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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2019 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open Util
open Names
open Constr
open Context
open Termops
open Univ
open Environ
open EConstr
open Vars
open Context.Rel.Declaration
(** This module implements a call by name reduction used by the cbn tactic.
It has an ability to "refold" constants by storing constants and
their parameters in its stack.
*)
(** Machinery to custom the behavior of the reduction *)
module ReductionBehaviour = Reductionops.ReductionBehaviour
type volatile = { volatile : bool } [@@unboxed]
(** Machinery about stack of unfolded constants *)
module Cst_stack = struct
open EConstr
(** constant * params * args
- constant applied to params = term in head applied to args
- there is at most one arguments with an empty list of args, it must be the first.
- in args, the int represents the indice of the first arg to consider *)
type t = (constr * constr list * (int * constr array) list * volatile) list
let empty = []
let all_volatile = CList.for_all (fun (_,_,_,{volatile}) -> volatile)
let drop_useless = function
| _ :: ((_,_,[],_)::_ as q) -> q
| l -> l
let add_param h cst_l =
let append2cst = function
| (c,params,[],vol) -> (c, h::params, [], vol)
| (c,params,((i,t)::q),vol) when i = pred (Array.length t) ->
(c, params, q, vol)
| (c,params,(i,t)::q, vol) ->
(c, params, (succ i,t)::q, vol)
in
drop_useless (List.map append2cst cst_l)
let add_args cl =
List.map (fun (a,b,args,vol) -> (a,b,(0,cl)::args,vol))
let add_cst ?(volatile=false) cst = function
| (_,_,[],_) :: q as l -> l
| l -> (cst,[],[],{volatile})::l
let best_cst = function
| (cst,params,[],_)::_ -> Some(cst,params)
| _ -> None
let reference sigma t = match best_cst t with
| Some (c, params) when isConst sigma c -> Some (fst (destConst sigma c), params)
| _ -> None
(** [best_replace d cst_l c] makes the best replacement for [d]
by [cst_l] in [c] *)
let best_replace sigma d cst_l c =
let reconstruct_head = List.fold_left
(fun t (i,args) -> mkApp (t,Array.sub args i (Array.length args - i))) in
List.fold_right
(fun (cst,params,args,_) t -> Termops.replace_term sigma
(reconstruct_head d args)
(applist (cst, List.rev params))
t) cst_l c
let pr env sigma l =
let open Pp in
let p_c c = Termops.Internal.print_constr_env env sigma c in
prlist_with_sep pr_semicolon
(fun (c,params,args,{volatile}) ->
hov 1 (str"(" ++ p_c c ++ str ")" ++ spc () ++ pr_sequence p_c params ++ spc () ++ str "(args:" ++
pr_sequence (fun (i,el) -> prvect_with_sep spc p_c (Array.sub el i (Array.length el - i))) args ++
str ")" ++
(if volatile then str " (volatile)" else mt()))) l
end
(** The type of (machine) stacks (= lambda-bar-calculus' contexts) *)
module Stack :
sig
open EConstr
type 'a app_node
type cst_member =
| Cst_const of pconstant
| Cst_proj of Projection.t * Sorts.relevance
type 'a case_stk =
case_info * EInstance.t * 'a array * 'a pcase_return * 'a pcase_invert * 'a pcase_branch array
type 'a member =
| App of 'a app_node
| Case of 'a case_stk * Cst_stack.t
| Proj of Projection.t * Sorts.relevance * Cst_stack.t
| Fix of ('a, 'a) pfixpoint * 'a t * Cst_stack.t
| Primitive of CPrimitives.t * (Constant.t * EInstance.t) * 'a t * CPrimitives.args_red * Cst_stack.t
| Cst of { const : cst_member;
curr : int;
remains : int list;
params : 'a t;
volatile : bool;
cst_l : Cst_stack.t;
}
and 'a t = 'a member list
val pr : ('a -> Pp.t) -> 'a t -> Pp.t
val empty : 'a t
val append_app : 'a array -> 'a t -> 'a t
val decomp : 'a t -> ('a * 'a t) option
val equal : ('a -> 'a -> bool) -> (('a, 'a) pfixpoint -> ('a, 'a) pfixpoint -> bool)
-> ('a case_stk -> 'a case_stk -> bool) -> 'a t -> 'a t -> bool
val strip_app : 'a t -> 'a t * 'a t
val strip_n_app : int -> 'a t -> ('a t * 'a * 'a t) option
val will_expose_iota : 'a t -> bool
val list_of_app_stack : constr t -> constr list option
val args_size : 'a t -> int
val tail : int -> 'a t -> 'a t
val nth : 'a t -> int -> 'a
val best_state : Evd.evar_map -> constr * constr t -> Cst_stack.t -> constr * constr t
val zip : ?refold:bool -> Evd.evar_map -> constr * constr t -> constr
val check_native_args : CPrimitives.t -> 'a t -> bool
val get_next_primitive_args : CPrimitives.args_red -> 'a t -> CPrimitives.args_red * ('a t * 'a * 'a t) option
end =
struct
open EConstr
type 'a app_node = int * 'a array * int
(* first releavnt position, arguments, last relevant position *)
(*
Invariant that this module must ensure :
(behare of direct access to app_node by the rest of Reductionops)
- in app_node (i,_,j) i <= j
- There is no array realocation (outside of debug printing)
*)
let pr_app_node pr (i,a,j) =
let open Pp in surround (
prvect_with_sep pr_comma pr (Array.sub a i (j - i + 1))
)
type cst_member =
| Cst_const of pconstant
| Cst_proj of Projection.t * Sorts.relevance
type 'a case_stk =
case_info * EInstance.t * 'a array * 'a pcase_return * 'a pcase_invert * 'a pcase_branch array
type 'a member =
| App of 'a app_node
| Case of 'a case_stk * Cst_stack.t
| Proj of Projection.t * Sorts.relevance * Cst_stack.t
| Fix of ('a, 'a) pfixpoint * 'a t * Cst_stack.t
| Primitive of CPrimitives.t * (Constant.t * EInstance.t) * 'a t * CPrimitives.args_red * Cst_stack.t
| Cst of { const : cst_member;
curr : int;
remains : int list;
params : 'a t;
volatile : bool;
cst_l : Cst_stack.t;
}
and 'a t = 'a member list
(* Debugging printer *)
let rec pr_member pr_c member =
let open Pp in
let pr_c x = hov 1 (pr_c x) in
match member with
| App app -> str "ZApp" ++ pr_app_node pr_c app
| Case ((_,_,_,_,_,br),cst) ->
str "ZCase(" ++
prvect_with_sep (pr_bar) (fun (_, b) -> pr_c b) br
++ str ")"
| Proj (p,_,cst) ->
str "ZProj(" ++ Projection.debug_print p ++ str ")"
| Fix (f,args,cst) ->
str "ZFix(" ++ Constr.debug_print_fix pr_c f
++ pr_comma () ++ pr pr_c args ++ str ")"
| Primitive (p,c,args,kargs,cst_l) ->
str "ZPrimitive(" ++ str (CPrimitives.to_string p)
++ pr_comma () ++ pr pr_c args ++ str ")"
| Cst {const=mem;curr;remains;params;cst_l} ->
str "ZCst(" ++ pr_cst_member pr_c mem ++ pr_comma () ++ int curr
++ pr_comma () ++
prlist_with_sep pr_semicolon int remains ++
pr_comma () ++ pr pr_c params ++ str ")"
and pr pr_c l =
let open Pp in
prlist_with_sep pr_semicolon (fun x -> hov 1 (pr_member pr_c x)) l
and pr_cst_member pr_c c =
let open Pp in
match c with
| Cst_const (c, u) ->
if UVars.Instance.is_empty u then Constant.debug_print c
else str"(" ++ Constant.debug_print c ++ str ", " ++
UVars.Instance.pr Sorts.QVar.raw_pr Univ.Level.raw_pr u ++ str")"
| Cst_proj (p,r) ->
str".(" ++ Projection.debug_print p ++ str")"
let empty = []
let append_app v s =
let le = Array.length v in
if Int.equal le 0 then s else App (0,v,pred le) :: s
let decomp_node (i,l,j) sk =
if i < j then (l.(i), App (succ i,l,j) :: sk)
else (l.(i), sk)
let decomp = function
| App node::s -> Some (decomp_node node s)
| _ -> None
let decomp_node_last (i,l,j) sk =
if i < j then (l.(j), App (i,l,pred j) :: sk)
else (l.(j), sk)
let equal f f_fix f_case sk1 sk2 =
let equal_cst_member x y =
match x, y with
| Cst_const (c1,u1), Cst_const (c2, u2) ->
Constant.CanOrd.equal c1 c2 && UVars.Instance.equal u1 u2
| Cst_proj (p1,_), Cst_proj (p2,_) -> Projection.Repr.CanOrd.equal (Projection.repr p1) (Projection.repr p2)
| _, _ -> false
in
let rec equal_rec sk1 sk2 =
match sk1,sk2 with
| [],[] -> true
| App a1 :: s1, App a2 :: s2 ->
let t1,s1' = decomp_node_last a1 s1 in
let t2,s2' = decomp_node_last a2 s2 in
(f t1 t2) && (equal_rec s1' s2')
| Case ((ci1,pms1,p1,t1,iv1,a1),_) :: s1, Case ((ci2,pms2,p2,iv2,t2,a2),_) :: s2 ->
f_case (ci1,pms1,p1,t1,iv1,a1) (ci2,pms2,p2,iv2,t2,a2) && equal_rec s1 s2
| (Proj (p,_,_)::s1, Proj(p2,_,_)::s2) ->
Projection.Repr.CanOrd.equal (Projection.repr p) (Projection.repr p2)
&& equal_rec s1 s2
| Fix (f1,s1,_) :: s1', Fix (f2,s2,_) :: s2' ->
f_fix f1 f2
&& equal_rec (List.rev s1) (List.rev s2)
&& equal_rec s1' s2'
| Cst c1::s1', Cst c2::s2' ->
equal_cst_member c1.const c2.const
&& equal_rec (List.rev c1.params) (List.rev c2.params)
&& equal_rec s1' s2'
| ((App _|Case _|Proj _|Fix _|Cst _|Primitive _)::_|[]), _ -> false
in equal_rec (List.rev sk1) (List.rev sk2)
let append_app_list l s =
let a = Array.of_list l in
append_app a s
let rec args_size = function
| App (i,_,j)::s -> j + 1 - i + args_size s
| (Case _|Fix _|Proj _|Cst _|Primitive _)::_ | [] -> 0
let strip_app s =
let rec aux out = function
| ( App _ as e) :: s -> aux (e :: out) s
| s -> List.rev out,s
in aux [] s
let strip_n_app n s =
let rec aux n out = function
| App (i,a,j) as e :: s ->
let nb = j - i + 1 in
if n >= nb then
aux (n - nb) (e::out) s
else
let p = i+n in
Some (CList.rev
(if Int.equal n 0 then out else App (i,a,p-1) :: out),
a.(p),
if j > p then App(succ p,a,j)::s else s)
| s -> None
in aux n [] s
let will_expose_iota args =
List.exists
(function (Fix (_,_,l) | Case (_,l) |
Proj (_,_,l) | Cst {cst_l=l}) when Cst_stack.all_volatile l -> true | _ -> false)
args
let list_of_app_stack s =
let rec aux = function
| App (i,a,j) :: s ->
let (args',s') = aux s in
let a' = Array.sub a i (j - i + 1) in
(Array.fold_right (fun x y -> x::y) a' args', s')
| s -> ([],s) in
let (out,s') = aux s in
let init = match s' with [] -> true | _ -> false in
Option.init init out
let tail n0 s0 =
let rec aux n s =
if Int.equal n 0 then s else
match s with
| App (i,a,j) :: s ->
let nb = j - i + 1 in
if n >= nb then
aux (n - nb) s
else
let p = i+n in
if j >= p then App(p,a,j)::s else s
| _ -> raise (Invalid_argument "Reductionops.Stack.tail")
in aux n0 s0
let nth s p =
match strip_n_app p s with
| Some (_,el,_) -> el
| None -> raise Not_found
(** This function breaks the abstraction of Cst_stack ! *)
let best_state sigma (_,sk as s) l =
let rec aux sk def = function
|(_,_,_,{volatile=true}) -> def
|(cst, params, [], _) -> (cst, append_app_list (List.rev params) sk)
|(cst, params, (i,t)::q, vol) -> match decomp sk with
| Some (el,sk') when EConstr.eq_constr sigma el t.(i) ->
if i = pred (Array.length t)
then aux sk' def (cst, params, q, vol)
else aux sk' def (cst, params, (succ i,t)::q, vol)
| _ -> def
in List.fold_left (aux sk) s l
let constr_of_cst_member f sk =
match f with
| Cst_const (c, u) -> mkConstU (c, EInstance.make u), sk
| Cst_proj (p,r) ->
match decomp sk with
| Some (hd, sk) -> mkProj (p, r, hd), sk
| None -> assert false
let zip ?(refold=false) sigma s =
let rec zip = function
| f, [] -> f
| f, (App (i,a,j) :: s) ->
let a' = if Int.equal i 0 && Int.equal j (Array.length a - 1)
then a
else Array.sub a i (j - i + 1) in
zip (mkApp (f, a'), s)
| f, (Case ((ci,u,pms,rt,iv,br),cst_l)::s) when refold ->
zip (best_state sigma (mkCase (ci,u,pms,rt,iv,f,br), s) cst_l)
| f, (Case ((ci,u,pms,rt,iv,br),_)::s) -> zip (mkCase (ci,u,pms,rt,iv,f,br), s)
| f, (Fix (fix,st,cst_l)::s) when refold ->
zip (best_state sigma (mkFix fix, st @ (append_app [|f|] s)) cst_l)
| f, (Fix (fix,st,_)::s) -> zip
(mkFix fix, st @ (append_app [|f|] s))
| f, (Cst {const;params;cst_l}::s) when refold ->
zip (best_state sigma (constr_of_cst_member const (params @ (append_app [|f|] s))) cst_l)
| f, (Cst {const;params}::s) ->
zip (constr_of_cst_member const (params @ (append_app [|f|] s)))
| f, (Proj (p,r,cst_l)::s) when refold ->
zip (best_state sigma (mkProj (p,r,f),s) cst_l)
| f, (Proj (p,r,_)::s) -> zip (mkProj (p,r,f),s)
| f, (Primitive (p,c,args,kargs,cst_l)::s) ->
zip (mkConstU c, args @ append_app [|f|] s)
in
zip s
(* Check if there is enough arguments on [stk] w.r.t. arity of [op] *)
let check_native_args op stk =
let nargs = CPrimitives.arity op in
let rargs = args_size stk in
nargs <= rargs
let get_next_primitive_args kargs stk =
let rec nargs = function
| [] -> 0
| CPrimitives.Kwhnf :: _ -> 0
| _ :: s -> 1 + nargs s
in
let n = nargs kargs in
(List.skipn (n+1) kargs, strip_n_app n stk)
end
(** The type of (machine) states (= lambda-bar-calculus' cuts) *)
(*************************************)
(*** Reduction Functions Operators ***)
(*************************************)
let safe_meta_value sigma ev =
try Some (Evd.meta_value sigma ev)
with Not_found -> None
(*************************************)
(*** Reduction using bindingss ***)
(*************************************)
(* Beta Reduction tools *)
let apply_subst env sigma cst_l t stack =
let rec aux env cst_l t stack =
match (Stack.decomp stack, EConstr.kind sigma t) with
| Some (h,stacktl), Lambda (_,_,c) ->
let cst_l' = Cst_stack.add_param h cst_l in
aux (h::env) cst_l' c stacktl
| _ -> (cst_l, (substl env t, stack))
in
aux env cst_l t stack
(* Iota reduction tools *)
(** @return c if there is a constant c whose body is bd
@return bd else.
It has only a meaning because internal representation of "Fixpoint f x
:= t" is Definition f := fix f x => t
Even more fragile that we could hope because do Module M. Fixpoint
f x := t. End M. Definition f := u. and say goodbye to any hope
of refolding M.f this way ...
*)
let magically_constant_of_fixbody env sigma (reference, params) bd = function
| Name.Anonymous -> bd
| Name.Name id ->
let open UnivProblem in
let cst_mod = KerName.modpath (Constant.user reference) in
let cst = Constant.make2 cst_mod (Label.of_id id) in
if not (Environ.mem_constant cst env) then bd
else
let (cst, u), ctx = UnivGen.fresh_constant_instance env cst in
match constant_opt_value_in env (cst,u) with
| None -> bd
| Some t ->
let csts = EConstr.eq_constr_universes env sigma (Reductionops.beta_applist sigma (EConstr.of_constr t, params)) bd in
begin match csts with
| Some csts ->
let addqs l r (qs,us) = Sorts.QVar.Map.add l r qs, us in
let addus l r (qs,us) = qs, Univ.Level.Map.add l r us in
let subst = Set.fold (fun cst acc ->
match cst with
| QEq (a,b) | QLeq (a,b) ->
let a = match a with
| QVar q -> q
| _ -> assert false
in
addqs a b acc
| ULub (u, v) | UWeak (u, v) -> addus u v acc
| UEq (u, v) | ULe (u, v) ->
(* XXX add something when qsort? *)
let get u = match u with
| Sorts.SProp | Sorts.Prop -> assert false
| Sorts.Set -> Level.set
| Sorts.Type u | Sorts.QSort (_, u) -> Option.get (Universe.level u)
in
addus (get u) (get v) acc)
csts UVars.empty_sort_subst
in
let inst = UVars.subst_sort_level_instance subst u in
applist (mkConstU (cst, EInstance.make inst), params)
| None -> bd
end
let contract_cofix env sigma ?reference (bodynum,(names,types,bodies as typedbodies)) =
let nbodies = Array.length bodies in
let make_Fi j =
let ind = nbodies-j-1 in
if Int.equal bodynum ind then mkCoFix (ind,typedbodies)
else
let bd = mkCoFix (ind,typedbodies) in
match reference with
| None -> bd
| Some r -> magically_constant_of_fixbody env sigma r bd names.(ind).binder_name in
let closure = List.init nbodies make_Fi in
substl closure bodies.(bodynum)
(** Similar to the "fix" case below *)
let reduce_and_refold_cofix recfun env sigma cst_l cofix sk =
let raw_answer =
contract_cofix env sigma ?reference:(Cst_stack.reference sigma cst_l) cofix in
let (x, (t, sk')) = apply_subst [] sigma Cst_stack.empty raw_answer sk in
let t' = Cst_stack.best_replace sigma (mkCoFix cofix) cst_l t in
recfun x (t', sk')
(* contracts fix==FIX[nl;i](A1...Ak;[F1...Fk]{B1....Bk}) to produce
Bi[Fj --> FIX[nl;j](A1...Ak;[F1...Fk]{B1...Bk})] *)
let contract_fix env sigma ?reference ((recindices,bodynum),(names,types,bodies as typedbodies)) =
let nbodies = Array.length recindices in
let make_Fi j =
let ind = nbodies-j-1 in
if Int.equal bodynum ind then mkFix ((recindices,ind),typedbodies)
else
let bd = mkFix ((recindices,ind),typedbodies) in
match reference with
| None -> bd
| Some r -> magically_constant_of_fixbody env sigma r bd names.(ind).binder_name in
let closure = List.init nbodies make_Fi in
substl closure bodies.(bodynum)
(** First we substitute the Rel bodynum by the fixpoint and then we try to
replace the fixpoint by the best constant from [cst_l]
Other rels are directly substituted by constants "magically found from the
context" in contract_fix *)
let reduce_and_refold_fix recfun env sigma cst_l fix sk =
let raw_answer =
contract_fix env sigma ?reference:(Cst_stack.reference sigma cst_l) fix in
let (x, (t, sk')) = apply_subst [] sigma Cst_stack.empty raw_answer sk in
let t' = Cst_stack.best_replace sigma (mkFix fix) cst_l t in
recfun x (t', sk')
module CredNative = Reductionops.CredNative
(** Generic reduction function with environment
Here is where unfolded constant are stored in order to be
eventually refolded.
It uses ReductionBehaviour, prefers
refold constant instead of value and tries to infer constants
fix and cofix came from.
It substitutes fix and cofix by the constant they come from in
contract_* in any case .
*)
let debug_RAKAM = Reductionops.debug_RAKAM
let equal_stacks sigma (x, l) (y, l') =
let f_equal x y = eq_constr sigma x y in
let eq_fix a b = f_equal (mkFix a) (mkFix b) in
let eq_case (ci1, u1, pms1, (p1,_), _, br1) (ci2, u2, pms2, (p2,_), _, br2) =
Array.equal f_equal pms1 pms2 &&
f_equal (snd p1) (snd p2) &&
Array.equal (fun (_, c1) (_, c2) -> f_equal c1 c2) br1 br2
in
Stack.equal f_equal eq_fix eq_case l l' && f_equal x y
let apply_branch env sigma (ind, i) args (ci, u, pms, iv, r, lf) =
let args = Stack.tail ci.ci_npar args in
let args = Option.get (Stack.list_of_app_stack args) in
let br = lf.(i - 1) in
let subst =
if Int.equal ci.ci_cstr_nargs.(i - 1) ci.ci_cstr_ndecls.(i - 1) then
(* No let-bindings *)
List.rev args
else
let ctx = expand_branch env sigma u pms (ind, i) br in
subst_of_rel_context_instance_list ctx args
in
Vars.substl subst (snd br)
let whd_state_gen ?csts flags env sigma =
let open Context.Named.Declaration in
let open ReductionBehaviour in
let rec whrec cst_l (x, stack) =
let () = debug_RAKAM (fun () ->
let open Pp in
let pr c = Termops.Internal.print_constr_env env sigma c in
(h (str "<<" ++ pr x ++
str "|" ++ cut () ++ Cst_stack.pr env sigma cst_l ++
str "|" ++ cut () ++ Stack.pr pr stack ++
str ">>")))
in
let c0 = EConstr.kind sigma x in
let fold () =
let () = debug_RAKAM (fun () ->
Pp.(str "<><><><><>")) in
((EConstr.of_kind c0, stack),cst_l)
in
match c0 with
| Rel n when RedFlags.red_set flags RedFlags.fDELTA ->
(match lookup_rel n env with
| LocalDef (_,body,_) -> whrec Cst_stack.empty (lift n body, stack)
| _ -> fold ())
| Var id when RedFlags.red_set flags (RedFlags.fVAR id) ->
(match lookup_named id env with
| LocalDef (_,body,_) ->
whrec (Cst_stack.add_cst (mkVar id) cst_l) (body, stack)
| _ -> fold ())
| Evar ev -> fold ()
| Meta ev ->
(match safe_meta_value sigma ev with
| Some body -> whrec cst_l (body, stack)
| None -> fold ())
| Const (c,u as const) ->
Reductionops.reduction_effect_hook env sigma c
(lazy (EConstr.to_constr sigma (Stack.zip sigma (x,fst (Stack.strip_app stack)))));
if RedFlags.red_set flags (RedFlags.fCONST c) then
let u' = EInstance.kind sigma u in
match constant_value_in env (c, u') with
| body ->
begin
let body = EConstr.of_constr body in
(* Looks for ReductionBehaviour *)
match ReductionBehaviour.get c with
| None -> whrec (Cst_stack.add_cst (mkConstU const) cst_l) (body, stack)
| Some behavior ->
begin match behavior with
| NeverUnfold -> fold ()
| (UnfoldWhen { nargs = Some n } |
UnfoldWhenNoMatch { nargs = Some n } )
when Stack.args_size stack < n ->
fold ()
| UnfoldWhenNoMatch { recargs; nargs } -> (* maybe unfolds *)
let app_sk,sk = Stack.strip_app stack in
let volatile = Option.has_some nargs in
let (tm',sk'),cst_l' =
match recargs with
| [] ->
whrec (Cst_stack.add_cst ~volatile (mkConstU const) cst_l) (body, app_sk)
| curr :: remains -> match Stack.strip_n_app curr app_sk with
| None -> (x,app_sk), cst_l
| Some (bef,arg,app_sk') ->
let cst_l = Stack.Cst
{ const = Stack.Cst_const (fst const, u');
volatile;
curr; remains; params=bef; cst_l;
}
in
whrec Cst_stack.empty (arg,cst_l :: app_sk')
in
let rec is_case x = match EConstr.kind sigma x with
| Lambda (_,_, x) | LetIn (_,_,_, x) | Cast (x, _,_) -> is_case x
| App (hd, _) -> is_case hd
| Case _ -> true
| _ -> false in
if equal_stacks sigma (x, app_sk) (tm', sk')
|| Stack.will_expose_iota sk'
|| is_case tm'
then fold ()
else whrec cst_l' (tm', sk' @ sk)
| UnfoldWhen { recargs; nargs } -> (* maybe unfolds *)
begin match recargs with
| [] -> (* if nargs has been specified *)
(* CAUTION : the constant is NEVER refolded (even when it hides a (co)fix) *)
whrec cst_l (body, stack)
| curr :: remains -> match Stack.strip_n_app curr stack with
| None -> fold ()
| Some (bef,arg,s') ->
let cst_l = Stack.Cst
{ const = Stack.Cst_const (fst const, u');
volatile = Option.has_some nargs;
curr; remains; params=bef; cst_l;
}
in
whrec Cst_stack.empty (arg,cst_l::s')
end
end
end
| exception NotEvaluableConst (IsPrimitive (u,p)) when Stack.check_native_args p stack ->
let kargs = CPrimitives.kind p in
let (kargs,o) = Stack.get_next_primitive_args kargs stack in
(* Should not fail thanks to [check_native_args] *)
let (before,a,after) = Option.get o in
whrec Cst_stack.empty (a,Stack.Primitive(p,const,before,kargs,cst_l)::after)
| exception NotEvaluableConst _ -> fold ()
else fold ()
| Proj (p, r, c) when RedFlags.red_projection flags p ->
(let npars = Projection.npars p in
match ReductionBehaviour.get (Projection.constant p) with
| None ->
let stack' = (c, Stack.Proj (p, r, cst_l) :: stack) in
let stack'', csts = whrec Cst_stack.empty stack' in
if equal_stacks sigma stack' stack'' then fold ()
else stack'', csts
| Some behavior ->
begin match behavior with
| NeverUnfold -> fold ()
| (UnfoldWhen { nargs = Some n }
| UnfoldWhenNoMatch { nargs = Some n })
when Stack.args_size stack < n - (npars + 1) -> fold ()
| UnfoldWhen { recargs }
| UnfoldWhenNoMatch { recargs }-> (* maybe unfolds *)
let recargs = List.map_filter (fun x ->
let idx = x - npars in
if idx < 0 then None else Some idx) recargs
in
let volatile = match behavior with
| UnfoldWhen {nargs} -> Option.has_some nargs
| UnfoldWhenNoMatch _ | NeverUnfold -> false
in
match recargs with
| [] -> (* if nargs has been specified *)
(* CAUTION : the constant is NEVER refold
(even when it hides a (co)fix) *)
let stack' = (c, Stack.Proj (p, r, cst_l) :: stack) in
whrec Cst_stack.empty(* cst_l *) stack'
| curr :: remains ->
if curr == 0 then (* Try to reduce the record argument *)
let cst_l = Stack.Cst
{ const=Stack.Cst_proj (p,r);
volatile; curr; remains;
params=Stack.empty;
cst_l;
}
in
whrec Cst_stack.empty (c, cst_l::stack)
else
match Stack.strip_n_app curr stack with
| None -> fold ()
| Some (bef,arg,s') ->
let cst_l = Stack.Cst
{ const=Stack.Cst_proj (p,r);
curr;
remains;
volatile;
params=Stack.append_app [|c|] bef;
cst_l;
}
in
whrec Cst_stack.empty (arg,cst_l::s')
end)
| LetIn (_,b,_,c) when RedFlags.red_set flags RedFlags.fZETA ->
let (cst_l, p) = apply_subst [b] sigma cst_l c stack in
whrec cst_l p
| Cast (c,_,_) -> whrec cst_l (c, stack)
| App (f,cl) ->
whrec
(Cst_stack.add_args cl cst_l)
(f, Stack.append_app cl stack)
| Lambda (na,t,c) ->
(match Stack.decomp stack with
| Some _ when RedFlags.red_set flags RedFlags.fBETA ->
let (cst_l, p) = apply_subst [] sigma cst_l x stack in
whrec cst_l p
| _ -> fold ())
| Case (ci,u,pms,p,iv,d,lf) ->
whrec Cst_stack.empty (d, Stack.Case ((ci,u,pms,p,iv,lf),cst_l) :: stack)
| Fix ((ri,n),_ as f) ->
(match Stack.strip_n_app ri.(n) stack with
|None -> fold ()
|Some (bef,arg,s') ->
whrec Cst_stack.empty (arg, Stack.Fix(f,bef,cst_l)::s'))
| Construct (cstr ,u) ->
let use_match = RedFlags.red_set flags RedFlags.fMATCH in
let use_fix = RedFlags.red_set flags RedFlags.fFIX in
if use_match || use_fix then
match Stack.strip_app stack with
|args, (Stack.Case(case,_)::s') when use_match ->
let r = apply_branch env sigma cstr args case in
whrec Cst_stack.empty (r, s')
|args, (Stack.Proj (p,_,_)::s') when use_match ->
whrec Cst_stack.empty (Stack.nth args (Projection.npars p + Projection.arg p), s')
|args, (Stack.Fix (f,s',cst_l)::s'') when use_fix ->
let x' = Stack.zip sigma (x, args) in
let out_sk = s' @ (Stack.append_app [|x'|] s'') in
reduce_and_refold_fix whrec env sigma cst_l f out_sk
|args, (Stack.Cst {const;curr;remains;volatile;params=s';cst_l} :: s'') ->
let x' = Stack.zip sigma (x, args) in
begin match remains with
| [] ->
(match const with
| Stack.Cst_const const ->
(match constant_opt_value_in env const with
| None -> fold ()
| Some body ->
let const = (fst const, EInstance.make (snd const)) in
let body = EConstr.of_constr body in
let cst_l = Cst_stack.add_cst ~volatile (mkConstU const) cst_l in
whrec cst_l (body, s' @ (Stack.append_app [|x'|] s'')))
| Stack.Cst_proj (p,r) ->
let stack = s' @ (Stack.append_app [|x'|] s'') in
match Stack.strip_n_app 0 stack with
| None -> assert false
| Some (_,arg,s'') ->
whrec Cst_stack.empty (arg, Stack.Proj (p,r,cst_l) :: s''))
| next :: remains' -> match Stack.strip_n_app (next-curr-1) s'' with
| None -> fold ()
| Some (bef,arg,s''') ->
let cst_l = Stack.Cst
{ const;
curr=next;
volatile;
remains=remains';
params=s' @ (Stack.append_app [|x'|] bef);
cst_l;
}
in
whrec Cst_stack.empty (arg, cst_l :: s''')
end
|_, (Stack.App _)::_ -> assert false
|_, _ -> fold ()
else fold ()
| CoFix cofix ->
if RedFlags.red_set flags RedFlags.fCOFIX then
match Stack.strip_app stack with
|args, ((Stack.Case _ |Stack.Proj _)::s') ->
reduce_and_refold_cofix whrec env sigma cst_l cofix stack
|_ -> fold ()
else fold ()
| Int _ | Float _ | Array _ ->
begin match Stack.strip_app stack with
| (_, Stack.Primitive(p,(_,u as kn),rargs,kargs,cst_l')::s) ->
let more_to_reduce = List.exists (fun k -> CPrimitives.Kwhnf = k) kargs in
if more_to_reduce then
let (kargs,o) = Stack.get_next_primitive_args kargs s in
(* Should not fail because Primitive is put on the stack only if fully applied *)
let (before,a,after) = Option.get o in
whrec Cst_stack.empty (a,Stack.Primitive(p,kn,rargs @ Stack.append_app [|x|] before,kargs,cst_l')::after)
else
let n = List.length kargs in
let (args,s) = Stack.strip_app s in
let (args,extra_args) =
try List.chop n args
with List.IndexOutOfRange -> (args,[]) (* FIXME probably useless *)
in
let s = extra_args @ s in
let args = Array.of_list (Option.get (Stack.list_of_app_stack (rargs @ Stack.append_app [|x|] args))) in
begin match CredNative.red_prim env sigma p u args with
| Some t -> whrec cst_l' (t,s)
| None -> ((mkApp (mkConstU kn, args), s), cst_l)
end
| _ -> fold ()
end
| Rel _ | Var _ | LetIn _ | Proj _ -> fold ()
| Sort _ | Ind _ | Prod _ -> fold ()
in
fun xs ->
let (s,cst_l as res) = whrec (Option.default Cst_stack.empty csts) xs in
(Stack.best_state sigma s cst_l)
let whd_cbn flags env sigma t =
let state = whd_state_gen flags env sigma (t, Stack.empty) in
Stack.zip ~refold:true sigma state
let norm_cbn flags env sigma t =
let push_rel_check_zeta d env =
let open RedFlags in
let d = match d with
| LocalDef (na,c,t) when not (red_set flags fZETA) -> LocalAssum (na,t)
| d -> d in
push_rel d env in
let rec strongrec env t =
map_constr_with_full_binders env sigma
push_rel_check_zeta strongrec env (whd_cbn flags env sigma t) in
strongrec env t