X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_kernel%2FnCicReduction.ml;h=2e13a5304b23b5adca91ef71dcb9c7d2f4349781;hb=235d5cc96af46d0406bdd28222f56b3ee2bf827e;hp=5bb6260ca57bb73a427b087c41a09129fb4c4b0f;hpb=3fb743f1c1fd5f5e49df2c5322e8c96a1a6ede67;p=helm.git diff --git a/helm/software/components/ng_kernel/nCicReduction.ml b/helm/software/components/ng_kernel/nCicReduction.ml index 5bb6260ca..2e13a5304 100644 --- a/helm/software/components/ng_kernel/nCicReduction.ml +++ b/helm/software/components/ng_kernel/nCicReduction.ml @@ -1,4 +1,5 @@ -(* ||M|| This file is part of HELM, an Hypertextual, Electronic +(* + ||M|| This file is part of HELM, an Hypertextual, Electronic ||A|| Library of Mathematics, developed at the Computer Science ||T|| Department, University of Bologna, Italy. ||I|| @@ -10,69 +11,42 @@ (* $Id$ *) -(* TODO unify exceptions *) - -exception WrongUriToInductiveDefinition;; -exception Impossible of int;; -exception ReferenceToConstant;; -exception ReferenceToVariable;; -exception ReferenceToCurrentProof;; -exception ReferenceToInductiveDefinition;; - -let debug = false -let profile = false -let debug_print s = if debug then prerr_endline (Lazy.force s) - -let fdebug = ref 1;; -let debug t env s = - let rec debug_aux t i = - let module C = Cic in - let module U = UriManager in - CicPp.ppobj (C.Variable ("DEBUG", None, t, [], [])) ^ "\n" ^ i - in - if !fdebug = 0 then - debug_print (lazy (s ^ "\n" ^ List.fold_right debug_aux (t::env) "")) -;; +module C = NCic +module Ref = NReference +module E = NCicEnvironment + +exception AssertFailure of string Lazy.t;; -module type Strategy = - sig +module type Strategy = sig type stack_term type env_term - type config = int * env_term list * NCic.term * stack_term list + type config = int * env_term list * C.term * stack_term list val to_env : - reduce: (config -> config) -> - unwind: (config -> NCic.term) -> - config -> env_term + reduce: (config -> config * bool) -> unwind: (config -> C.term) -> + config -> env_term val from_stack : stack_term -> config val from_stack_list_for_unwind : - unwind: (config -> NCic.term) -> - stack_term list -> NCic.term list + unwind: (config -> C.term) -> stack_term list -> C.term list val from_env : env_term -> config val from_env_for_unwind : - unwind: (config -> NCic.term) -> - env_term -> NCic.term + unwind: (config -> C.term) -> env_term -> C.term val stack_to_env : - reduce: (config -> config) -> - unwind: (config -> NCic.term) -> - stack_term -> env_term + reduce: (config -> config * bool) -> unwind: (config -> C.term) -> + stack_term -> env_term val compute_to_env : - reduce: (config -> config) -> - unwind: (config -> NCic.term) -> - int -> env_term list -> - NCic.term -> env_term + reduce: (config -> config * bool) -> unwind: (config -> C.term) -> + int -> env_term list -> C.term -> env_term val compute_to_stack : - reduce: (config -> config) -> - unwind: (config -> NCic.term) -> - config -> stack_term + reduce: (config -> config * bool) -> unwind: (config -> C.term) -> + config -> stack_term end ;; -module CallByValueByNameForUnwind' = - struct - type config = int * env_term list * NCic.term * stack_term list - and stack_term = config lazy_t * NCic.term lazy_t (* cbv, cbn *) - and env_term = config lazy_t * NCic.term lazy_t (* cbv, cbn *) - let to_env ~reduce ~unwind c = lazy (reduce c),lazy (unwind c) +module CallByValueByNameForUnwind' = struct + type config = int * env_term list * C.term * stack_term list + and stack_term = config lazy_t * C.term lazy_t (* cbv, cbn *) + and env_term = config lazy_t * C.term lazy_t (* cbv, cbn *) + let to_env ~reduce ~unwind c = lazy (fst (reduce c)),lazy (unwind c) let from_stack (c,_) = Lazy.force c let from_stack_list_for_unwind ~unwind:_ l = List.map (function (_,c) -> Lazy.force c) l @@ -80,302 +54,26 @@ module CallByValueByNameForUnwind' = let from_env_for_unwind ~unwind:_ (_,c) = Lazy.force c let stack_to_env ~reduce:_ ~unwind:_ config = config let compute_to_env ~reduce ~unwind k e t = - lazy (reduce (k,e,t,[])), lazy (unwind (k,e,t,[])) + lazy (fst (reduce (k,e,t,[]))), lazy (unwind (k,e,t,[])) let compute_to_stack ~reduce ~unwind config = - lazy (reduce config), lazy (unwind config) - end -;; - - -(* {{{ module CallByValueByNameForUnwind = - struct - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - and stack_term = config - and env_term = config * config (* cbv, cbn *) - and ens_term = config * config (* cbv, cbn *) - - let to_env c = c,c - let to_ens c = c,c - let from_stack config = config - let from_stack_list_for_unwind ~unwind l = List.map unwind l - let from_env (c,_) = c - let from_ens (c,_) = c - let from_env_for_unwind ~unwind (_,c) = unwind c - let from_ens_for_unwind ~unwind (_,c) = unwind c - let stack_to_env ~reduce ~unwind config = reduce config, (0,[],[],unwind config,[]) - let compute_to_env ~reduce ~unwind k e ens t = (k,e,ens,t,[]), (k,e,ens,t,[]) - let compute_to_stack ~reduce ~unwind config = config - end -;; - - -(* Old Machine *) -module CallByNameStrategy = - struct - type stack_term = Cic.term - type env_term = Cic.term - type ens_term = Cic.term - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - let to_env v = v - let to_ens v = v - let from_stack ~unwind v = v - let from_stack_list ~unwind l = l - let from_env v = v - let from_ens v = v - let from_env_for_unwind ~unwind v = v - let from_ens_for_unwind ~unwind v = v - let stack_to_env ~reduce ~unwind v = v - let compute_to_stack ~reduce ~unwind k e ens t = unwind k e ens t - let compute_to_env ~reduce ~unwind k e ens t = unwind k e ens t - end -;; - -module CallByNameStrategy = - struct - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - and stack_term = config - and env_term = config - and ens_term = config - - let to_env c = c - let to_ens c = c - let from_stack config = config - let from_stack_list_for_unwind ~unwind l = List.map unwind l - let from_env c = c - let from_ens c = c - let from_env_for_unwind ~unwind c = unwind c - let from_ens_for_unwind ~unwind c = unwind c - let stack_to_env ~reduce ~unwind config = 0,[],[],unwind config,[] - let compute_to_env ~reduce ~unwind k e ens t = k,e,ens,t,[] - let compute_to_stack ~reduce ~unwind config = config - end -;; - -module CallByValueStrategy = - struct - type stack_term = Cic.term - type env_term = Cic.term - type ens_term = Cic.term - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - let to_env v = v - let to_ens v = v - let from_stack ~unwind v = v - let from_stack_list ~unwind l = l - let from_env v = v - let from_ens v = v - let from_env_for_unwind ~unwind v = v - let from_ens_for_unwind ~unwind v = v - let stack_to_env ~reduce ~unwind v = v - let compute_to_stack ~reduce ~unwind k e ens t = reduce (k,e,ens,t,[]) - let compute_to_env ~reduce ~unwind k e ens t = reduce (k,e,ens,t,[]) - end -;; - -module CallByValueStrategyByNameOnConstants = - struct - type stack_term = Cic.term - type env_term = Cic.term - type ens_term = Cic.term - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - let to_env v = v - let to_ens v = v - let from_stack ~unwind v = v - let from_stack_list ~unwind l = l - let from_env v = v - let from_ens v = v - let from_env_for_unwind ~unwind v = v - let from_ens_for_unwind ~unwind v = v - let stack_to_env ~reduce ~unwind v = v - let compute_to_stack ~reduce ~unwind k e ens = - function - Cic.Const _ as t -> unwind k e ens t - | t -> reduce (k,e,ens,t,[]) - let compute_to_env ~reduce ~unwind k e ens = - function - Cic.Const _ as t -> unwind k e ens t - | t -> reduce (k,e,ens,t,[]) - end -;; - -module LazyCallByValueStrategy = - struct - type stack_term = Cic.term lazy_t - type env_term = Cic.term lazy_t - type ens_term = Cic.term lazy_t - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - let to_env v = lazy v - let to_ens v = lazy v - let from_stack ~unwind v = Lazy.force v - let from_stack_list ~unwind l = List.map (from_stack ~unwind) l - let from_env v = Lazy.force v - let from_ens v = Lazy.force v - let from_env_for_unwind ~unwind v = Lazy.force v - let from_ens_for_unwind ~unwind v = Lazy.force v - let stack_to_env ~reduce ~unwind v = v - let compute_to_stack ~reduce ~unwind k e ens t = lazy (reduce (k,e,ens,t,[])) - let compute_to_env ~reduce ~unwind k e ens t = lazy (reduce (k,e,ens,t,[])) - end -;; - -module LazyCallByValueStrategyByNameOnConstants = - struct - type stack_term = Cic.term lazy_t - type env_term = Cic.term lazy_t - type ens_term = Cic.term lazy_t - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - let to_env v = lazy v - let to_ens v = lazy v - let from_stack ~unwind v = Lazy.force v - let from_stack_list ~unwind l = List.map (from_stack ~unwind) l - let from_env v = Lazy.force v - let from_ens v = Lazy.force v - let from_env_for_unwind ~unwind v = Lazy.force v - let from_ens_for_unwind ~unwind v = Lazy.force v - let stack_to_env ~reduce ~unwind v = v - let compute_to_stack ~reduce ~unwind k e ens t = - lazy ( - match t with - Cic.Const _ as t -> unwind k e ens t - | t -> reduce (k,e,ens,t,[])) - let compute_to_env ~reduce ~unwind k e ens t = - lazy ( - match t with - Cic.Const _ as t -> unwind k e ens t - | t -> reduce (k,e,ens,t,[])) - end -;; - -module LazyCallByNameStrategy = - struct - type stack_term = Cic.term lazy_t - type env_term = Cic.term lazy_t - type ens_term = Cic.term lazy_t - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - let to_env v = lazy v - let to_ens v = lazy v - let from_stack ~unwind v = Lazy.force v - let from_stack_list ~unwind l = List.map (from_stack ~unwind) l - let from_env v = Lazy.force v - let from_ens v = Lazy.force v - let from_env_for_unwind ~unwind v = Lazy.force v - let from_ens_for_unwind ~unwind v = Lazy.force v - let stack_to_env ~reduce ~unwind v = v - let compute_to_stack ~reduce ~unwind k e ens t = lazy (unwind k e ens t) - let compute_to_env ~reduce ~unwind k e ens t = lazy (unwind k e ens t) - end -;; - -module - LazyCallByValueByNameOnConstantsWhenFromStack_ByNameStrategyWhenFromEnvOrEns -= - struct - type stack_term = reduce:bool -> Cic.term - type env_term = reduce:bool -> Cic.term - type ens_term = reduce:bool -> Cic.term - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - let to_env v = - let value = lazy v in - fun ~reduce -> Lazy.force value - let to_ens v = - let value = lazy v in - fun ~reduce -> Lazy.force value - let from_stack ~unwind v = (v ~reduce:false) - let from_stack_list ~unwind l = List.map (from_stack ~unwind) l - let from_env v = (v ~reduce:true) - let from_ens v = (v ~reduce:true) - let from_env_for_unwind ~unwind v = (v ~reduce:true) - let from_ens_for_unwind ~unwind v = (v ~reduce:true) - let stack_to_env ~reduce ~unwind v = v - let compute_to_stack ~reduce ~unwind k e ens t = - let svalue = - lazy ( - match t with - Cic.Const _ as t -> unwind k e ens t - | t -> reduce (k,e,ens,t,[]) - ) in - let lvalue = - lazy (unwind k e ens t) - in - fun ~reduce -> - if reduce then Lazy.force svalue else Lazy.force lvalue - let compute_to_env ~reduce ~unwind k e ens t = - let svalue = - lazy ( - match t with - Cic.Const _ as t -> unwind k e ens t - | t -> reduce (k,e,ens,t,[]) - ) in - let lvalue = - lazy (unwind k e ens t) - in - fun ~reduce -> - if reduce then Lazy.force svalue else Lazy.force lvalue + lazy (fst (reduce config)), lazy (unwind config) end ;; -module ClosuresOnStackByValueFromEnvOrEnsStrategy = - struct - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - and stack_term = config - and env_term = config - and ens_term = config - - let to_env config = config - let to_ens config = config - let from_stack config = config - let from_stack_list_for_unwind ~unwind l = List.map unwind l - let from_env v = v - let from_ens v = v - let from_env_for_unwind ~unwind config = unwind config - let from_ens_for_unwind ~unwind config = unwind config - let stack_to_env ~reduce ~unwind config = reduce config - let compute_to_env ~reduce ~unwind k e ens t = (k,e,ens,t,[]) - let compute_to_stack ~reduce ~unwind config = config - end -;; - -module ClosuresOnStackByValueFromEnvOrEnsByNameOnConstantsStrategy = - struct - type stack_term = - int * Cic.term list * Cic.term Cic.explicit_named_substitution * Cic.term - type env_term = Cic.term - type ens_term = Cic.term - type config = int * env_term list * ens_term Cic.explicit_named_substitution * Cic.term * stack_term list - let to_env v = v - let to_ens v = v - let from_stack ~unwind (k,e,ens,t) = unwind k e ens t - let from_stack_list ~unwind l = List.map (from_stack ~unwind) l - let from_env v = v - let from_ens v = v - let from_env_for_unwind ~unwind v = v - let from_ens_for_unwind ~unwind v = v - let stack_to_env ~reduce ~unwind (k,e,ens,t) = - match t with - Cic.Const _ as t -> unwind k e ens t - | t -> reduce (k,e,ens,t,[]) - let compute_to_env ~reduce ~unwind k e ens t = - unwind k e ens t - let compute_to_stack ~reduce ~unwind k e ens t = (k,e,ens,t) - end -;; - -}}} *) - -module Reduction(RS : Strategy) = - struct +module Reduction(RS : Strategy) = struct type env = RS.env_term list type stack = RS.stack_term list - type config = int * env * NCic.term * stack + type config = int * env * C.term * stack let rec unwind (k,e,t,s) = let t = if k = 0 then t else NCicSubstitution.psubst ~avoid_beta_redexes:true - true 0 (RS.from_env_for_unwind ~unwind) e t + (RS.from_env_for_unwind ~unwind) e t in if s = [] then t - else NCic.Appl(t::(RS.from_stack_list_for_unwind ~unwind s)) + else C.Appl(t::(RS.from_stack_list_for_unwind ~unwind s)) ;; let list_nth l n = try List.nth l n with Failure _ -> assert false;; @@ -386,518 +84,350 @@ module Reduction(RS : Strategy) = | _,_ -> assert false ;; - let rec reduce ~delta ?(subst = []) context : config -> config = + let rec reduce ~delta ?(subst = []) context : config -> config * bool = let rec aux = function - | k, e, NCic.Rel n, s when n <= k -> + | k, e, C.Rel n, s when n <= k -> let k',e',t',s' = RS.from_env (list_nth e (n-1)) in aux (k',e',t',s'@s) - | k, _, NCic.Rel n, s as config (* when n > k *) -> - (match List.nth context (n - 1 - k) with - | (_,NCic.Decl _) -> config - | (_,NCic.Def (x,_)) -> aux (0,[],NCicSubstitution.lift (n - k) x,s)) - | (k, e, NCic.Meta (n,l), s) as config -> + | k, _, C.Rel n, s as config (* when n > k *) -> + let x= try Some (List.nth context (n - 1 - k)) with Failure _ -> None in + (match x with + | Some(_,C.Def(x,_)) -> aux (0,[],NCicSubstitution.lift (n - k) x,s) + | _ -> config, true) + | (k, e, C.Meta (n,l), s) as config -> (try let _,_, term,_ = NCicUtils.lookup_subst n subst in aux (k, e, NCicSubstitution.subst_meta l term,s) - with NCicUtils.Subst_not_found _ -> config) - | (_, _, NCic.Sort _, _) as config -> config - | (_, _, NCic.Implicit _, _) -> assert false - | (_, _, NCic.Prod _, _) as config -> config - | (_, _, NCic.Lambda _, []) as config -> config - | (k, e, NCic.Lambda (_,_,t), p::s) -> + with NCicUtils.Subst_not_found _ -> config, true) + | (_, _, C.Implicit _, _) -> assert false + | (_, _, C.Sort _, _) + | (_, _, C.Prod _, _) + | (_, _, C.Lambda _, []) as config -> config, true + | (k, e, C.Lambda (_,_,t), p::s) -> aux (k+1, (RS.stack_to_env ~reduce:aux ~unwind p)::e, t,s) - | (k, e, NCic.LetIn (_,_,m,t), s) -> + | (k, e, C.LetIn (_,_,m,t), s) -> let m' = RS.compute_to_env ~reduce:aux ~unwind k e m in aux (k+1, m'::e, t, s) - | (_, _, NCic.Appl [], _) -> assert false - | (k, e, NCic.Appl (he::tl), s) -> + | (_, _, C.Appl ([]|[_]), _) -> assert false + | (k, e, C.Appl (he::tl), s) -> let tl' = List.map (fun t->RS.compute_to_stack ~reduce:aux ~unwind (k,e,t,[])) tl in aux (k, e, he, tl' @ s) - | (_, _, NCic.Const - (NReference.Ref (_,_,NReference.Def) as refer), s) as config -> - let _,_,body,_,_,height = NCicEnvironment.get_checked_def refer in - if delta >= height then config else aux (0, [], body, s) - | (_, _, NCic.Const (NReference.Ref - (_,_,NReference.Fix (_,recindex)) as refer),s) as config -> - let _,_,body,_, _, height = NCicEnvironment.get_checked_fix refer in - if delta >= height then config else + | (_, _, C.Const + (Ref.Ref (_,Ref.Def height) as refer), s) as config -> + if delta >= height then + config, false + else + let _,_,body,_,_,_ = NCicEnvironment.get_checked_def refer in + aux (0, [], body, s) + | (_, _, C.Const (Ref.Ref (_, + (Ref.Decl|Ref.Ind _|Ref.Con _|Ref.CoFix _))), _) as config -> + config, true + | (_, _, (C.Const (Ref.Ref + (_,Ref.Fix (fixno,recindex,height)) as refer) as head),s) as config -> +(* if delta >= height then config else *) (match try Some (RS.from_stack (List.nth s recindex)) with Failure _ -> None with - | None -> config + | None -> config, true | Some recparam -> + let fixes,_,_ = NCicEnvironment.get_checked_fixes_or_cofixes refer in match reduce ~delta:0 ~subst context recparam with - | (_,_,NCic.Const (NReference.Ref (_,_,NReference.Con _)), _) as c -> + | (_,_,C.Const (Ref.Ref (_,Ref.Con _)), _) as c, _ + when delta >= height -> + let new_s = + replace recindex s (RS.compute_to_stack ~reduce:aux ~unwind c) + in + (0, [], head, new_s), false + | (_,_,C.Const (Ref.Ref (_,Ref.Con _)), _) as c, _ -> let new_s = replace recindex s (RS.compute_to_stack ~reduce:aux ~unwind c) in + let _,_,_,_,body = List.nth fixes fixno in aux (0, [], body, new_s) - | _ -> config) - | (_, _, NCic.Const _, _) as config -> config - | (k, e, NCic.Match (_,_,term,pl),s) as config -> + | _ -> config, true) + | (k, e, C.Match (_,_,term,pl),s) as config -> let decofix = function - | (_,_,NCic.Const(NReference.Ref(_,_,NReference.CoFix _)as refer),s)-> - let _,_,body,_,_,_ = NCicEnvironment.get_checked_cofix refer in - reduce ~delta:0 ~subst context (0,[],body,s) + | (_,_,C.Const(Ref.Ref(_,Ref.CoFix c)as refer),s)-> + let cofixes,_,_ = + NCicEnvironment.get_checked_fixes_or_cofixes refer in + let _,_,_,_,body = List.nth cofixes c in + let c,_ = reduce ~delta:0 ~subst context (0,[],body,s) in + c | config -> config in - (match decofix (reduce ~delta:0 ~subst context (k,e,term,[])) with - | (_, _, NCic.Const (NReference.Ref (_,_,NReference.Con (_,j))),[]) -> + let match_head = k,e,term,[] in + let reduced,_ = reduce ~delta:0 ~subst context match_head in + (match decofix reduced with + | (_, _, C.Const (Ref.Ref (_,Ref.Con (_,j,_))),[]) -> aux (k, e, List.nth pl (j-1), s) - | (_, _, NCic.Const - (NReference.Ref (_,_,NReference.Con (_,j)) as refer), s') -> - let leftno = NCicEnvironment.get_indty_leftno refer in - let _,params = HExtlib.split_nth leftno s' in + | (_, _, C.Const (Ref.Ref (_,Ref.Con (_,j,lno))), s')-> + let _,params = HExtlib.split_nth lno s' in aux (k, e, List.nth pl (j-1), params@s) - | _ -> config) + | _ -> config, true) in aux ;; - let whd ?(delta=0) ?(subst=[]) context t = - unwind (reduce ~delta ~subst context (0, [], t, [])) + let whd ?(delta=0) ~subst context t = + unwind (fst (reduce ~delta ~subst context (0, [], t, []))) ;; end ;; -(* {{{ ROTTO = rompe l'unificazione poiche' riduce gli argomenti di un'applicazione - senza ridurre la testa -module R = Reduction CallByNameStrategy;; OK 56.368s -module R = Reduction CallByValueStrategy;; ROTTO -module R = Reduction CallByValueStrategyByNameOnConstants;; ROTTO -module R = Reduction LazyCallByValueStrategy;; ROTTO -module R = Reduction LazyCallByValueStrategyByNameOnConstants;; ROTTO -module R = Reduction LazyCallByNameStrategy;; OK 0m56.398s -module R = Reduction - LazyCallByValueByNameOnConstantsWhenFromStack_ByNameStrategyWhenFromEnvOrEns;; - OK 59.058s -module R = Reduction ClosuresOnStackByValueFromEnvOrEnsStrategy;; OK 58.583s -module R = Reduction - ClosuresOnStackByValueFromEnvOrEnsByNameOnConstantsStrategy;; OK 58.094s -module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);; OK 58.127s -module R = Reduction(CallByValueByNameForUnwind);; -module R = Reduction(CallByNameStrategy);; -module R = Reduction(ClosuresOnStackByValueFromEnvOrEnsStrategy);;}}} *) module RS = CallByValueByNameForUnwind';; - module R = Reduction(RS);; -module U = UriManager;; let whd = R.whd -(* -let whd = - let profiler_whd = HExtlib.profile ~enable:profile "are_convertible.whd" in - fun ?(delta=true) ?(subst=[]) context t -> - profiler_whd.HExtlib.profile (whd ~delta ~subst context) t -*) - -(* - - (* mimic ocaml (<< 3.08) "=" behaviour. Tests physical equality first then - * fallbacks to structural equality *) let (===) x y = Pervasives.compare x y = 0 ;; -module C = NCic +let get_relevance = ref (fun ~metasenv:_ ~subst:_ _ _ -> assert false);; + +let set_get_relevance f = get_relevance := f;; + +let alpha_eq ~test_lambda_source aux test_eq_only metasenv subst context t1 t2 = + if t1 === t2 then + true + else + match (t1,t2) with + | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only -> + NCicEnvironment.universe_leq a b + | (C.Sort (C.Type a), C.Sort (C.Type b)) -> + NCicEnvironment.universe_eq a b + | (C.Sort C.Prop,C.Sort (C.Type _)) -> (not test_eq_only) + | (C.Sort C.Prop, C.Sort C.Prop) -> true + + | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) -> + aux true context s1 s2 && + aux test_eq_only ((name1, C.Decl s1)::context) t1 t2 + | (C.Lambda (name1,s1,t1), C.Lambda(_,_,t2)) -> + if test_lambda_source then + aux test_eq_only context t1 t2 + else + (* thanks to inversion of well typedness, the source + * of these lambdas must be already convertible *) + aux test_eq_only ((name1, C.Decl s1)::context) t1 t2 + | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) -> + aux test_eq_only context ty1 ty2 && + aux test_eq_only context s1 s2 && + aux test_eq_only ((name1, C.Def (s1,ty1))::context) t1 t2 + + | (C.Meta (n1,(s1, C.Irl _)), C.Meta (n2,(s2, C.Irl _))) + when n1 = n2 && s1 = s2 -> true + | (C.Meta (n1,(s1, l1)), C.Meta (n2,(s2, l2))) when n1 = n2 && + let l1 = NCicUtils.expand_local_context l1 in + let l2 = NCicUtils.expand_local_context l2 in + (try List.for_all2 + (fun t1 t2 -> aux test_eq_only context + (NCicSubstitution.lift s1 t1) + (NCicSubstitution.lift s2 t2)) + l1 l2 + with Invalid_argument "List.for_all2" -> + prerr_endline ("Meta " ^ string_of_int n1 ^ + " occurrs with local contexts of different lenght\n"^ + NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " === " ^ + NCicPp.ppterm ~metasenv ~subst ~context t2); + assert false) -> true + + | C.Meta (n1,l1), _ -> + (try + let _,_,term,_ = NCicUtils.lookup_subst n1 subst in + let term = NCicSubstitution.subst_meta l1 term in + aux test_eq_only context term t2 + with NCicUtils.Subst_not_found _ -> false) + | _, C.Meta (n2,l2) -> + (try + let _,_,term,_ = NCicUtils.lookup_subst n2 subst in + let term = NCicSubstitution.subst_meta l2 term in + aux test_eq_only context t1 term + with NCicUtils.Subst_not_found _ -> false) + + | (C.Appl ((C.Const r1) as hd1::tl1), C.Appl (C.Const r2::tl2)) + when (Ref.eq r1 r2 && + List.length (E.get_relevance r1) >= List.length tl1) -> + let relevance = E.get_relevance r1 in + let relevance = match r1 with + | Ref.Ref (_,Ref.Con (_,_,lno)) -> + let _,relevance = HExtlib.split_nth lno relevance in + HExtlib.mk_list false lno @ relevance + | _ -> relevance + in + (try + HExtlib.list_forall_default3_var + (fun t1 t2 b -> not b || aux true context t1 t2 ) + tl1 tl2 true relevance + with Invalid_argument _ -> false + | HExtlib.FailureAt fail -> + let relevance = + !get_relevance ~metasenv ~subst context hd1 tl1 in + let _,relevance = HExtlib.split_nth fail relevance in + let b,relevance = (match relevance with + | [] -> assert false + | b::tl -> b,tl) in + if (not b) then + let _,tl1 = HExtlib.split_nth (fail+1) tl1 in + let _,tl2 = HExtlib.split_nth (fail+1) tl2 in + try + HExtlib.list_forall_default3 + (fun t1 t2 b -> not b || aux true context t1 t2) + tl1 tl2 true relevance + with Invalid_argument _ -> false + else false) + + | (C.Appl (hd1::tl1), C.Appl (hd2::tl2)) -> + aux test_eq_only context hd1 hd2 && + let relevance = !get_relevance ~metasenv ~subst context hd1 tl1 in + (try + HExtlib.list_forall_default3 + (fun t1 t2 b -> not b || aux true context t1 t2) + tl1 tl2 true relevance + with Invalid_argument _ -> false) + + | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1), + C.Match (ref2,outtype2,term2,pl2)) -> + let _,_,itl,_,_ = E.get_checked_indtys ref1 in + let _,_,ty,_ = List.nth itl tyno in + let rec remove_prods ~subst context ty = + let ty = whd ~subst context ty in + match ty with + | C.Sort _ -> ty + | C.Prod (name,so,ta) -> remove_prods ~subst ((name,(C.Decl so))::context) ta + | _ -> assert false + in + let is_prop = + match remove_prods ~subst [] ty with + | C.Sort C.Prop -> true + | _ -> false + in + Ref.eq ref1 ref2 && + aux test_eq_only context outtype1 outtype2 && + (is_prop || aux test_eq_only context term1 term2) && + (try List.for_all2 (aux test_eq_only context) pl1 pl2 + with Invalid_argument _ -> false) + | (C.Implicit _, _) | (_, C.Implicit _) -> assert false + | (_,_) -> false +;; (* t1, t2 must be well-typed *) -let are_convertible whd ?(subst=[]) ?(metasenv=[]) = - let heuristic = ref true in - let rec aux test_equality_only context t1 t2 = - let rec aux2 test_equality_only t1 t2 = - if t1 === t2 then - true - else - match (t1,t2) with - | (C.Rel n1, C.Rel n2) -> n1 = n2 - - | (C.Sort (C.Type a), C.Sort (C.Type b)) -> a <= b - | (C.Sort (C.Type a), C.Sort (C.Type b)) when test_equality_only -> a=b - | (C.Sort s1,C.Sort (C.Type _)) -> (not test_equality_only) - | (C.Sort s1, C.Sort s2) -> s1 = s2 - - | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) -> - aux true context s1 s2 && - aux test_equality_only ((name1, C.Decl s1)::context) t1 t2 - | (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2)) -> - aux test_equality_only context s1 s2 && (* sure?! *) - aux test_equality_only ((name1, C.Decl s1)::context) t1 t2 - - | (C.Meta (n1,l1), C.Meta (n2,l2)) -> - if n1 = n2 then - let b2, ugraph1 = - let l1 = CicUtil.clean_up_local_context subst metasenv n1 l1 in - let l2 = CicUtil.clean_up_local_context subst metasenv n2 l2 in - List.fold_left2 - (fun (b,ugraph) t1 t2 -> - if b then - match t1,t2 with - None,_ - | _,None -> true,ugraph - | Some t1',Some t2' -> - aux test_equality_only context t1' t2' ugraph - else - false,ugraph - ) (true,ugraph) l1 l2 - in - if b2 then true,ugraph1 else false,ugraph - else - false,ugraph - | C.Meta (n1,l1), _ -> - (try - let _,term,_ = NCicUtils.lookup_subst n1 subst in - let term' = CicSubstitution.subst_meta l1 term in - aux test_equality_only context term' t2 ugraph - with CicUtil.Subst_not_found _ -> false,ugraph) - | _, C.Meta (n2,l2) -> - (try - let _,term,_ = CicUtil.lookup_subst n2 subst in - let term' = CicSubstitution.subst_meta l2 term in - aux test_equality_only context t1 term' ugraph - with CicUtil.Subst_not_found _ -> false,ugraph) - | (C.LetIn (name1,s1,t1), C.LetIn(_,s2,t2)) -> - let b',ugraph' = aux test_equality_only context s1 s2 ugraph in - if b' then - aux test_equality_only - ((Some (name1, (C.Def (s1,None))))::context) t1 t2 ugraph' - else - false,ugraph - | (C.Appl l1, C.Appl l2) -> - (try - List.fold_right2 - (fun x y (b,ugraph) -> - if b then - aux test_equality_only context x y ugraph - else - false,ugraph) l1 l2 (true,ugraph) - with - Invalid_argument _ -> false,ugraph - ) - | (C.Const (uri1,exp_named_subst1), C.Const (uri2,exp_named_subst2)) -> - let b' = U.eq uri1 uri2 in - if b' then - (try - List.fold_right2 - (fun (uri1,x) (uri2,y) (b,ugraph) -> - if b && U.eq uri1 uri2 then - aux test_equality_only context x y ugraph - else - false,ugraph - ) exp_named_subst1 exp_named_subst2 (true,ugraph) - with - Invalid_argument _ -> false,ugraph - ) - else - false,ugraph - | (C.MutInd (uri1,i1,exp_named_subst1), - C.MutInd (uri2,i2,exp_named_subst2) - ) -> - let b' = U.eq uri1 uri2 && i1 = i2 in - if b' then - (try - List.fold_right2 - (fun (uri1,x) (uri2,y) (b,ugraph) -> - if b && U.eq uri1 uri2 then - aux test_equality_only context x y ugraph - else - false,ugraph - ) exp_named_subst1 exp_named_subst2 (true,ugraph) - with - Invalid_argument _ -> false,ugraph - ) - else - false,ugraph - | (C.MutConstruct (uri1,i1,j1,exp_named_subst1), - C.MutConstruct (uri2,i2,j2,exp_named_subst2) - ) -> - let b' = U.eq uri1 uri2 && i1 = i2 && j1 = j2 in - if b' then - (try - List.fold_right2 - (fun (uri1,x) (uri2,y) (b,ugraph) -> - if b && U.eq uri1 uri2 then - aux test_equality_only context x y ugraph - else - false,ugraph - ) exp_named_subst1 exp_named_subst2 (true,ugraph) - with - Invalid_argument _ -> false,ugraph - ) - else - false,ugraph - | (C.MutCase (uri1,i1,outtype1,term1,pl1), - C.MutCase (uri2,i2,outtype2,term2,pl2)) -> - let b' = U.eq uri1 uri2 && i1 = i2 in - if b' then - let b'',ugraph''=aux test_equality_only context - outtype1 outtype2 ugraph in - if b'' then - let b''',ugraph'''= aux test_equality_only context - term1 term2 ugraph'' in - List.fold_right2 - (fun x y (b,ugraph) -> - if b then - aux test_equality_only context x y ugraph - else - false,ugraph) - pl1 pl2 (b''',ugraph''') - else - false,ugraph - else - false,ugraph - | (C.Fix (i1,fl1), C.Fix (i2,fl2)) -> - let tys,_ = - List.fold_left - (fun (types,len) (n,_,ty,_) -> - (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, - len+1) - ) ([],0) fl1 - in - if i1 = i2 then - List.fold_right2 - (fun (_,recindex1,ty1,bo1) (_,recindex2,ty2,bo2) (b,ugraph) -> - if b && recindex1 = recindex2 then - let b',ugraph' = aux test_equality_only context ty1 ty2 - ugraph in - if b' then - aux test_equality_only (tys@context) bo1 bo2 ugraph' - else - false,ugraph - else - false,ugraph) - fl1 fl2 (true,ugraph) - else - false,ugraph - | (C.CoFix (i1,fl1), C.CoFix (i2,fl2)) -> - let tys,_ = - List.fold_left - (fun (types,len) (n,ty,_) -> - (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, - len+1) - ) ([],0) fl1 - in - if i1 = i2 then - List.fold_right2 - (fun (_,ty1,bo1) (_,ty2,bo2) (b,ugraph) -> - if b then - let b',ugraph' = aux test_equality_only context ty1 ty2 - ugraph in - if b' then - aux test_equality_only (tys@context) bo1 bo2 ugraph' - else - false,ugraph - else - false,ugraph) - fl1 fl2 (true,ugraph) - else - false,ugraph - | C.Cast (bo,_),t -> aux2 test_equality_only bo t ugraph - | t,C.Cast (bo,_) -> aux2 test_equality_only t bo ugraph - | (C.Implicit _, _) | (_, C.Implicit _) -> assert false - | (_,_) -> false,ugraph +let are_convertible ~metasenv ~subst = + let rec aux test_eq_only context t1 t2 = + let alpha_eq test_eq_only = + alpha_eq ~test_lambda_source:false aux test_eq_only metasenv subst context in - let res = - if !heuristic then - aux2 test_equality_only t1 t2 ugraph - else - false,ugraph - in - if fst res = true then - res - else -begin -(*if !heuristic then prerr_endline ("NON FACILE: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2);*) - (* heuristic := false; *) - debug t1 [t2] "PREWHD"; -(*prerr_endline ("PREWHD: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2);*) -(* -prerr_endline ("PREWHD: " ^ CicPp.ppterm t1 ^ " <===> " ^ CicPp.ppterm t2); - let t1' = whd ?delta:(Some true) ?subst:(Some subst) context t1 in - let t2' = whd ?delta:(Some true) ?subst:(Some subst) context t2 in - debug t1' [t2'] "POSTWHD"; -*) -let rec convert_machines ugraph = - function - [] -> true,ugraph - | ((k1,env1,ens1,h1,s1),(k2,env2,ens2,h2,s2))::tl -> - let (b,ugraph) as res = - aux2 test_equality_only - (R.unwind (k1,env1,ens1,h1,[])) (R.unwind (k2,env2,ens2,h2,[])) ugraph + if alpha_eq test_eq_only t1 t2 then + true + else + let height_of = function + | C.Const (Ref.Ref (_,Ref.Def h)) + | C.Const (Ref.Ref (_,Ref.Fix (_,_,h))) + | C.Appl(C.Const(Ref.Ref(_,Ref.Def h))::_) + | C.Appl(C.Const(Ref.Ref(_,Ref.Fix (_,_,h)))::_) -> h + | _ -> 0 + in + let put_in_whd m1 m2 = + R.reduce ~delta:max_int ~subst context m1, + R.reduce ~delta:max_int ~subst context m2 in - if b then - let problems = + let small_delta_step + ((_,_,t1,_ as m1), norm1 as x1) ((_,_,t2,_ as m2), norm2 as x2) + = + assert(not (norm1 && norm2)); + if norm1 then + x1, R.reduce ~delta:(height_of t2 -1) ~subst context m2 + else if norm2 then + R.reduce ~delta:(height_of t1 -1) ~subst context m1, x2 + else + let h1 = height_of t1 in + let h2 = height_of t2 in + let delta = if h1 = h2 then max 0 (h1 -1) else min h1 h2 in + R.reduce ~delta ~subst context m1, + R.reduce ~delta ~subst context m2 + in + let rec convert_machines test_eq_only + ((k1,e1,t1,s1),norm1 as m1),((k2,e2,t2,s2), norm2 as m2) + = + (alpha_eq test_eq_only + (R.unwind (k1,e1,t1,[])) (R.unwind (k2,e2,t2,[])) && + let relevance = + match t1 with + C.Const r -> NCicEnvironment.get_relevance r + | _ -> [] in try - Some - (List.combine - (List.map - (fun si-> R.reduce ~delta:false ~subst context(RS.from_stack si)) - s1) - (List.map - (fun si-> R.reduce ~delta:false ~subst context(RS.from_stack si)) - s2) - @ tl) - with - Invalid_argument _ -> None - in - match problems with - None -> false,ugraph - | Some problems -> convert_machines ugraph problems - else - res -in - convert_machines ugraph - [R.reduce ~delta:true ~subst context (0,[],[],t1,[]), - R.reduce ~delta:true ~subst context (0,[],[],t2,[])] -(*prerr_endline ("POSTWH: " ^ CicPp.ppterm t1' ^ " <===> " ^ CicPp.ppterm t2');*) -(* - aux2 test_equality_only t1' t2' ugraph -*) -end + HExtlib.list_forall_default3 + (fun t1 t2 b -> + not b || + let t1 = RS.from_stack t1 in + let t2 = RS.from_stack t2 in + convert_machines true (put_in_whd t1 t2)) s1 s2 true relevance + with Invalid_argument _ -> false) || + (not (norm1 && norm2) && convert_machines test_eq_only (small_delta_step m1 m2)) + in + convert_machines test_eq_only (put_in_whd (0,[],t1,[]) (0,[],t2,[])) in - aux false (*c t1 t2 ugraph *) + aux false ;; -*) - -(* {{{ DEBUGGING ONLY -let whd ?(delta=true) ?(subst=[]) context t = - let res = whd ~delta ~subst context t in - let rescsc = CicReductionNaif.whd ~delta ~subst context t in - if not (fst (are_convertible CicReductionNaif.whd ~subst context res rescsc CicUniv.empty_ugraph)) then - begin - debug_print (lazy ("PRIMA: " ^ CicPp.ppterm t)) ; - flush stderr ; - debug_print (lazy ("DOPO: " ^ CicPp.ppterm res)) ; - flush stderr ; - debug_print (lazy ("CSC: " ^ CicPp.ppterm rescsc)) ; - flush stderr ; -fdebug := 0 ; -let _ = are_convertible CicReductionNaif.whd ~subst context res rescsc CicUniv.empty_ugraph in - assert false ; - end - else - res + +let alpha_eq metasenv subst = + let rec aux test_lambda_source context t1 t2 = + alpha_eq ~test_lambda_source aux true metasenv subst context t1 t2 + in + aux true ;; - }}} *) -(*let are_convertible = are_convertible whd*) +let rec head_beta_reduce ~delta ~upto ~subst t l = + match upto, t, l with + | 0, C.Appl l1, _ -> C.Appl (l1 @ l) + | 0, t, [] -> t + | 0, t, _ -> C.Appl (t::l) + | _, C.Meta (n,ctx), _ -> + (try + let _,_, term,_ = NCicUtils.lookup_subst n subst in + head_beta_reduce ~delta ~upto ~subst + (NCicSubstitution.subst_meta ctx term) l + with NCicUtils.Subst_not_found _ -> if l = [] then t else C.Appl (t::l)) + | _, C.Appl (hd::tl), _ -> head_beta_reduce ~delta ~upto ~subst hd (tl @ l) + | _, C.Lambda(_,_,bo), arg::tl -> + let bo = NCicSubstitution.subst arg bo in + head_beta_reduce ~delta ~upto:(upto - 1) ~subst bo tl + | _, C.Const (Ref.Ref (_, Ref.Def height) as re), _ + when delta <= height -> + let _, _, bo, _, _, _ = NCicEnvironment.get_checked_def re in + head_beta_reduce ~upto ~delta ~subst bo l + | _, t, [] -> t + | _, t, _ -> C.Appl (t::l) +;; -(* {{{ let profiler_other_whd = HExtlib.profile ~enable:profile "~are_convertible.whd" -let whd ?(delta=true) ?(subst=[]) context t = - let foo () = - whd ~delta ~subst context t - in - profiler_other_whd.HExtlib.profile foo () - }}} *) - -(* {{{ let rec normalize ?(delta=true) ?(subst=[]) ctx term = - let module C = Cic in - let t = whd ~delta ~subst ctx term in - let aux = normalize ~delta ~subst in - let decl name t = Some (name, C.Decl t) in - match t with - | C.Rel n -> t - | C.Var (uri,exp_named_subst) -> - C.Var (uri, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst) - | C.Meta (i,l) -> - C.Meta (i,List.map (function Some t -> Some (aux ctx t) | None -> None) l) - | C.Sort _ -> t - | C.Implicit _ -> t - | C.Cast (te,ty) -> C.Cast (aux ctx te, aux ctx ty) - | C.Prod (n,s,t) -> - let s' = aux ctx s in - C.Prod (n, s', aux ((decl n s')::ctx) t) - | C.Lambda (n,s,t) -> - let s' = aux ctx s in - C.Lambda (n, s', aux ((decl n s')::ctx) t) - | C.LetIn (n,s,t) -> - (* the term is already in weak head normal form *) - assert false - | C.Appl (h::l) -> C.Appl (h::(List.map (aux ctx) l)) - | C.Appl [] -> assert false - | C.Const (uri,exp_named_subst) -> - C.Const (uri, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst) - | C.MutInd (uri,typeno,exp_named_subst) -> - C.MutInd (uri,typeno, List.map (fun (n,t) -> n,aux ctx t) exp_named_subst) - | C.MutConstruct (uri,typeno,consno,exp_named_subst) -> - C.MutConstruct (uri, typeno, consno, - List.map (fun (n,t) -> n,aux ctx t) exp_named_subst) - | C.MutCase (sp,i,outt,t,pl) -> - C.MutCase (sp,i, aux ctx outt, aux ctx t, List.map (aux ctx) pl) -(*CSC: to be completed, I suppose *) - | C.Fix _ -> t - | C.CoFix _ -> t - -let normalize ?delta ?subst ctx term = -(* prerr_endline ("NORMALIZE:" ^ CicPp.ppterm term); *) - let t = normalize ?delta ?subst ctx term in -(* prerr_endline ("NORMALIZED:" ^ CicPp.ppterm t); *) - t - }}} *) - -(* {{{ performs an head beta/cast reduction -let rec head_beta_reduce ?(delta=false) ?(upto=(-1)) t = - match upto with - 0 -> t - | n -> - match t with - (Cic.Appl (Cic.Lambda (_,_,t)::he'::tl')) -> - let he'' = CicSubstitution.subst he' t in - if tl' = [] then - he'' - else - let he''' = - match he'' with - Cic.Appl l -> Cic.Appl (l@tl') - | _ -> Cic.Appl (he''::tl') - in - head_beta_reduce ~delta ~upto:(upto - 1) he''' - | Cic.Cast (te,_) -> head_beta_reduce ~delta ~upto te - | Cic.Appl (Cic.Const (uri,ens)::tl) as t when delta=true -> - let bo = - match fst (CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri) with - Cic.Constant (_,bo,_,_,_) -> bo - | Cic.Variable _ -> raise ReferenceToVariable - | Cic.CurrentProof (_,_,bo,_,_,_) -> Some bo - | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - in - (match bo with - None -> t - | Some bo -> - head_beta_reduce ~upto - ~delta (Cic.Appl ((CicSubstitution.subst_vars ens bo)::tl))) - | Cic.Const (uri,ens) as t when delta=true -> - let bo = - match fst (CicEnvironment.get_cooked_obj CicUniv.empty_ugraph uri) with - Cic.Constant (_,bo,_,_,_) -> bo - | Cic.Variable _ -> raise ReferenceToVariable - | Cic.CurrentProof (_,_,bo,_,_,_) -> Some bo - | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - in - (match bo with - None -> t - | Some bo -> - head_beta_reduce ~delta ~upto (CicSubstitution.subst_vars ens bo)) - | t -> t - }}} *) - -(* {{{ -let are_convertible ?subst ?metasenv context t1 t2 ugraph = - let before = Unix.gettimeofday () in - let res = are_convertible ?subst ?metasenv context t1 t2 ugraph in - let after = Unix.gettimeofday () in - let diff = after -. before in - if diff > 0.1 then - begin - let nc = List.map (function None -> None | Some (n,_) -> Some n) context in - prerr_endline - ("\n#(" ^ string_of_float diff ^ "):\n" ^ CicPp.pp t1 nc ^ "\n<=>\n" ^ CicPp.pp t2 nc); - end; - res - }}} *) +let head_beta_reduce ?(delta=max_int) ?(upto= -1) ?(subst=[]) t = + head_beta_reduce ~delta ~upto ~subst t [] +;; + +type stack_item = RS.stack_term +type environment_item = RS.env_term + +type machine = int * environment_item list * NCic.term * stack_item list + +let reduce_machine = R.reduce +let from_stack = RS.from_stack +let unwind = R.unwind + +let _ = + NCicUtils.set_head_beta_reduce (fun ~upto t -> head_beta_reduce ~upto t); + NCicPp.set_head_beta_reduce (fun ~upto t -> head_beta_reduce ~upto t); +;; + +(* if n < 0, then splits all prods from an arity, returning a sort *) +let rec split_prods ~subst context n te = + match (n, R.whd ~subst context te) with + | (0, _) -> context,te + | (n, C.Sort _) when n <= 0 -> context,te + | (n, C.Prod (name,so,ta)) -> + split_prods ~subst ((name,(C.Decl so))::context) (n - 1) ta + | (_, _) -> raise (AssertFailure (lazy "split_prods")) +;; (* vim:set foldmethod=marker: *)