(* 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 mk_appl t l =
+ if l = [] then
+ t
+ else
+ match t with
+ | Cic.Appl l' -> Cic.Appl (l'@l)
+ | _ -> Cic.Appl (t::l)
+ in
(* reduceaux is equal to the reduceaux locally defined inside *)
(* reduce, but for the const case. *)
(**** Step 1 ****)
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) =
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 ->
| Cic.Appl (he::tl) -> hd_delta_beta context tl he
| t -> cannot_delta_expand t
in
- let context, where' =
+ let context_and_matched_term_list =
match what with
- None -> context, where
+ None -> [context, where]
| Some what ->
- try
+ let res =
ProofEngineHelpers.locate_in_term
~equality:first_is_the_expandable_head_of_second
what ~where context
- with
- ProofEngineHelpers.TermNotFound ->
+ in
+ 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
- let reduced_term = hd_delta_beta context [] where' in
- match what with
- None -> reduced_term
- | Some what ->
- replace ~equality:first_is_the_expandable_head_of_second
- ~what:[what] ~with_what:[reduced_term] ~where
+ 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