X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2FgTopLevel%2FproofEngineReduction.ml;h=21f2cbebf72aa68f375e204345dbed3a52b717c0;hb=7e9ee837f75f38bf01240cdc03dd51c764c2665f;hp=bb724fc758d2736c40a7c199b60898501fe4308a;hpb=86122a3ce11bdf45ecb93f8f7efaffa49bd31fa2;p=helm.git diff --git a/helm/gTopLevel/proofEngineReduction.ml b/helm/gTopLevel/proofEngineReduction.ml index bb724fc75..21f2cbebf 100644 --- a/helm/gTopLevel/proofEngineReduction.ml +++ b/helm/gTopLevel/proofEngineReduction.ml @@ -37,47 +37,47 @@ (* The code of this module is derived from the code of CicReduction *) exception Impossible of int;; -exception ReferenceToDefinition;; -exception ReferenceToAxiom;; +exception ReferenceToConstant;; exception ReferenceToVariable;; exception ReferenceToCurrentProof;; exception ReferenceToInductiveDefinition;; exception WrongUriToInductiveDefinition;; exception RelToHiddenHypothesis;; -(* syntactic_equality up to cookingsno for uris *) -(* (which is often syntactically irrilevant) *) -let syntactic_equality ~alpha_equivalence = +let alpha_equivalence = let module C = Cic in let rec aux t t' = if t = t' then true else match t,t' with - C.Rel _, C.Rel _ - | C.Var _, C.Var _ - | C.Meta _, C.Meta _ - | C.Sort _, C.Sort _ - | C.Implicit, C.Implicit -> false (* we already know that t != t' *) + C.Var (uri1,exp_named_subst1), C.Var (uri2,exp_named_subst2) -> + UriManager.eq uri1 uri2 && + aux_exp_named_subst exp_named_subst1 exp_named_subst2 | C.Cast (te,ty), C.Cast (te',ty') -> aux te te' && aux ty ty' - | C.Prod (n,s,t), C.Prod (n',s',t') -> - (alpha_equivalence || n = n') && aux s s' && aux t t' - | C.Lambda (n,s,t), C.Lambda (n',s',t') -> - (alpha_equivalence || n = n') && aux s s' && aux t t' - | C.LetIn (n,s,t), C.LetIn(n',s',t') -> - (alpha_equivalence || n = n') && aux s s' && aux t t' + | C.Prod (_,s,t), C.Prod (_,s',t') -> + aux s s' && aux t t' + | C.Lambda (_,s,t), C.Lambda (_,s',t') -> + aux s s' && aux t t' + | C.LetIn (_,s,t), C.LetIn(_,s',t') -> + aux s s' && aux t t' | C.Appl l, C.Appl l' -> (try List.fold_left2 (fun b t1 t2 -> b && aux t1 t2) true l l' with Invalid_argument _ -> false) - | C.Const (uri,_), C.Const (uri',_) -> UriManager.eq uri uri' - | C.MutInd (uri,_,i), C.MutInd (uri',_,i') -> - UriManager.eq uri uri' && i = i' - | C.MutConstruct (uri,_,i,j), C.MutConstruct (uri',_,i',j') -> - UriManager.eq uri uri' && i = i' && j = j' - | C.MutCase (sp,_,i,outt,t,pl), C.MutCase (sp',_,i',outt',t',pl') -> + | C.Const (uri,exp_named_subst1), C.Const (uri',exp_named_subst2) -> + UriManager.eq uri uri' && + aux_exp_named_subst exp_named_subst1 exp_named_subst2 + | C.MutInd (uri,i,exp_named_subst1), C.MutInd (uri',i',exp_named_subst2) -> + UriManager.eq uri uri' && i = i' && + aux_exp_named_subst exp_named_subst1 exp_named_subst2 + | C.MutConstruct (uri,i,j,exp_named_subst1), + C.MutConstruct (uri',i',j',exp_named_subst2) -> + UriManager.eq uri uri' && i = i' && j = j' && + aux_exp_named_subst exp_named_subst1 exp_named_subst2 + | C.MutCase (sp,i,outt,t,pl), C.MutCase (sp',i',outt',t',pl') -> UriManager.eq sp sp' && i = i' && aux outt outt' && aux t t' && (try @@ -89,23 +89,31 @@ let syntactic_equality ~alpha_equivalence = i = i' && (try List.fold_left2 - (fun b (name,i,ty,bo) (name',i',ty',bo') -> - b && (alpha_equivalence || name = name') && i = i' && - aux ty ty' && aux bo bo') true fl fl' + (fun b (_,i,ty,bo) (_,i',ty',bo') -> + b && i = i' && aux ty ty' && aux bo bo' + ) true fl fl' with Invalid_argument _ -> false) | C.CoFix (i,fl), C.CoFix (i',fl') -> i = i' && (try List.fold_left2 - (fun b (name,ty,bo) (name',ty',bo') -> - b && (alpha_equivalence || name = name') && - aux ty ty' && aux bo bo') true fl fl' + (fun b (_,ty,bo) (_,ty',bo') -> + b && aux ty ty' && aux bo bo' + ) true fl fl' with Invalid_argument _ -> false) - | _,_ -> false - in - aux + | _,_ -> false (* we already know that t != t' *) + and aux_exp_named_subst exp_named_subst1 exp_named_subst2 = + try + List.fold_left2 + (fun b (uri1,t1) (uri2,t2) -> + b && UriManager.eq uri1 uri2 && aux t1 t2 + ) true exp_named_subst1 exp_named_subst2 + with + Invalid_argument _ -> false + in + aux ;; (* "textual" replacement of a subterm with another one *) @@ -115,7 +123,8 @@ let replace ~equality ~what ~with_what ~where = function t when (equality t what) -> with_what | C.Rel _ as t -> t - | C.Var _ as t -> t + | C.Var (uri,exp_named_subst) -> + C.Var (uri,List.map (function (uri,t) -> uri, aux t) exp_named_subst) | C.Meta _ as t -> t | C.Sort _ as t -> t | C.Implicit as t -> t @@ -128,12 +137,16 @@ let replace ~equality ~what ~with_what ~where = (match List.map aux l with (C.Appl l')::tl -> C.Appl (l'@tl) | l' -> C.Appl l') - | C.Const _ as t -> t - | C.MutInd _ as t -> t - | C.MutConstruct _ as t -> t - | C.MutCase (sp,cookingsno,i,outt,t,pl) -> - C.MutCase (sp,cookingsno,i,aux outt, aux t, - List.map aux pl) + | C.Const (uri,exp_named_subst) -> + C.Const (uri,List.map (function (uri,t) -> uri, aux t) exp_named_subst) + | C.MutInd (uri,i,exp_named_subst) -> + C.MutInd + (uri,i,List.map (function (uri,t) -> uri, aux t) exp_named_subst) + | C.MutConstruct (uri,i,j,exp_named_subst) -> + C.MutConstruct + (uri,i,j,List.map (function (uri,t) -> uri, aux t) exp_named_subst) + | C.MutCase (sp,i,outt,t,pl) -> + C.MutCase (sp,i,aux outt, aux t,List.map aux pl) | C.Fix (i,fl) -> let substitutedfl = List.map @@ -161,7 +174,11 @@ let replace_lifting ~equality ~what ~with_what ~where = function t when (equality t what) -> S.lift (k-1) with_what | C.Rel n as t -> t - | C.Var _ as t -> t + | C.Var (uri,exp_named_subst) -> + let exp_named_subst' = + List.map (function (uri,t) -> uri,substaux k what t) exp_named_subst + in + C.Var (uri,exp_named_subst') | C.Meta (i, l) as t -> let l' = List.map @@ -189,11 +206,23 @@ let replace_lifting ~equality ~what ~with_what ~where = | _ as he' -> C.Appl (he'::tl') end | C.Appl _ -> assert false - | C.Const _ as t -> t - | C.MutInd _ as t -> t - | C.MutConstruct _ as t -> t - | C.MutCase (sp,cookingsno,i,outt,t,pl) -> - C.MutCase (sp,cookingsno,i,substaux k what outt, substaux k what t, + | C.Const (uri,exp_named_subst) -> + let exp_named_subst' = + List.map (function (uri,t) -> uri,substaux k what t) exp_named_subst + in + C.Const (uri,exp_named_subst') + | C.MutInd (uri,i,exp_named_subst) -> + let exp_named_subst' = + List.map (function (uri,t) -> uri,substaux k what t) exp_named_subst + in + C.MutInd (uri,i,exp_named_subst') + | C.MutConstruct (uri,i,j,exp_named_subst) -> + let exp_named_subst' = + List.map (function (uri,t) -> uri,substaux k what t) exp_named_subst + in + C.MutConstruct (uri,i,j,exp_named_subst') + | C.MutCase (sp,i,outt,t,pl) -> + C.MutCase (sp,i,substaux k what outt, substaux k what t, List.map (substaux k what) pl) | C.Fix (i,fl) -> let len = List.length fl in @@ -230,14 +259,20 @@ let reduce context = | Some (_,C.Def bo) -> reduceaux context l (S.lift n bo) | None -> raise RelToHiddenHypothesis ) - | C.Var uri as t -> - (match CicEnvironment.get_cooked_obj uri 0 with - C.Definition _ -> raise ReferenceToDefinition - | C.Axiom _ -> raise ReferenceToAxiom + | C.Var (uri,exp_named_subst) -> + let exp_named_subst' = + reduceaux_exp_named_subst context l exp_named_subst + in + (match CicEnvironment.get_obj uri with + C.Constant _ -> raise ReferenceToConstant | C.CurrentProof _ -> raise ReferenceToCurrentProof | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - | C.Variable (_,None,_) -> if l = [] then t else C.Appl (t::l) - | C.Variable (_,Some body,_) -> reduceaux context l body + | C.Variable (_,None,_,_) -> + let t' = C.Var (uri,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) + | C.Variable (_,Some body,_,_) -> + (reduceaux context l + (CicSubstitution.subst_vars exp_named_subst' body)) ) | C.Meta _ as t -> if l = [] then t else C.Appl (t::l) | C.Sort _ as t -> t (* l should be empty *) @@ -264,17 +299,36 @@ let reduce context = let tl' = List.map (reduceaux context []) tl in reduceaux context (tl'@l) he | C.Appl [] -> raise (Impossible 1) - | C.Const (uri,cookingsno) as t -> - (match CicEnvironment.get_cooked_obj uri cookingsno with - C.Definition (_,body,_,_) -> reduceaux context l body - | C.Axiom _ -> if l = [] then t else C.Appl (t::l) - | C.Variable _ -> raise ReferenceToVariable - | C.CurrentProof (_,_,body,_) -> reduceaux context l body - | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - ) - | C.MutInd (uri,_,_) as t -> if l = [] then t else C.Appl (t::l) - | C.MutConstruct (uri,_,_,_) as t -> if l = [] then t else C.Appl (t::l) - | C.MutCase (mutind,cookingsno,i,outtype,term,pl) -> + | C.Const (uri,exp_named_subst) -> + let exp_named_subst' = + reduceaux_exp_named_subst context l exp_named_subst + in + (match CicEnvironment.get_obj uri with + C.Constant (_,Some body,_,_) -> + (reduceaux context l + (CicSubstitution.subst_vars exp_named_subst' body)) + | C.Constant (_,None,_,_) -> + let t' = C.Const (uri,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) + | C.Variable _ -> raise ReferenceToVariable + | C.CurrentProof (_,_,body,_,_) -> + (reduceaux context l + (CicSubstitution.subst_vars exp_named_subst' body)) + | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition + ) + | C.MutInd (uri,i,exp_named_subst) -> + let exp_named_subst' = + reduceaux_exp_named_subst context l exp_named_subst + in + let t' = C.MutInd (uri,i,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) + | C.MutConstruct (uri,i,j,exp_named_subst) as t -> + let exp_named_subst' = + reduceaux_exp_named_subst context l exp_named_subst + in + let t' = C.MutConstruct (uri,i,j,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) + | C.MutCase (mutind,i,outtype,term,pl) -> let decofix = function C.CoFix (i,fl) as t -> @@ -307,30 +361,23 @@ let reduce context = | t -> t in (match decofix (reduceaux context [] term) with - C.MutConstruct (_,_,_,j) -> reduceaux context l (List.nth pl (j-1)) - | C.Appl (C.MutConstruct (_,_,_,j) :: tl) -> - let (arity, r, num_ingredients) = + C.MutConstruct (_,_,j,_) -> reduceaux context l (List.nth pl (j-1)) + | C.Appl (C.MutConstruct (_,_,j,_) :: tl) -> + let (arity, r) = match CicEnvironment.get_obj mutind with - C.InductiveDefinition (tl,ingredients,r) -> - let (_,_,arity,_) = List.nth tl i - and num_ingredients = - List.fold_right - (fun (k,l) i -> - if k < cookingsno then i + List.length l else i - ) ingredients 0 - in - (arity,r,num_ingredients) + C.InductiveDefinition (tl,_,r) -> + let (_,_,arity,_) = List.nth tl i in + (arity,r) | _ -> raise WrongUriToInductiveDefinition in let ts = - let num_to_eat = r + num_ingredients in - let rec eat_first = - function - (0,l) -> l - | (n,he::tl) when n > 0 -> eat_first (n - 1, tl) - | _ -> raise (Impossible 5) - in - eat_first (num_to_eat,tl) + let rec eat_first = + function + (0,l) -> l + | (n,he::tl) when n > 0 -> eat_first (n - 1, tl) + | _ -> raise (Impossible 5) + in + eat_first (r,tl) in reduceaux context (ts@l) (List.nth pl (j-1)) | C.Cast _ | C.Implicit -> @@ -340,7 +387,7 @@ let reduce context = let term' = reduceaux context [] term in let pl' = List.map (reduceaux context []) pl in let res = - C.MutCase (mutind,cookingsno,i,outtype',term',pl') + C.MutCase (mutind,i,outtype',term',pl') in if l = [] then res else C.Appl (res::l) ) @@ -396,6 +443,8 @@ let reduce context = C.CoFix (i, fl') in if l = [] then t' else C.Appl (t'::l) + and reduceaux_exp_named_subst context l = + List.map (function uri,t -> uri,reduceaux context [] t) in reduceaux context [] ;; @@ -438,15 +487,21 @@ let simpl context = | Some (_,C.Def bo) -> reduceaux context l (S.lift n bo) | None -> raise RelToHiddenHypothesis ) - | C.Var uri as t -> - (match CicEnvironment.get_cooked_obj uri 0 with - C.Definition _ -> raise ReferenceToDefinition - | C.Axiom _ -> raise ReferenceToAxiom - | C.CurrentProof _ -> raise ReferenceToCurrentProof - | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - | C.Variable (_,None,_) -> if l = [] then t else C.Appl (t::l) - | C.Variable (_,Some body,_) -> reduceaux context l body - ) + | C.Var (uri,exp_named_subst) -> + let exp_named_subst' = + reduceaux_exp_named_subst context l exp_named_subst + in + (match CicEnvironment.get_obj uri with + C.Constant _ -> raise ReferenceToConstant + | C.CurrentProof _ -> raise ReferenceToCurrentProof + | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition + | C.Variable (_,None,_,_) -> + let t' = C.Var (uri,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) + | C.Variable (_,Some body,_,_) -> + reduceaux context l + (CicSubstitution.subst_vars exp_named_subst' body) + ) | C.Meta _ as t -> if l = [] then t else C.Appl (t::l) | C.Sort _ as t -> t (* l should be empty *) | C.Implicit as t -> t @@ -472,88 +527,102 @@ let simpl context = let tl' = List.map (reduceaux context []) tl in reduceaux context (tl'@l) he | C.Appl [] -> raise (Impossible 1) - | C.Const (uri,cookingsno) as t -> - (match CicEnvironment.get_cooked_obj uri cookingsno with - C.Definition (_,body,_,_) -> - begin - try - (**** Step 2 ****) - let res,constant_args = - let rec aux rev_constant_args l = - function - C.Lambda (name,s,t) as t' -> - begin - match l with - [] -> raise WrongShape - | he::tl -> - (* when name is Anonimous the substitution should be *) - (* superfluous *) - aux (he::rev_constant_args) tl (S.subst he t) - end - | C.LetIn (_,s,t) -> - aux rev_constant_args l (S.subst s t) - | C.Fix (i,fl) as t -> - let tys = - List.map (function (name,_,ty,_) -> - Some (C.Name name, C.Decl ty)) fl - in - let (_,recindex,_,body) = List.nth fl i in - let recparam = - try - List.nth l recindex - with - _ -> raise AlreadySimplified - in - (match CicReduction.whd context recparam with - C.MutConstruct _ - | C.Appl ((C.MutConstruct _)::_) -> - let body' = - let counter = ref (List.length fl) in - List.fold_right - (function _ -> - decr counter ; S.subst (C.Fix (!counter,fl)) - ) fl body - in - (* Possible optimization: substituting whd *) - (* recparam in l *) - reduceaux (tys@context) l body', - List.rev rev_constant_args - | _ -> raise AlreadySimplified - ) - | _ -> raise WrongShape - in - aux [] l body - in - (**** Step 3 ****) - let term_to_fold = - match constant_args with - [] -> C.Const (uri,cookingsno) - | _ -> C.Appl ((C.Const (uri,cookingsno))::constant_args) + | C.Const (uri,exp_named_subst) -> + let exp_named_subst' = + reduceaux_exp_named_subst context l exp_named_subst + in + (match CicEnvironment.get_obj uri with + C.Constant (_,Some body,_,_) -> + begin + try + (**** Step 2 ****) + let res,constant_args = + let rec aux rev_constant_args l = + function + C.Lambda (name,s,t) as t' -> + begin + match l with + [] -> raise WrongShape + | he::tl -> + (* when name is Anonimous the substitution should *) + (* be superfluous *) + aux (he::rev_constant_args) tl (S.subst he t) + end + | C.LetIn (_,s,t) -> + aux rev_constant_args l (S.subst s t) + | C.Fix (i,fl) as t -> + let tys = + List.map (function (name,_,ty,_) -> + Some (C.Name name, C.Decl ty)) fl + in + let (_,recindex,_,body) = List.nth fl i in + let recparam = + try + List.nth l recindex + with + _ -> raise AlreadySimplified + in + (match CicReduction.whd context recparam with + C.MutConstruct _ + | C.Appl ((C.MutConstruct _)::_) -> + let body' = + let counter = ref (List.length fl) in + List.fold_right + (function _ -> + decr counter ; S.subst (C.Fix (!counter,fl)) + ) fl body + in + (* Possible optimization: substituting whd *) + (* recparam in l *) + reduceaux (tys@context) l body', + List.rev rev_constant_args + | _ -> raise AlreadySimplified + ) + | _ -> raise WrongShape + in + aux [] l (CicSubstitution.subst_vars exp_named_subst' body) in - let reduced_term_to_fold = reduce context term_to_fold in - replace (=) reduced_term_to_fold term_to_fold res - with - WrongShape -> - (* The constant does not unfold to a Fix lambda-abstracted *) - (* w.r.t. zero or more variables. We just perform reduction. *) - reduceaux context l body - | AlreadySimplified -> - (* If we performed delta-reduction, we would find a Fix *) - (* not applied to a constructor. So, we refuse to perform *) - (* delta-reduction. *) - if l = [] then - t - else - C.Appl (t::l) - end - | C.Axiom _ -> if l = [] then t else C.Appl (t::l) + (**** Step 3 ****) + let term_to_fold = + match constant_args with + [] -> C.Const (uri,exp_named_subst') + | _ -> C.Appl ((C.Const(uri,exp_named_subst'))::constant_args) + in + let reduced_term_to_fold = reduce context term_to_fold in + replace (=) reduced_term_to_fold term_to_fold res + with + WrongShape -> + (* The constant does not unfold to a Fix lambda-abstracted *) + (* w.r.t. zero or more variables. We just perform reduction.*) + reduceaux context l + (CicSubstitution.subst_vars exp_named_subst' body) + | AlreadySimplified -> + (* If we performed delta-reduction, we would find a Fix *) + (* not applied to a constructor. So, we refuse to perform *) + (* delta-reduction. *) + let t' = C.Const (uri,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) + end + | C.Constant (_,None,_,_) -> + let t' = C.Const (uri,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) | C.Variable _ -> raise ReferenceToVariable - | C.CurrentProof (_,_,body,_) -> reduceaux context l body + | C.CurrentProof (_,_,body,_,_) -> reduceaux context l body | C.InductiveDefinition _ -> raise ReferenceToInductiveDefinition ) - | C.MutInd (uri,_,_) as t -> if l = [] then t else C.Appl (t::l) - | C.MutConstruct (uri,_,_,_) as t -> if l = [] then t else C.Appl (t::l) - | C.MutCase (mutind,cookingsno,i,outtype,term,pl) -> + | C.MutInd (uri,i,exp_named_subst) -> + let exp_named_subst' = + reduceaux_exp_named_subst context l exp_named_subst + in + let t' = C.MutInd (uri,i,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) + | C.MutConstruct (uri,i,j,exp_named_subst) -> + let exp_named_subst' = + reduceaux_exp_named_subst context l exp_named_subst + in + let t' = C.MutConstruct(uri,i,j,exp_named_subst') in + if l = [] then t' else C.Appl (t'::l) + | C.MutCase (mutind,i,outtype,term,pl) -> let decofix = function C.CoFix (i,fl) as t -> @@ -584,30 +653,23 @@ let simpl context = | t -> t in (match decofix (reduceaux context [] term) with - C.MutConstruct (_,_,_,j) -> reduceaux context l (List.nth pl (j-1)) - | C.Appl (C.MutConstruct (_,_,_,j) :: tl) -> - let (arity, r, num_ingredients) = + C.MutConstruct (_,_,j,_) -> reduceaux context l (List.nth pl (j-1)) + | C.Appl (C.MutConstruct (_,_,j,_) :: tl) -> + let (arity, r) = match CicEnvironment.get_obj mutind with C.InductiveDefinition (tl,ingredients,r) -> - let (_,_,arity,_) = List.nth tl i - and num_ingredients = - List.fold_right - (fun (k,l) i -> - if k < cookingsno then i + List.length l else i - ) ingredients 0 - in - (arity,r,num_ingredients) + let (_,_,arity,_) = List.nth tl i in + (arity,r) | _ -> raise WrongUriToInductiveDefinition in let ts = - let num_to_eat = r + num_ingredients in - let rec eat_first = - function - (0,l) -> l - | (n,he::tl) when n > 0 -> eat_first (n - 1, tl) - | _ -> raise (Impossible 5) - in - eat_first (num_to_eat,tl) + let rec eat_first = + function + (0,l) -> l + | (n,he::tl) when n > 0 -> eat_first (n - 1, tl) + | _ -> raise (Impossible 5) + in + eat_first (r,tl) in reduceaux context (ts@l) (List.nth pl (j-1)) | C.Cast _ | C.Implicit -> @@ -617,7 +679,7 @@ let simpl context = let term' = reduceaux context [] term in let pl' = List.map (reduceaux context []) pl in let res = - C.MutCase (mutind,cookingsno,i,outtype',term',pl') + C.MutCase (mutind,i,outtype',term',pl') in if l = [] then res else C.Appl (res::l) ) @@ -673,6 +735,8 @@ let simpl context = C.CoFix (i, fl') in if l = [] then t' else C.Appl (t'::l) + and reduceaux_exp_named_subst context l = + List.map (function uri,t -> uri,reduceaux context [] t) in reduceaux context [] ;;