate 0 c in
let vars = VarSet.variables (Global.env ()) in
let hypnaming = if program_mode then ProgramNaming vars else RenameExistingBut vars in
let arsign,env' = List.fold_right_map (push_rel_context ~hypnaming sigma) arsign env in
try let sigma' = fst (Typing.type_of !!env' sigma p) in
Some (sigma', p, arsign)
with e when precatchable_exception e -> None
let expected_elimination_sorts env sigma tomatchl =
List.map_filter (fun (_,tm) -> match tm with
| NotInd _ -> None
| IsInd (_,IndType(indf,_),_) ->
let (ind, u), _ = dest_ind_family indf in
Inductiveops.is_squashed sigma (Inductive.lookup_mind_specif env ind, u))
tomatchl
let prepare_predicate ?loc ~program_mode typing_fun env sigma tomatchs arsign tycon pred =
let refresh_tycon sigma t =
refresh_universes ~status:Evd.univ_flexible ~onlyalg:true (Some true)
!!env sigma t
in
let preds =
match pred with
| None ->
let sigma,t =
match tycon with
| Some t -> refresh_tycon sigma t
| None ->
let src = (loc, Evar_kinds.CasesType false) in
let sigma, (t, _) = Evarutil.new_type_evar !!env sigma univ_flexible ~src in
sigma, t in
let sigma1,pred1 = build_inversion_problem loc ~program_mode env sigma tomatchs t in
let p2 =
prepare_predicate_from_arsign_tycon ~program_mode env sigma loc tomatchs arsign t in
let pred3 = lift (List.length (List.flatten arsign)) t in
(match p2 with
| Some (sigma2,pred2,arsign) when not (EConstr.eq_constr sigma pred2 pred3) ->
[sigma1, pred1, arsign; sigma2, pred2, arsign; sigma, pred3, arsign]
| _ ->
[sigma1, pred1, arsign; sigma, pred3, arsign])
| Some rtntyp ->
let hypnaming = RenameExistingBut (VarSet.variables (Global.env ())) in
let building_arsign,envar = List.fold_right_map (push_rel_context ~hypnaming sigma) arsign env in
let sigma, rtnsort = Evd.new_sort_variable univ_flexible sigma in
let sigma, predcclj = typing_fun (Some (mkSort rtnsort)) envar sigma rtntyp in
let check_elim_sort sigma squash =
try Inductiveops.squash_elim_sort !!env sigma squash rtnsort
with UGraph.UniverseInconsistency _ ->
sigma
in
let sigma = List.fold_left check_elim_sort sigma
(expected_elimination_sorts !!env sigma tomatchs)
in
let predccl = nf_evar sigma predcclj.uj_val in
[sigma, predccl, building_arsign]
in
List.map
(fun (sigma,pred,arsign) ->
let (nal,pred) = build_initial_predicate arsign pred in
sigma,nal,pred)
preds
(** Program cases *)
open Program
let ($) f x = f x
let string_of_name name =
match name with
| Anonymous -> "anonymous"
| Name n -> Id.to_string n
let make_prime_id name =
let str = string_of_name name in
Id.of_string str, Id.of_string (str ^ "'")
let prime avoid name =
let previd, id = make_prime_id name in
previd, next_ident_away id avoid
let make_prime avoid prevname =
let previd, id = prime !avoid prevname in
avoid := Id.Set.add id !avoid;
previd, id
let eq_id avoid id =
let hid = Id.of_string ("Heq_" ^ Id.to_string id) in
let hid' = next_ident_away hid avoid in
hid'
let mk_eq env sigma typ x y = papp env sigma coq_eq_ind [| typ; x ; y |]
let mk_eq_refl env sigma typ x = papp env sigma coq_eq_refl [| typ; x |]
let mk_JMeq env sigma typ x typ' y =
papp env sigma coq_JMeq_ind [| typ; x ; typ'; y |]
let mk_JMeq_refl env sigma typ x =
papp env sigma coq_JMeq_refl [| typ; x |]
let hole na = DAst.make @@
GHole (GQuestionMark {
Evar_kinds.qm_obligation= Evar_kinds.Define false;
Evar_kinds.qm_name=na;
Evar_kinds.qm_record_field=None})
let constr_of_pat env sigma arsign pat avoid =
let rec typ env sigma (ty, realargs) pat avoid =
let loc = pat.CAst.loc in
match DAst.get pat with
| PatVar name ->
let name, avoid = match name with
Name n -> name, avoid
| Anonymous ->
let id = next_ident_away wildcard_id avoid in
Name id, Id.Set.add id avoid
in
let realargs = List.map (map_name (fun _ -> Anonymous)) realargs in
let r = ERelevance.relevant in
(sigma, (DAst.make ?loc @@ PatVar name), [LocalAssum (make_annot name r, ty)] @ realargs, mkRel 1, lift 1 ty,
rel_list 1 (List.length realargs), 1, avoid)
| PatCstr (((_, i) as cstr),patargs,alias) ->
let cind = inductive_of_constructor cstr in
let IndType (indf, _) =
try find_rectype env sigma (lift (-(List.length realargs)) ty)
with Not_found -> error_case_not_inductive env sigma
{uj_val = ty; uj_type = Retyping.get_type_of env sigma ty}
in
let (ind,u), params = dest_ind_family indf in
if not (QInd.equal env ind cind) then error_bad_constructor ?loc env cstr ind;
let cstrs = get_constructors env indf in
let ci = cstrs.(i-1) in
let nb_args_constr = ci.cs_nargs in
assert (Int.equal nb_args_constr (List.length patargs));
let sigma, patargs, args, sign, env, n, m, avoid =
List.fold_right2
(fun decl pat (sigma, patargs, pats_c, sign, env, n, m, avoid) ->
let t = RelDecl.get_type decl in
let sigma, patarg', sign', pat_c', typ', argtypargs, n', avoid =
let liftt = liftn (List.length sign) (succ (List.length pats_c)) t in
typ env sigma (substl pats_c liftt, []) pat avoid
in
let pats_c = pat_c' :: List.map (lift n') pats_c in
let env' = EConstr.push_rel_context sign' env in
(sigma, patarg' :: patargs, pats_c, sign' @ sign, env', n' + n, succ m, avoid))
ci.cs_args (List.rev patargs) (sigma, [], [], [], env, 0, 0, avoid)
in
let args = List.rev args in
let patargs = List.rev patargs in
let pat' = DAst.make ?loc @@ PatCstr (cstr, patargs, alias) in
let cstr = mkConstructU ci.cs_cstr in
let app = applist (cstr, List.map (lift (List.length sign)) params) in
let app = applist (app, args) in
let apptype = Retyping.get_type_of env sigma app in
let IndType (indf, realargs) = find_rectype env sigma apptype in
match alias with
Anonymous ->
sigma, pat', sign, app, apptype, realargs, n, avoid
| Name id ->
let r = Inductiveops.relevance_of_inductive_family env indf in
let sign = LocalAssum (make_annot alias r, lift m ty) :: sign in
let avoid = Id.Set.add id avoid in
let sigma, sign, i, avoid =
try
let env = EConstr.push_rel_context sign env in
let sigma = unify_leq_delay (EConstr.push_rel_context sign env) sigma
(lift (succ m) ty) (lift 1 apptype) in
let sigma, eq_t = mk_eq env sigma (lift (succ m) ty)
(mkRel 1)
(lift 1 app)
in
let neq = eq_id avoid id in
sigma, LocalDef (nameR neq, mkRel 0, eq_t) :: sign, 2, Id.Set.add neq avoid
with Evarconv.UnableToUnify _ -> sigma, sign, 1, avoid
in
sigma, pat', sign, lift i app, lift i apptype, realargs, n + i, avoid
in
let sigma, pat', sign, patc, patty, args, z, avoid = typ env sigma (RelDecl.get_type (List.hd arsign), List.tl arsign) pat avoid in
sigma, pat', (sign, patc, (patty, args), pat'), avoid
let eq_id avoid id =
let hid = Id.of_string ("Heq_" ^ Id.to_string id) in
let hid' = next_ident_away hid !avoid in
avoid := Id.Set.add hid' !avoid;
hid'
let is_topvar sigma t =
match EConstr.kind sigma t with
| Rel 0 -> true
| _ -> false
let rels_of_patsign sigma =
List.map (fun decl ->
match decl with
| LocalDef (na,t',t) when is_topvar sigma t' -> LocalAssum (na,t)
| _ -> decl)
let vars_of_ctx sigma ctx =
let _, y =
List.fold_right (fun decl (prev, vars) ->
match decl with
| LocalDef (na,t',t) when is_topvar sigma t' ->
prev,
(DAst.make @@ GApp (
(DAst.make @@ GRef (delayed_force coq_eq_refl_ref, None)),
[hole na.binder_name; DAst.make @@ GVar prev])) :: vars
| _ ->
match RelDecl.get_name decl with
Anonymous -> prev, (DAst.make @@ GHole GInternalHole) :: vars
| Name n -> n, (DAst.make @@ GVar n) :: vars)
ctx (Id.of_string "vars_of_ctx_error", [])
in List.rev y
let rec is_included x y =
match DAst.get x, DAst.get y with
| PatVar _, _ -> true
| _, PatVar _ -> true
| PatCstr ((_, i), args, alias), PatCstr ((_, i'), args', alias') ->
if Int.equal i i' then List.for_all2 is_included args args'
else false
let build_ineqs env sigma prevpatterns curpats curpat_sign_len =
let sigma, ineqs =
List.fold_left
(fun (sigma, ineqs) ppats ->
let sigma, acc = List.fold_left2
(fun (sigma, acc) (ppat_sign, ppat_c, (ppat_ty, ppat_tyargs), ppat)
(curpat_sign, curpat_c, (curpat_ty, curpat_tyargs), curpat) ->
match acc with
None -> sigma, None
| Some (old_ppat_sign, old_ppats_len, old_eqs) ->
(try
if is_included curpat ppat then
let ppat_len = List.length ppat_sign in
let new_ppats_len = ppat_len + old_ppats_len in
let sigma, this_eq =
let ppat_ty = liftn (old_ppats_len + curpat_sign_len) (succ ppat_len) ppat_ty in
let ppat_c = liftn (old_ppats_len + curpat_sign_len) (succ ppat_len) ppat_c in
let cur_ty = lift new_ppats_len curpat_ty in
let cur_c = lift new_ppats_len curpat_c in
if Reductionops.is_conv env sigma cur_ty ppat_ty then
mk_eq env sigma
cur_ty
ppat_c
cur_c
else
let can_we_make_sense_of_JMeq = false in
if can_we_make_sense_of_JMeq then
mk_JMeq env sigma
ppat_ty
ppat_c
cur_ty
cur_c
else
raise Exit
in
let acc =
(
lift_rel_context old_ppats_len ppat_sign @ old_ppat_sign,
new_ppats_len,
this_eq :: List.map (lift ppat_len ) old_eqs)
in sigma, Some acc
else sigma, None
with Exit -> sigma, None))
(sigma, Some ([], 0, [])) ppats curpats
in match acc with
None -> sigma, ineqs
| Some (sign, len, eqs) ->
let sigma, conj = mk_coq_and env sigma eqs in
let sigma, neg = mk_coq_not env sigma conj in
let ineq = it_mkProd_or_LetIn neg (lift_rel_context curpat_sign_len sign) in
sigma, ineq :: ineqs)
(sigma, []) prevpatterns
in match ineqs with [] -> sigma, None
| _ -> let sigma, conj = mk_coq_and env sigma ineqs in sigma, Some conj
let constrs_of_pats typing_fun env sigma eqns tomatchs sign neqs arity =
let i = ref 0 in
let hypnaming = ProgramNaming (VarSet.variables (Global.env ())) in
let (sigma, x, y, z) =
List.fold_left
(fun (sigma, branches, eqns, prevpatterns) eqn ->
let sigma, _, newpatterns, pats =
List.fold_left2
(fun (sigma, idents, newpatterns, pats) pat arsign ->
let sigma, pat', cpat, idents = constr_of_pat !!env sigma arsign pat idents in
(sigma, idents, pat' :: newpatterns, cpat :: pats))
(sigma, Id.Set.empty, [], []) eqn.patterns (List.rev sign)
in
let newpatterns = List.rev newpatterns and opats = List.rev pats in
let rhs_rels, pats, signlen =
List.fold_left
(fun (renv, pats, n) (sign, pat_c, (ty, args), pat) ->
let sign' = lift_rel_context n sign in
let len = List.length sign' in
(sign' @ renv,
(sign', liftn n (succ len) pat_c,
(liftn n (succ len) ty, List.map (liftn n (succ len)) args), pat) :: pats,
len + n))
([], [], 0) opats in
let pats, _ = List.fold_left
(fun (pats, n) (sign, pat_c, (ty, args), pat) ->
let len = List.length sign in
((rels_of_patsign sigma sign, lift n pat_c,
(lift n ty, List.map (lift n) args), pat) :: pats, len + n))
([], 0) pats
in
let sigma, ineqs = build_ineqs !!env sigma prevpatterns pats signlen in
let rhs_rels' = rels_of_patsign sigma rhs_rels in
let arity =
let args, nargs =
List.fold_right (fun (sign, pat_c, (_, args), _) (allargs,n) ->
(args @ pat_c :: allargs, List.length args + succ n))
pats ([], 0)
in
let args = List.rev args in
substl args (liftn signlen (succ nargs) arity)
in
let r = ERelevance.relevant in
let rhs_rels', tycon =
let neqs_rels, arity =
match ineqs with
| None -> [], arity
| Some ineqs ->
[LocalAssum (make_annot Anonymous r, ineqs)], lift 1 arity
in
let eqs_rels, arity = decompose_prod_n_decls sigma neqs arity in
eqs_rels @ neqs_rels @ rhs_rels', arity
in
let _,rhs_env = push_rel_context ~hypnaming sigma rhs_rels' env in
let sigma, j = typing_fun (mk_tycon tycon) rhs_env sigma eqn.rhs.it in
let bbody = it_mkLambda_or_LetIn j.uj_val rhs_rels'
and btype = it_mkProd_or_LetIn j.uj_type rhs_rels' in
let sigma, _btype = Typing.type_of !!env sigma bbody in
let branch_name = Id.of_string ("program_branch_" ^ (string_of_int !i)) in
let branch_decl = LocalDef (make_annot (Name branch_name) r, lift !i bbody, lift !i btype) in
let branch =
let bref = DAst.make @@ GVar branch_name in
match vars_of_ctx sigma rhs_rels with
[] -> bref
| l -> DAst.make @@ GApp (bref, l)
in
let branch = match ineqs with
Some _ -> DAst.make @@ GApp (branch, [ hole Anonymous ])
| None -> branch
in
incr i;
let rhs = { eqn.rhs with it = Some branch } in
(sigma, branch_decl :: branches,
{ eqn with patterns = newpatterns; rhs = rhs } :: eqns,
opats :: prevpatterns))
(sigma, [], [], []) eqns
in
sigma, x, y
let lift_ctx n ctx =
let ctx', _ =
List.fold_right (fun (c, t) (ctx, n') ->
(liftn n n' c, liftn_tomatch_type n n' t) :: ctx, succ n')
ctx ([], 0)
in ctx'
let abstract_tomatch env sigma tomatchs tycon =
let prev, ctx, names, tycon =
List.fold_left
(fun (prev, ctx, names, tycon) (c, t) ->
let lenctx = List.length ctx in
match EConstr.kind sigma c with
Rel n -> (lift lenctx c, lift_tomatch_type lenctx t) :: prev, ctx, names, tycon
| _ ->
let tycon = Option.map
(fun t -> subst_term sigma (lift 1 c) (lift 1 t)) tycon in
let name = next_ident_away (Id.of_string "filtered_var") names in
let r = ERelevance.relevant in
(mkRel 1, lift_tomatch_type (succ lenctx) t) :: lift_ctx 1 prev,
LocalDef (make_annot (Name name) r, lift lenctx c, lift lenctx $ type_of_tomatch t) :: ctx,
Id.Set.add name names, tycon)
([], [], Id.Set.empty, tycon) tomatchs
in List.rev prev, ctx, tycon
let build_dependent_signature env sigma avoid tomatchs arsign =
let avoid = ref avoid in
let arsign = List.rev arsign in
let allnames = List.rev_map (List.map RelDecl.get_name) arsign in
let nar = List.fold_left (fun n names -> List.length names + n) 0 allnames in
let sigma, eqs, neqs, refls, slift, arsign' =
List.fold_left2
(fun (sigma, eqs, neqs, refls, slift, arsigns) (tm, ty) arsign ->
match ty with
| IsInd (ty, IndType (indf, args), _) when List.length args > 0 ->
let argsign = List.tl arsign in
let app_decl = List.hd arsign in
let argsign = List.rev argsign in
let sigma, env', nargeqs, argeqs, refl_args, slift, argsign' =
List.fold_left2
(fun (sigma, env, nargeqs, argeqs, refl_args, slift, argsign') arg decl ->
let name = RelDecl.get_name decl in
let t = liftn neqs (succ nargeqs) (RelDecl.get_type decl) in
let argt = Retyping.get_type_of env sigma arg in
assert (neqs + nargeqs + slift = nar);
let sigma, eq, refl_arg =
let t' = lift (nargeqs + slift) t in
let argt' = lift (nargeqs + nar) argt in
if Reductionops.is_conv env sigma argt' t' then
let sigma, eq =
mk_eq env sigma argt'
(mkRel (nargeqs + slift))
(lift (nargeqs + nar) arg)
in
let sigma, refl = mk_eq_refl env sigma argt arg in
sigma, eq, refl
else
let sigma, eq =
mk_JMeq env sigma
t'
(mkRel (nargeqs + slift))
argt'
(lift (nargeqs + nar) arg)
in
let sigma, refl = mk_JMeq_refl env sigma argt arg in
(sigma, eq, refl)
in
let previd, id =
let name =
match EConstr.kind sigma arg with
Rel n -> RelDecl.get_name (lookup_rel n env)
| _ -> name
in
make_prime avoid name
in
(sigma, env, succ nargeqs,
(LocalAssum (make_annot (Name (eq_id avoid previd)) ERelevance.relevant, eq)) :: argeqs,
refl_arg :: refl_args,
pred slift,
RelDecl.set_name (Name id) decl :: argsign'))
(sigma, env, 0, [], [], slift, []) args argsign
in
assert (neqs + nargeqs + slift = nar);
let appn = RelDecl.get_name app_decl in
let appt = liftn neqs (succ nargeqs) (RelDecl.get_type app_decl) in
let sigma, eq =
mk_JMeq env sigma
(lift (nargeqs + slift) appt)
(mkRel (nargeqs + slift))
(lift (nargeqs + nar) ty)
(lift (nargeqs + nar) tm)
in
let sigma, refl_eq = mk_JMeq_refl env sigma ty tm in
let previd, id = make_prime avoid appn in
(sigma, (LocalAssum (make_annot (Name (eq_id avoid previd)) ERelevance.relevant, eq) :: argeqs) :: eqs,
succ (nargeqs + neqs),
refl_eq :: refl_args @ refls,
pred slift,
((RelDecl.set_name (Name id) app_decl :: argsign') :: arsigns))
| _ ->
let decl = match arsign with [x] -> x | _ -> assert(false) in
let name = RelDecl.get_name decl in
let previd, id = make_prime avoid name in
let arsign' = RelDecl.set_name (Name id) decl in
let tomatch_ty = type_of_tomatch ty in
assert (neqs + slift = nar);
let sigma, eq =
mk_eq env sigma
(lift nar tomatch_ty)
(mkRel slift)
(lift nar tm)
in
let sigma, refl = mk_eq_refl env sigma tomatch_ty tm in
let na = make_annot (Name (eq_id avoid previd)) ERelevance.relevant in
(sigma,
[LocalAssum (na, eq)] :: eqs, succ neqs,
refl :: refls,
pred slift, (arsign' :: []) :: arsigns))
(sigma, [], 0, [], nar, []) tomatchs arsign
in
assert (Int.equal slift 0);
assert (neqs = nar);
sigma, arsign', nar, eqs, refls
let context_of_arsign l =
let (x, _) = List.fold_right
(fun ctx (prev_ctx, n) ->
(lift_rel_context n ctx @ prev_ctx, List.length ctx + n))
l ([], 0)
in x
let compile_program_cases ?loc style (typing_function, sigma) tycon env
(predopt, tomatchl, eqns) =
let hypnaming = ProgramNaming (VarSet.variables (Global.env ())) in
let typing_fun tycon env sigma = function
| Some t -> typing_function tycon env sigma t
| None -> coq_unit_judge !!env sigma in
let matx = matx_of_eqns env eqns in
let env, sigma, tomatchs = coerce_to_indtype ~program_mode:true typing_function env sigma matx tomatchl in
let tycon = valcon_of_tycon tycon in
let tomatchs, tomatchs_lets, tycon' = abstract_tomatch env sigma tomatchs tycon in
let _,env = push_rel_context ~hypnaming sigma tomatchs_lets env in
let len = List.length eqns in
let sigma, sign, signlen, eqs, args =
let arsign = extract_arity_signature ~dolift:false !!env tomatchs tomatchl in
let avoid = Id.Set.empty in
build_dependent_signature !!env sigma avoid tomatchs arsign
in
let sigma, tycon, arity =
let nar = List.fold_left (fun n sign -> List.length sign + n) 0 sign in
match tycon' with
| None ->
let sigma, ev = mkExistential !!env sigma in
sigma, ev, lift nar ev
| Some t ->
let sigma, pred =
match prepare_predicate_from_arsign_tycon ~program_mode:true env sigma loc tomatchs sign t with
| Some (evd, pred, arsign) -> evd, pred
| None -> sigma, lift nar t
in
sigma, lift (List.length tomatchs_lets) (Option.get tycon), pred
in
let neqs, arity =
let ctx = context_of_arsign eqs in
let neqs = List.length ctx in
neqs, it_mkProd_or_LetIn (lift neqs arity) ctx
in
let sigma, lets, matx =
constrs_of_pats typing_fun env sigma matx tomatchs sign neqs arity
in
let matx = List.rev matx in
let _ = assert (Int.equal len (List.length lets)) in
let _,env = push_rel_context ~hypnaming sigma lets env in
let matx = List.map (fun eqn -> { eqn with rhs = { eqn.rhs with rhs_env = env } }) matx in
let tomatchs = List.map (fun (x, y) -> lift len x, lift_tomatch_type len y) tomatchs in
let args = List.rev_map (lift len) args in
let pred = liftn len (succ signlen) arity in
let nal, pred = build_initial_predicate sign pred in
let out_tmt na = function NotInd (None,t) -> LocalAssum (make_annot na ERelevance.relevant,t)
| NotInd (Some b, t) -> LocalDef (make_annot na ERelevance.relevant,b,t)
| IsInd (typ,_,_) -> LocalAssum (make_annot na ERelevance.relevant,typ) in
let typs = List.map2 (fun (na,_) (tm,tmt) -> (tm,out_tmt na tmt)) nal tomatchs in
let typs =
List.map (fun (c,d) -> (c,extract_inductive_data !!env sigma d,d)) typs in
let dep_sign =
find_dependencies_signature sigma
(List.make (List.length typs) true)
typs in
let typs' =
List.map3
(fun (tm,tmt) deps (na,realnames) ->
let deps = if not (isRel sigma tm) then [] else deps in
let tmt = set_tomatch_realnames realnames tmt in
((tm,tmt),deps,na))
tomatchs dep_sign nal in
let initial_pushed = List.map (fun x -> Pushed (true,x)) typs' in
let typing_function tycon env sigma = function
| Some t -> typing_function tycon env sigma t
| None -> coq_unit_judge !!env sigma in
let pb =
{ env = env;
pred = pred;
tomatch = initial_pushed;
history = start_history (List.length initial_pushed);
mat = matx;
caseloc = loc;
casestyle= style;
typing_function = typing_function } in
let used, sigma, j = compile ~program_mode:true sigma pb in
check_unused_pattern !!env used matx;
let body = it_mkLambda_or_LetIn (applist (j.uj_val, args)) lets in
let tycon = it_mkProd_wo_LetIn tycon tomatchs_lets in
let j =
{ uj_val = it_mkLambda_or_LetIn body tomatchs_lets;
uj_type = Evarutil.nf_evar sigma tycon; }
in sigma, j
let compile_cases ?loc ~program_mode style (typing_fun, sigma) tycon env (predopt, tomatchl, eqns) =
if predopt == None && program_mode && Program.is_program_cases () then
compile_program_cases ?loc style (typing_fun, sigma)
tycon env (predopt, tomatchl, eqns)
else
let matx = matx_of_eqns env eqns in
let predenv, sigma, tomatchs = coerce_to_indtype ~program_mode typing_fun env sigma matx tomatchl in
let arsign = extract_arity_signature !!env tomatchs tomatchl in
let preds = prepare_predicate ?loc ~program_mode typing_fun predenv sigma tomatchs arsign tycon predopt in
let compile_for_one_predicate (sigma,nal,pred) =
let out_tmt na = function NotInd (None,t) -> LocalAssum (na,t)
| NotInd (Some b,t) -> LocalDef (na,b,t)
| IsInd (typ,_,_) -> LocalAssum (na,typ) in
let typs = List.map2 (fun (na,_) (tm,tmt) -> (tm,out_tmt (make_annot na ERelevance.relevant) tmt)) nal tomatchs in
let typs =
List.map (fun (c,d) -> (c,extract_inductive_data !!env sigma d,d)) typs in
let dep_sign =
find_dependencies_signature sigma
(List.make (List.length typs) true)
typs in
let typs' =
List.map3
(fun (tm,tmt) deps (na,realnames) ->
let deps = if not (isRel sigma tm) then [] else deps in
let tmt = set_tomatch_realnames realnames tmt in
((tm,tmt),deps,na))
tomatchs dep_sign nal in
let initial_pushed = List.map (fun x -> Pushed (true,x)) typs' in
let typing_fun tycon env sigma = function
| Some t -> typing_fun tycon env sigma t
| None -> coq_unit_judge !!env sigma in
let pb =
{ env = env;
pred = pred;
tomatch = initial_pushed;
history = start_history (List.length initial_pushed);
mat = matx;
caseloc = loc;
casestyle = style;
typing_function = typing_fun } in
let used, sigma, j = compile ~program_mode sigma pb in
let sigma, j = inh_conv_coerce_to_tycon ?loc ~program_mode !!env sigma j tycon in
used, sigma, j
in
let used, sigma, j = list_try_compile compile_for_one_predicate preds in
check_unused_pattern !!env used matx;
sigma, j