X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Ftactics%2FproofEngineReduction.ml;h=3892ace35a14e49b9ad834b2f9de08ee5c93bc14;hb=cc23f034c9419186602d9250456241f2eba90d7c;hp=6d198d4d133e721539c30e77d86196787ff6c1b5;hpb=707c29a9125acc5b1b1fdee6e93ca551744ba946;p=helm.git diff --git a/helm/software/components/tactics/proofEngineReduction.ml b/helm/software/components/tactics/proofEngineReduction.ml index 6d198d4d1..3892ace35 100644 --- a/helm/software/components/tactics/proofEngineReduction.ml +++ b/helm/software/components/tactics/proofEngineReduction.ml @@ -46,83 +46,22 @@ exception WrongUriToInductiveDefinition;; exception WrongUriToConstant;; exception RelToHiddenHypothesis;; -let alpha_equivalence = - let module C = Cic in - let rec aux t t' = - if t = t' then true - else - match t,t' with - 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 (_,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,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 - List.fold_left2 - (fun b t1 t2 -> b && aux t1 t2) true pl pl' - with - Invalid_argument _ -> false) - | C.Fix (i,fl), C.Fix (i',fl') -> - i = i' && - (try - List.fold_left2 - (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 (_,ty,bo) (_,ty',bo') -> - b && aux ty ty' && aux bo bo' - ) true fl fl' - with - Invalid_argument _ -> false) - | _,_ -> 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 +module C = Cic +module S = CicSubstitution + +let debug = false +let prerr_endline = + if debug then prerr_endline else (fun x -> ()) ;; exception WhatAndWithWhatDoNotHaveTheSameLength;; -(* "textual" replacement of several subterms with other ones *) +(* Replaces "textually" in "where" every term in "what" with the corresponding + term in "with_what". The terms in "what" ARE NOT lifted when binders are + crossed. The terms in "with_what" ARE NOT lifted when binders are crossed. + Every free variable in "where" IS NOT lifted by nnn. +*) let replace ~equality ~what ~with_what ~where = - let module C = Cic in let find_image t = let rec find_image_aux = function @@ -147,7 +86,7 @@ let replace ~equality ~what ~with_what ~where = | C.Cast (te,ty) -> C.Cast (aux te, aux ty) | C.Prod (n,s,t) -> C.Prod (n, aux s, aux t) | C.Lambda (n,s,t) -> C.Lambda (n, aux s, aux t) - | C.LetIn (n,s,t) -> C.LetIn (n, aux s, aux t) + | C.LetIn (n,s,ty,t) -> C.LetIn (n, aux s, aux ty, aux t) | C.Appl l -> (* Invariant enforced: no application of an application *) (match List.map aux l with @@ -181,30 +120,35 @@ let replace ~equality ~what ~with_what ~where = aux where ;; -(* replaces in a term a term with another one. *) -(* Lifting are performed as usual. *) -let replace_lifting ~equality ~what ~with_what ~where = - let module C = Cic in - let module S = CicSubstitution in - let find_image what t = +(* Replaces in "where" every term in "what" with the corresponding + term in "with_what". The terms in "what" ARE lifted when binders are + crossed. The terms in "with_what" ARE lifted when binders are crossed. + Every free variable in "where" IS NOT lifted by nnn. + Thus "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" is the + inverse of subst up to the fact that free variables in "where" are NOT + lifted. *) +let replace_lifting ~equality ~context ~what ~with_what ~where = + let find_image ctx what t = let rec find_image_aux = function [],[] -> raise Not_found | what::tl1,with_what::tl2 -> - if equality what t then with_what else find_image_aux (tl1,tl2) + if equality ctx what t then with_what else find_image_aux (tl1,tl2) | _,_ -> raise WhatAndWithWhatDoNotHaveTheSameLength in find_image_aux (what,with_what) in - let rec substaux k what t = + let add_ctx ctx n s = (Some (n, Cic.Decl s))::ctx in + let add_ctx1 ctx n s ty = (Some (n, Cic.Def (s,ty)))::ctx in + let rec substaux k ctx what t = try - S.lift (k-1) (find_image what t) + S.lift (k-1) (find_image ctx what t) with Not_found -> match t with C.Rel n 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 + List.map (function (uri,t) -> uri,substaux k ctx what t) exp_named_subst in C.Var (uri,exp_named_subst') | C.Meta (i, l) -> @@ -212,56 +156,56 @@ let replace_lifting ~equality ~what ~with_what ~where = List.map (function None -> None - | Some t -> Some (substaux k what t) + | Some t -> Some (substaux k ctx what t) ) l in C.Meta(i,l') | C.Sort _ as t -> t | C.Implicit _ as t -> t - | C.Cast (te,ty) -> C.Cast (substaux k what te, substaux k what ty) + | C.Cast (te,ty) -> C.Cast (substaux k ctx what te, substaux k ctx what ty) | C.Prod (n,s,t) -> C.Prod - (n, substaux k what s, substaux (k + 1) (List.map (S.lift 1) what) t) + (n, substaux k ctx what s, substaux (k + 1) (add_ctx ctx n s) (List.map (S.lift 1) what) t) | C.Lambda (n,s,t) -> C.Lambda - (n, substaux k what s, substaux (k + 1) (List.map (S.lift 1) what) t) - | C.LetIn (n,s,t) -> + (n, substaux k ctx what s, substaux (k + 1) (add_ctx ctx n s) (List.map (S.lift 1) what) t) + | C.LetIn (n,s,ty,t) -> C.LetIn - (n, substaux k what s, substaux (k + 1) (List.map (S.lift 1) what) t) + (n, substaux k ctx what s, substaux k ctx what ty, substaux (k + 1) (add_ctx1 ctx n s ty) (List.map (S.lift 1) what) t) | C.Appl (he::tl) -> (* Invariant: no Appl applied to another Appl *) - let tl' = List.map (substaux k what) tl in + let tl' = List.map (substaux k ctx what) tl in begin - match substaux k what he with + match substaux k ctx what he with C.Appl l -> C.Appl (l@tl') | _ as he' -> C.Appl (he'::tl') end | C.Appl _ -> assert false | C.Const (uri,exp_named_subst) -> let exp_named_subst' = - List.map (function (uri,t) -> uri,substaux k what t) exp_named_subst + List.map (function (uri,t) -> uri,substaux k ctx 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 + List.map (function (uri,t) -> uri,substaux k ctx 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 + List.map (function (uri,t) -> uri,substaux k ctx 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.MutCase (sp,i,substaux k ctx what outt, substaux k ctx what t, + List.map (substaux k ctx what) pl) | C.Fix (i,fl) -> let len = List.length fl in let substitutedfl = List.map - (fun (name,i,ty,bo) -> - (name, i, substaux k what ty, - substaux (k+len) (List.map (S.lift len) what) bo) + (fun (name,i,ty,bo) -> (* WRONG CTX *) + (name, i, substaux k ctx what ty, + substaux (k+len) ctx (List.map (S.lift len) what) bo) ) fl in C.Fix (i, substitutedfl) @@ -269,27 +213,29 @@ let replace_lifting ~equality ~what ~with_what ~where = let len = List.length fl in let substitutedfl = List.map - (fun (name,ty,bo) -> - (name, substaux k what ty, - substaux (k+len) (List.map (S.lift len) what) bo) + (fun (name,ty,bo) -> (* WRONG CTX *) + (name, substaux k ctx what ty, + substaux (k+len) ctx (List.map (S.lift len) what) bo) ) fl in C.CoFix (i, substitutedfl) in - substaux 1 what where + substaux 1 context what where ;; -(* replaces in a term a list of terms with other ones. *) -(* Lifting are performed as usual. *) +(* Replaces in "where" every term in "what" with the corresponding + term in "with_what". The terms in "what" ARE NOT lifted when binders are + crossed. The terms in "with_what" ARE lifted when binders are crossed. + Every free variable in "where" IS lifted by nnn. + Thus "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" is the + inverse of subst up to the fact that "what" terms are NOT lifted. *) let replace_lifting_csc nnn ~equality ~what ~with_what ~where = - let module C = Cic in - let module S = CicSubstitution in let find_image t = let rec find_image_aux = function [],[] -> raise Not_found | what::tl1,with_what::tl2 -> - if equality what t then with_what else find_image_aux (tl1,tl2) + if equality what t then with_what else find_image_aux (tl1,tl2) | _,_ -> raise WhatAndWithWhatDoNotHaveTheSameLength in find_image_aux (what,with_what) @@ -322,8 +268,8 @@ let replace_lifting_csc nnn ~equality ~what ~with_what ~where = C.Prod (n, substaux k s, substaux (k + 1) t) | C.Lambda (n,s,t) -> C.Lambda (n, substaux k s, substaux (k + 1) t) - | C.LetIn (n,s,t) -> - C.LetIn (n, substaux k s, substaux (k + 1) t) + | C.LetIn (n,s,ty,t) -> + C.LetIn (n, substaux k s, substaux k ty, substaux (k + 1) t) | C.Appl (he::tl) -> (* Invariant: no Appl applied to another Appl *) let tl' = List.map (substaux k) tl in @@ -373,204 +319,151 @@ let replace_lifting_csc nnn ~equality ~what ~with_what ~where = substaux 1 where ;; -(* Takes a well-typed term and fully reduces it. *) -(*CSC: It does not perform reduction in a Case *) -let reduce context = - let rec reduceaux context l = - let module C = Cic in - let module S = CicSubstitution in - function - C.Rel n as t -> - (match List.nth context (n-1) with - Some (_,C.Decl _) -> if l = [] then t else C.Appl (t::l) - | Some (_,C.Def (bo,_)) -> reduceaux context l (S.lift n bo) - | None -> raise RelToHiddenHypothesis - ) - | C.Var (uri,exp_named_subst) -> - let exp_named_subst' = - reduceaux_exp_named_subst context l exp_named_subst - in - (let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in - match o 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 - | C.Cast (te,ty) -> - C.Cast (reduceaux context l te, reduceaux context l ty) - | C.Prod (name,s,t) -> - assert (l = []) ; - C.Prod (name, - reduceaux context [] s, - reduceaux ((Some (name,C.Decl s))::context) [] t) - | C.Lambda (name,s,t) -> - (match l with - [] -> - C.Lambda (name, - reduceaux context [] s, - reduceaux ((Some (name,C.Decl s))::context) [] t) - | he::tl -> reduceaux context tl (S.subst he t) - (* when name is Anonimous the substitution should be superfluous *) - ) - | C.LetIn (n,s,t) -> - reduceaux context l (S.subst (reduceaux context [] s) t) - | C.Appl (he::tl) -> - let tl' = List.map (reduceaux context []) tl in - reduceaux context (tl'@l) he - | C.Appl [] -> raise (Impossible 1) - | C.Const (uri,exp_named_subst) -> - let exp_named_subst' = - reduceaux_exp_named_subst context l exp_named_subst - in - (let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in - match o 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) -> - 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) -> - let (_,_,body) = List.nth fl i in - let body' = - let counter = ref (List.length fl) in - List.fold_right - (fun _ -> decr counter ; S.subst (C.CoFix (!counter,fl))) - fl - body - in - reduceaux context [] body' - | C.Appl (C.CoFix (i,fl) :: tl) -> - let (_,_,body) = List.nth fl i in - let body' = - let counter = ref (List.length fl) in - List.fold_right - (fun _ -> decr counter ; S.subst (C.CoFix (!counter,fl))) - fl - body - in - let tl' = List.map (reduceaux context []) tl in - reduceaux context tl' body' - | 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) = - let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph mutind in - match o with - C.InductiveDefinition (tl,_,r,_) -> - let (_,_,arity,_) = List.nth tl i in - (arity,r) - | _ -> raise WrongUriToInductiveDefinition - in - let ts = - 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 _ -> - raise (Impossible 2) (* we don't trust our whd ;-) *) - | _ -> - let outtype' = reduceaux context [] outtype in - let term' = reduceaux context [] term in - let pl' = List.map (reduceaux context []) pl in - let res = - C.MutCase (mutind,i,outtype',term',pl') - in - if l = [] then res else C.Appl (res::l) - ) - | C.Fix (i,fl) -> - let tys = - List.map (function (name,_,ty,_) -> Some (C.Name name, C.Decl ty)) fl - in - let t' () = - let fl' = - List.map - (function (n,recindex,ty,bo) -> - (n,recindex,reduceaux context [] ty, reduceaux (tys@context) [] bo) - ) fl - in - C.Fix (i, fl') - in - let (_,recindex,_,body) = List.nth fl i in - let recparam = - try - Some (List.nth l recindex) - with - _ -> None - in - (match recparam with - Some recparam -> - (match reduceaux context [] recparam with - C.MutConstruct _ - | C.Appl ((C.MutConstruct _)::_) -> - let body' = - let counter = ref (List.length fl) in - List.fold_right - (fun _ -> decr counter ; S.subst (C.Fix (!counter,fl))) - fl - body - in - (* Possible optimization: substituting whd recparam in l*) - reduceaux context l body' - | _ -> if l = [] then t' () else C.Appl ((t' ())::l) - ) - | None -> if l = [] then t' () else C.Appl ((t' ())::l) - ) - | C.CoFix (i,fl) -> - let tys = - List.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) fl - in - let t' = - let fl' = - List.map - (function (n,ty,bo) -> - (n,reduceaux context [] ty, reduceaux (tys@context) [] bo) - ) fl - in - 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) +(* This is like "replace_lifting_csc 1 ~with_what:[Rel 1; ... ; Rel 1]" + up to the fact that the index to start from can be specified *) +let replace_with_rel_1_from ~equality ~what = + let rec find_image t = function + | [] -> false + | hd :: tl -> equality t hd || find_image t tl + in + let rec subst_term k t = + if find_image t what then C.Rel k else inspect_term k t + and inspect_term k = function + | C.Rel i -> if i < k then C.Rel i else C.Rel (succ i) + | C.Sort _ as t -> t + | C.Implicit _ as t -> t + | C.Var (uri, enss) -> + let enss = List.map (subst_ens k) enss in + C.Var (uri, enss) + | C.Const (uri ,enss) -> + let enss = List.map (subst_ens k) enss in + C.Const (uri, enss) + | C.MutInd (uri, tyno, enss) -> + let enss = List.map (subst_ens k) enss in + C.MutInd (uri, tyno, enss) + | C.MutConstruct (uri, tyno, consno, enss) -> + let enss = List.map (subst_ens k) enss in + C.MutConstruct (uri, tyno, consno, enss) + | C.Meta (i, mss) -> + let mss = List.map (subst_ms k) mss in + C.Meta(i, mss) + | C.Cast (t, v) -> C.Cast (subst_term k t, subst_term k v) + | C.Appl ts -> + let ts = List.map (subst_term k) ts in + C.Appl ts + | C.MutCase (uri, tyno, outty, t, cases) -> + let cases = List.map (subst_term k) cases in + C.MutCase (uri, tyno, subst_term k outty, subst_term k t, cases) + | C.Prod (n, v, t) -> + C.Prod (n, subst_term k v, subst_term (succ k) t) + | C.Lambda (n, v, t) -> + C.Lambda (n, subst_term k v, subst_term (succ k) t) + | C.LetIn (n, v, ty, t) -> + C.LetIn (n, subst_term k v, subst_term k ty, subst_term (succ k) t) + | C.Fix (i, fixes) -> + let fixesno = List.length fixes in + let fixes = List.map (subst_fix fixesno k) fixes in + C.Fix (i, fixes) + | C.CoFix (i, cofixes) -> + let cofixesno = List.length cofixes in + let cofixes = List.map (subst_cofix cofixesno k) cofixes in + C.CoFix (i, cofixes) + and subst_ens k (uri, t) = uri, subst_term k t + and subst_ms k = function + | None -> None + | Some t -> Some (subst_term k t) + and subst_fix fixesno k (n, ind, ty, bo) = + n, ind, subst_term k ty, subst_term (k + fixesno) bo + and subst_cofix cofixesno k (n, ty, bo) = + n, subst_term k ty, subst_term (k + cofixesno) bo +in +subst_term + +let unfold ?what context where = + let contextlen = List.length context in + let first_is_the_expandable_head_of_second context' t1 t2 = + match t1,t2 with + Cic.Const (uri,_), Cic.Const (uri',_) + | Cic.Var (uri,_), Cic.Var (uri',_) + | Cic.Const (uri,_), Cic.Appl (Cic.Const (uri',_)::_) + | Cic.Var (uri,_), Cic.Appl (Cic.Var (uri',_)::_) -> UriManager.eq uri uri' + | Cic.Const _, _ + | Cic.Var _, _ -> false + | Cic.Rel n, Cic.Rel m + | Cic.Rel n, Cic.Appl (Cic.Rel m::_) -> + n + (List.length context' - contextlen) = m + | Cic.Rel _, _ -> false + | _,_ -> + raise + (ProofEngineTypes.Fail + (lazy "The term to unfold is not a constant, a variable or a bound variable ")) in - reduceaux context [] + let appl he tl = + if tl = [] then he else Cic.Appl (he::tl) in + let cannot_delta_expand t = + raise + (ProofEngineTypes.Fail + (lazy ("The term " ^ CicPp.ppterm t ^ " cannot be delta-expanded"))) in + let rec hd_delta_beta context tl = + function + Cic.Rel n as t -> + (try + match List.nth context (n-1) with + Some (_,Cic.Decl _) -> cannot_delta_expand t + | Some (_,Cic.Def (bo,_)) -> + CicReduction.head_beta_reduce + (appl (CicSubstitution.lift n bo) tl) + | None -> raise RelToHiddenHypothesis + with + Failure _ -> assert false) + | Cic.Const (uri,exp_named_subst) as t -> + let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in + (match o with + Cic.Constant (_,Some body,_,_,_) -> + CicReduction.head_beta_reduce + (appl (CicSubstitution.subst_vars exp_named_subst body) tl) + | Cic.Constant (_,None,_,_,_) -> cannot_delta_expand t + | Cic.Variable _ -> raise ReferenceToVariable + | Cic.CurrentProof _ -> raise ReferenceToCurrentProof + | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition + ) + | Cic.Var (uri,exp_named_subst) as t -> + let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in + (match o with + Cic.Constant _ -> raise ReferenceToConstant + | Cic.CurrentProof _ -> raise ReferenceToCurrentProof + | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition + | Cic.Variable (_,Some body,_,_,_) -> + CicReduction.head_beta_reduce + (appl (CicSubstitution.subst_vars exp_named_subst body) tl) + | Cic.Variable (_,None,_,_,_) -> cannot_delta_expand t + ) + | Cic.Appl [] -> assert false + | Cic.Appl (he::tl) -> hd_delta_beta context tl he + | t -> cannot_delta_expand t + in + let context_and_matched_term_list = + match what with + None -> [context, where] + | Some what -> + let res = + ProofEngineHelpers.locate_in_term + ~equality:first_is_the_expandable_head_of_second + what ~where context + in + if res = [] then + raise + (ProofEngineTypes.Fail + (lazy ("Term "^ CicPp.ppterm what ^ " not found in " ^ CicPp.ppterm where))) + else + res + in + let reduced_terms = + List.map + (function (context,where) -> hd_delta_beta context [] where) + context_and_matched_term_list in + let whats = List.map snd context_and_matched_term_list in + replace ~equality:(==) ~what:whats ~with_what:reduced_terms ~where ;; exception WrongShape;; @@ -595,8 +488,6 @@ exception AlreadySimplified;; (*CSC: It does not perform simplification in a Case *) let simpl context = - let module C = Cic in - let module S = CicSubstitution in (* a simplified term is active if it can create a redex when used as an *) (* actual parameter *) let rec is_active = @@ -652,7 +543,7 @@ let simpl context = | he::tl -> reduceaux context tl (S.subst he t) (* when name is Anonimous the substitution should be superfluous *) ) - | C.LetIn (n,s,t) -> + | C.LetIn (n,s,ty,t) -> reduceaux context l (S.subst (reduceaux context [] s) t) | C.Appl (he::tl) -> let tl' = List.map (reduceaux context []) tl in @@ -750,8 +641,12 @@ let simpl context = if l = [] then res else C.Appl (res::l) ) | C.Fix (i,fl) -> - let tys = - List.map (function (name,_,ty,_) -> Some (C.Name name, C.Decl ty)) fl + let tys,_ = + List.fold_left + (fun (types,len) (n,_,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl in let t' () = let fl' = @@ -788,8 +683,12 @@ let simpl context = | None -> if l = [] then t' () else C.Appl ((t' ())::l) ) | C.CoFix (i,fl) -> - let tys = - List.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) fl + let tys,_ = + List.fold_left + (fun (types,len) (n,ty,_) -> + (Some (C.Name n,(C.Decl (CicSubstitution.lift len ty)))::types, + len+1) + ) ([],0) fl in let t' = let fl' = @@ -804,9 +703,16 @@ let simpl context = and reduceaux_exp_named_subst context l = List.map (function uri,t -> uri,reduceaux context [] t) (**** Step 2 ****) + and reduce_with_no_hope_to_fold_back t l = + prerr_endline "reduce_with_no_hope_to_fold_back"; + let simplified = reduceaux context l t in + let t' = if l = [] then t else C.Appl (t::l) in + if t' = simplified then + raise AlreadySimplified + else + simplified + and try_delta_expansion context l term body = - let module C = Cic in - let module S = CicSubstitution in try let res,constant_args = let rec aux rev_constant_args l = @@ -820,7 +726,7 @@ let simpl context = (* be superfluous *) aux (he::rev_constant_args) tl (S.subst he t) end - | C.LetIn (_,s,t) -> + | C.LetIn (_,s,_,t) -> aux rev_constant_args l (S.subst s t) | C.Fix (i,fl) -> let (_,recindex,_,body) = List.nth fl i in @@ -859,28 +765,153 @@ let simpl context = let simplified_term_to_fold = reduceaux context [] delta_expanded_term_to_fold in - replace_lifting (=) [simplified_term_to_fold] [term_to_fold] res + replace_lifting ~equality:(fun _ x y -> x = y) ~context + ~what:[simplified_term_to_fold] ~with_what:[term_to_fold] ~where:res with WrongShape -> + let rec skip_lambda n = function + | Cic.Lambda (_,_,t) -> skip_lambda (n+1) t | t -> t, n + in + let is_fix uri = + match fst(CicEnvironment.get_obj CicUniv.oblivion_ugraph uri) with + | Cic.Constant (_,Some bo, _, _,_) -> + (let t, _ = skip_lambda 0 bo in + match t with | Cic.Fix _ -> true | _ -> false) + | _ -> false + in + let guess_recno uri = + prerr_endline ("GUESS: " ^ UriManager.string_of_uri uri); + match fst(CicEnvironment.get_obj CicUniv.oblivion_ugraph uri) with + | Cic.Constant (_,Some bo, _, _,_ ) -> + let t, n = skip_lambda 0 bo in + (match t with + | Cic.Fix (i,fl) -> + let _,recno,_,_ = List.nth fl i in + prerr_endline ("GUESSED: " ^ string_of_int recno ^ " after " ^ + string_of_int n ^ " lambdas"); + recno + n + | _ -> assert false) + | _ -> assert false + in + let original_args = l in (**** Step 3.2 ****) let rec aux l = function - C.Lambda (name,s,t) -> + | C.Lambda (name,s,t) -> (match l with - [] -> raise AlreadySimplified + | [] -> raise AlreadySimplified | he::tl -> (* when name is Anonimous the substitution should *) (* be superfluous *) aux tl (S.subst he t)) - | C.LetIn (_,s,t) -> aux l (S.subst s t) - | t -> - let simplified = reduceaux context l t in - let t' = if l = [] then t else C.Appl (t::l) in - if t' = simplified then - raise AlreadySimplified + | C.LetIn (_,s,_,t) -> aux l (S.subst s t) + | Cic.Appl (Cic.Const (uri,_) :: args) as t when is_fix uri -> + let recno = + prerr_endline ("cerco : " ^ string_of_int (guess_recno uri) + ^ " in: " ^ String.concat " " + (List.map (fun x -> CicPp.ppterm x) args)); + prerr_endline ("e piglio il rispettivo in :"^String.concat " " + (List.map (fun x -> CicPp.ppterm x) original_args)); + (* look for args[regno] in saved_args *) + let wanted = List.nth (args@l) (guess_recno uri) in + let rec aux n = function + | [] -> n (* DA CAPIRE *) + | t::_ when t = wanted -> n + | _::tl -> aux (n+1) tl + in + aux 0 original_args + in + if recno = List.length original_args then + reduce_with_no_hope_to_fold_back t l else - simplified - in + let simplified = reduceaux context l t in + let rec mk_implicits = function + | n,_::tl when n = recno -> + Cic.Implicit None :: (mk_implicits (n+1,tl)) + | n,arg::tl -> arg :: (mk_implicits (n+1,tl)) + | _,[] -> [] + in + (* we try to fold back constant that do not expand to Fix *) + let _ = prerr_endline + ("INIZIO (" ^ string_of_int recno ^ ") : " ^ CicPp.ppterm + simplified) in + let term_to_fold = + Cic.Appl (term:: mk_implicits (0,original_args)) + in + (try + let term_to_fold, _, metasenv, _ = + CicRefine.type_of_aux' [] context term_to_fold + CicUniv.oblivion_ugraph + in + let _ = + prerr_endline ("RAFFINA: "^CicPp.ppterm term_to_fold) in + let _ = + prerr_endline + ("RAFFINA: "^CicMetaSubst.ppmetasenv [] metasenv) in + let simplified_term_to_fold = unfold context term_to_fold in + let _ = + prerr_endline ("SEMPLIFICA: " ^ + CicPp.ppterm simplified_term_to_fold) + in + let rec do_n f t = + let t1 = f t in + if t1 = t then t else do_n f t1 + in + do_n + (fun simplified -> + let subst = ref [] in + let myunif ctx t1 t2 = + if !subst <> [] then false + else + try + prerr_endline "MUNIF"; + prerr_endline (CicPp.ppterm t1); + prerr_endline "VS"; + prerr_endline (CicPp.ppterm t2 ^ "\n"); + let subst1, _, _ = + CicUnification.fo_unif metasenv ctx t1 t2 + CicUniv.empty_ugraph + in + prerr_endline "UNIFICANO\n\n\n"; + subst := subst1; + true + with + | CicUnification.UnificationFailure s + | CicUnification.Uncertain s + | CicUnification.AssertFailure s -> + prerr_endline (Lazy.force s); false + | CicUtil.Meta_not_found _ -> false + (* + | _ as exn -> + prerr_endline (Printexc.to_string exn); + false*) + in + let t = + replace_lifting myunif context + [simplified_term_to_fold] [term_to_fold] simplified + in + let _ = prerr_endline "UNIFICA" in + if List.length metasenv <> List.length !subst then + let _ = prerr_endline ("SUBST CORTA " ^ + CicMetaSubst.ppsubst !subst ~metasenv) + in + simplified + else + if t = simplified then + let _ = prerr_endline "NULLA DI FATTO" in + simplified + else + let t = CicMetaSubst.apply_subst !subst t in + prerr_endline ("ECCO: " ^ CicPp.ppterm t); t) + simplified + with + | CicRefine.RefineFailure s + | CicRefine.Uncertain s + | CicRefine.AssertFailure s -> + prerr_endline (Lazy.force s); simplified + (*| exn -> prerr_endline (Printexc.to_string exn); simplified*)) + | t -> reduce_with_no_hope_to_fold_back t l + in (try aux l body with AlreadySimplified -> @@ -893,90 +924,3 @@ let simpl context = in reduceaux context [] ;; - -let unfold ?what context where = - let contextlen = List.length context in - let first_is_the_expandable_head_of_second context' t1 t2 = - match t1,t2 with - Cic.Const (uri,_), Cic.Const (uri',_) - | Cic.Var (uri,_), Cic.Var (uri',_) - | Cic.Const (uri,_), Cic.Appl (Cic.Const (uri',_)::_) - | Cic.Var (uri,_), Cic.Appl (Cic.Var (uri',_)::_) -> UriManager.eq uri uri' - | Cic.Const _, _ - | Cic.Var _, _ -> false - | Cic.Rel n, Cic.Rel m - | Cic.Rel n, Cic.Appl (Cic.Rel m::_) -> - n + (List.length context' - contextlen) = m - | Cic.Rel _, _ -> false - | _,_ -> - raise - (ProofEngineTypes.Fail - (lazy "The term to unfold is not a constant, a variable or a bound variable ")) - in - let appl he tl = - if tl = [] then he else Cic.Appl (he::tl) in - let cannot_delta_expand t = - raise - (ProofEngineTypes.Fail - (lazy ("The term " ^ CicPp.ppterm t ^ " cannot be delta-expanded"))) in - let rec hd_delta_beta context tl = - function - Cic.Rel n as t -> - (try - match List.nth context (n-1) with - Some (_,Cic.Decl _) -> cannot_delta_expand t - | Some (_,Cic.Def (bo,_)) -> - CicReduction.head_beta_reduce - (appl (CicSubstitution.lift n bo) tl) - | None -> raise RelToHiddenHypothesis - with - Failure _ -> assert false) - | Cic.Const (uri,exp_named_subst) as t -> - let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in - (match o with - Cic.Constant (_,Some body,_,_,_) -> - CicReduction.head_beta_reduce - (appl (CicSubstitution.subst_vars exp_named_subst body) tl) - | Cic.Constant (_,None,_,_,_) -> cannot_delta_expand t - | Cic.Variable _ -> raise ReferenceToVariable - | Cic.CurrentProof _ -> raise ReferenceToCurrentProof - | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - ) - | Cic.Var (uri,exp_named_subst) as t -> - let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in - (match o with - Cic.Constant _ -> raise ReferenceToConstant - | Cic.CurrentProof _ -> raise ReferenceToCurrentProof - | Cic.InductiveDefinition _ -> raise ReferenceToInductiveDefinition - | Cic.Variable (_,Some body,_,_,_) -> - CicReduction.head_beta_reduce - (appl (CicSubstitution.subst_vars exp_named_subst body) tl) - | Cic.Variable (_,None,_,_,_) -> cannot_delta_expand t - ) - | Cic.Appl [] -> assert false - | Cic.Appl (he::tl) -> hd_delta_beta context tl he - | t -> cannot_delta_expand t - in - let context_and_matched_term_list = - match what with - None -> [context, where] - | Some what -> - let res = - ProofEngineHelpers.locate_in_term - ~equality:first_is_the_expandable_head_of_second - what ~where context - in - if res = [] then - raise - (ProofEngineTypes.Fail - (lazy ("Term "^ CicPp.ppterm what ^ " not found in " ^ CicPp.ppterm where))) - else - res - in - let reduced_terms = - List.map - (function (context,where) -> hd_delta_beta context [] where) - context_and_matched_term_list in - let whats = List.map snd context_and_matched_term_list in - replace ~equality:(==) ~what:whats ~with_what:reduced_terms ~where -;;