(* *)
(******************************************************************************)
+(* $Id$ *)
(* The code of this module is derived from the code of CicReduction *)
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 ->
+ | C.Meta (i, l) ->
let l' =
List.map
(function
S.lift (k-1) (find_image t)
with Not_found ->
match t with
- C.Rel n as t ->
+ C.Rel n ->
if n < k then C.Rel n else C.Rel (n + nnn)
| C.Var (uri,exp_named_subst) ->
let exp_named_subst' =
List.map (function (uri,t) -> uri,substaux k t) exp_named_subst
in
C.Var (uri,exp_named_subst')
- | C.Meta (i, l) as t ->
+ | C.Meta (i, l) ->
let l' =
List.map
(function
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 ->
+ | C.MutConstruct (uri,i,j,exp_named_subst) ->
let exp_named_subst' =
reduceaux_exp_named_subst context l exp_named_subst
in
| C.MutCase (mutind,i,outtype,term,pl) ->
let decofix =
function
- C.CoFix (i,fl) as t ->
- let tys =
- List.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) fl
- in
+ C.CoFix (i,fl) ->
let (_,_,body) = List.nth fl i in
let body' =
let counter = ref (List.length fl) in
in
reduceaux context [] body'
| C.Appl (C.CoFix (i,fl) :: tl) ->
- let tys =
- List.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) fl
- in
let (_,_,body) = List.nth fl i in
let body' =
let counter = ref (List.length fl) in
(* Takes a well-typed term and *)
(* 1) Performs beta-iota-zeta reduction until delta reduction is needed *)
(* 2) Attempts delta-reduction. If the residual is a Fix lambda-abstracted *)
-(* w.r.t. zero or more variables and if the Fix can be reductaed, than it *)
+(* w.r.t. zero or more variables and if the Fix can be reductaed, than it*)
(* is reduced, the delta-reduction is succesfull and the whole algorithm *)
-(* is applied again to the new redex; Step 3) is applied to the result *)
+(* is applied again to the new redex; Step 3.1) is applied to the result *)
(* of the recursive simplification. Otherwise, if the Fix can not be *)
(* reduced, than the delta-reductions fails and the delta-redex is *)
(* not reduced. Otherwise, if the delta-residual is not the *)
-(* lambda-abstraction of a Fix, then it is reduced and the result is *)
-(* directly returned, without performing step 3). *)
-(* 3) Folds the application of the constant to the arguments that did not *)
+(* lambda-abstraction of a Fix, then it performs step 3.2). *)
+(* 3.1) Folds the application of the constant to the arguments that did not *)
(* change in every iteration, i.e. to the actual arguments for the *)
(* lambda-abstractions that precede the Fix. *)
+(* 3.2) Computes the head beta-zeta normal form of the term. Then it tries *)
+(* reductions. If the reduction cannot be performed, it returns the *)
+(* original term (not the head beta-zeta normal form of the definiendum) *)
(*CSC: It does not perform simplification in a Case *)
let simpl context =
let module S = CicSubstitution in
function
C.Rel n as t ->
- (try
- match List.nth context (n-1) with
- Some (_,C.Decl _) -> if l = [] then t else C.Appl (t::l)
- | Some (_,C.Def (bo,_)) ->
- try_delta_expansion context l t (S.lift n bo)
- | None -> raise RelToHiddenHypothesis
- with
- Failure _ -> assert false)
+ (* we never perform delta expansion automatically *)
+ if l = [] then t else C.Appl (t::l)
| C.Var (uri,exp_named_subst) ->
let exp_named_subst' =
reduceaux_exp_named_subst context l exp_named_subst
| 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.Cast (reduceaux context l te, reduceaux context [] ty)
| C.Prod (name,s,t) ->
assert (l = []) ;
C.Prod (name,
| C.MutCase (mutind,i,outtype,term,pl) ->
let decofix =
function
- C.CoFix (i,fl) as t ->
- let tys =
- List.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) fl in
+ C.CoFix (i,fl) ->
let (_,_,body) = List.nth fl i in
let body' =
let counter = ref (List.length fl) in
in
reduceaux context [] body'
| C.Appl (C.CoFix (i,fl) :: tl) ->
- let tys =
- List.map (function (name,ty,_) -> Some (C.Name name, C.Decl ty)) fl in
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'
+ 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
+ (match decofix (CicReduction.whd context term) with
C.MutConstruct (_,_,j,_) -> reduceaux context l (List.nth pl (j-1))
| C.Appl (C.MutConstruct (_,_,j,_) :: tl) ->
let (arity, r) =
let res,constant_args =
let rec aux rev_constant_args l =
function
- C.Lambda (name,s,t) as t' ->
+ C.Lambda (name,s,t) ->
begin
match l with
[] -> raise WrongShape
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
+ | C.Fix (i,fl) ->
let (_,recindex,_,body) = List.nth fl i in
let recparam =
try
in
aux [] l body
in
- (**** Step 3 ****)
+ (**** Step 3.1 ****)
let term_to_fold, delta_expanded_term_to_fold =
match constant_args with
[] -> term,body
replace (=) [simplified_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
+ (**** Step 3.2 ****)
+ let rec aux l =
+ function
+ C.Lambda (name,s,t) ->
+ (match l with
+ [] -> 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
+ if t = simplified then
+ raise AlreadySimplified
+ else
+ simplified
+ in
+ (try aux l body
+ with
+ AlreadySimplified ->
+ if l = [] then term else C.Appl (term::l))
| AlreadySimplified ->
(* If we performed delta-reduction, we would find a Fix *)
(* not applied to a constructor. So, we refuse to perform *)
;;
let unfold ?what context where =
- let first_is_the_expandable_head_of_second t1 t2 =
+ 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.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
- "The term to unfold is neither a constant nor a variable")
+ (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
- ("The term " ^ CicPp.ppterm t ^ " cannot be delta-expanded")) in
+ (lazy ("The term " ^ CicPp.ppterm t ^ " cannot be delta-expanded"))) in
let rec hd_delta_beta context tl =
function
Cic.Rel n as t ->
if res = [] then
raise
(ProofEngineTypes.Fail
- ("Term "^ CicPp.ppterm what ^ " not found in " ^ CicPp.ppterm where))
+ (lazy ("Term "^ CicPp.ppterm what ^ " not found in " ^ CicPp.ppterm where)))
else
res
in
projects / helm.git / blobdiff