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
| 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
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) ->
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)
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)
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
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;;
(*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 =
| 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
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' =
| 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' =
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 =
(* 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
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 ->
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
-;;
projects / helm.git / blobdiff