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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Util
open Pp
open Errors
open Names
open Context
open Vars
(**********************************************************************)
(** Redeclaration of types from module Constr *)
(**********************************************************************)
type contents = Sorts.contents = Pos | Null
type sorts = Sorts.t =
| Prop of contents (** Prop and Set *)
| Type of Univ.universe (** Type *)
type sorts_family = Sorts.family = InProp | InSet | InType
type constr = Constr.t
(** Alias types, for compatibility. *)
type types = Constr.t
(** Same as [constr], for documentation purposes. *)
type existential_key = Constr.existential_key
type existential = Constr.existential
type metavariable = Constr.metavariable
type case_style = Constr.case_style =
LetStyle | IfStyle | LetPatternStyle | MatchStyle | RegularStyle
type case_printing = Constr.case_printing =
{ ind_tags : bool list; cstr_tags : bool list array; style : case_style }
type case_info = Constr.case_info =
{ ci_ind : inductive;
ci_npar : int;
ci_cstr_ndecls : int array;
ci_cstr_nargs : int array;
ci_pp_info : case_printing
}
type cast_kind = Constr.cast_kind =
VMcast | NATIVEcast | DEFAULTcast | REVERTcast
(********************************************************************)
(* Constructions as implemented *)
(********************************************************************)
type rec_declaration = Constr.rec_declaration
type fixpoint = Constr.fixpoint
type cofixpoint = Constr.cofixpoint
type 'constr pexistential = 'constr Constr.pexistential
type ('constr, 'types) prec_declaration =
('constr, 'types) Constr.prec_declaration
type ('constr, 'types) pfixpoint = ('constr, 'types) Constr.pfixpoint
type ('constr, 'types) pcofixpoint = ('constr, 'types) Constr.pcofixpoint
type 'a puniverses = 'a Univ.puniverses
(** Simply type aliases *)
type pconstant = constant puniverses
type pinductive = inductive puniverses
type pconstructor = constructor puniverses
type ('constr, 'types) kind_of_term = ('constr, 'types) Constr.kind_of_term =
| Rel of int
| Var of Id.t
| Meta of metavariable
| Evar of 'constr pexistential
| Sort of sorts
| Cast of 'constr * cast_kind * 'types
| Prod of Name.t * 'types * 'types
| Lambda of Name.t * 'types * 'constr
| LetIn of Name.t * 'constr * 'types * 'constr
| App of 'constr * 'constr array
| Const of pconstant
| Ind of pinductive
| Construct of pconstructor
| Case of case_info * 'constr * 'constr * 'constr array
| Fix of ('constr, 'types) pfixpoint
| CoFix of ('constr, 'types) pcofixpoint
| Proj of projection * 'constr
type values = Constr.values
(**********************************************************************)
(** Redeclaration of functions from module Constr *)
(**********************************************************************)
let set_sort = Sorts.set
let prop_sort = Sorts.prop
let type1_sort = Sorts.type1
let sorts_ord = Sorts.compare
let is_prop_sort = Sorts.is_prop
let family_of_sort = Sorts.family
let univ_of_sort = Sorts.univ_of_sort
let sort_of_univ = Sorts.sort_of_univ
(** {6 Term constructors. } *)
let mkRel = Constr.mkRel
let mkVar = Constr.mkVar
let mkMeta = Constr.mkMeta
let mkEvar = Constr.mkEvar
let mkSort = Constr.mkSort
let mkProp = Constr.mkProp
let mkSet = Constr.mkSet
let mkType = Constr.mkType
let mkCast = Constr.mkCast
let mkProd = Constr.mkProd
let mkLambda = Constr.mkLambda
let mkLetIn = Constr.mkLetIn
let mkApp = Constr.mkApp
let mkConst = Constr.mkConst
let mkProj = Constr.mkProj
let mkInd = Constr.mkInd
let mkConstruct = Constr.mkConstruct
let mkConstU = Constr.mkConstU
let mkIndU = Constr.mkIndU
let mkConstructU = Constr.mkConstructU
let mkConstructUi = Constr.mkConstructUi
let mkCase = Constr.mkCase
let mkFix = Constr.mkFix
let mkCoFix = Constr.mkCoFix
(**********************************************************************)
(** Aliases of functions from module Constr *)
(**********************************************************************)
let eq_constr = Constr.equal
let eq_constr_univs = Constr.eq_constr_univs
let leq_constr_univs = Constr.leq_constr_univs
let eq_constr_nounivs = Constr.eq_constr_nounivs
let kind_of_term = Constr.kind
let constr_ord = Constr.compare
let fold_constr = Constr.fold
let map_puniverses = Constr.map_puniverses
let map_constr = Constr.map
let map_constr_with_binders = Constr.map_with_binders
let iter_constr = Constr.iter
let iter_constr_with_binders = Constr.iter_with_binders
let compare_constr = Constr.compare_head
let hash_constr = Constr.hash
let hcons_sorts = Sorts.hcons
let hcons_constr = Constr.hcons
let hcons_types = Constr.hcons
(**********************************************************************)
(** HERE BEGINS THE INTERESTING STUFF *)
(**********************************************************************)
(**********************************************************************)
(* Non primitive term destructors *)
(**********************************************************************)
(* Destructor operations : partial functions
Raise [DestKO] if the const has not the expected form *)
exception DestKO
(* Destructs a DeBrujin index *)
let destRel c = match kind_of_term c with
| Rel n -> n
| _ -> raise DestKO
(* Destructs an existential variable *)
let destMeta c = match kind_of_term c with
| Meta n -> n
| _ -> raise DestKO
let isMeta c = match kind_of_term c with Meta _ -> true | _ -> false
let isMetaOf mv c =
match kind_of_term c with Meta mv' -> Int.equal mv mv' | _ -> false
(* Destructs a variable *)
let destVar c = match kind_of_term c with
| Var id -> id
| _ -> raise DestKO
(* Destructs a type *)
let isSort c = match kind_of_term c with
| Sort _ -> true
| _ -> false
let destSort c = match kind_of_term c with
| Sort s -> s
| _ -> raise DestKO
let rec isprop c = match kind_of_term c with
| Sort (Prop _) -> true
| Cast (c,_,_) -> isprop c
| _ -> false
let rec is_Prop c = match kind_of_term c with
| Sort (Prop Null) -> true
| Cast (c,_,_) -> is_Prop c
| _ -> false
let rec is_Set c = match kind_of_term c with
| Sort (Prop Pos) -> true
| Cast (c,_,_) -> is_Set c
| _ -> false
let rec is_Type c = match kind_of_term c with
| Sort (Type _) -> true
| Cast (c,_,_) -> is_Type c
| _ -> false
let is_small = Sorts.is_small
let iskind c = isprop c || is_Type c
(* Tests if an evar *)
let isEvar c = match kind_of_term c with Evar _ -> true | _ -> false
let isEvar_or_Meta c = match kind_of_term c with
| Evar _ | Meta _ -> true
| _ -> false
(* Destructs a casted term *)
let destCast c = match kind_of_term c with
| Cast (t1,k,t2) -> (t1,k,t2)
| _ -> raise DestKO
let isCast c = match kind_of_term c with Cast _ -> true | _ -> false
(* Tests if a de Bruijn index *)
let isRel c = match kind_of_term c with Rel _ -> true | _ -> false
let isRelN n c =
match kind_of_term c with Rel n' -> Int.equal n n' | _ -> false
(* Tests if a variable *)
let isVar c = match kind_of_term c with Var _ -> true | _ -> false
let isVarId id c =
match kind_of_term c with Var id' -> Id.equal id id' | _ -> false
(* Tests if an inductive *)
let isInd c = match kind_of_term c with Ind _ -> true | _ -> false
(* Destructs the product (x:t1)t2 *)
let destProd c = match kind_of_term c with
| Prod (x,t1,t2) -> (x,t1,t2)
| _ -> raise DestKO
let isProd c = match kind_of_term c with | Prod _ -> true | _ -> false
(* Destructs the abstraction [x:t1]t2 *)
let destLambda c = match kind_of_term c with
| Lambda (x,t1,t2) -> (x,t1,t2)
| _ -> raise DestKO
let isLambda c = match kind_of_term c with | Lambda _ -> true | _ -> false
(* Destructs the let [x:=b:t1]t2 *)
let destLetIn c = match kind_of_term c with
| LetIn (x,b,t1,t2) -> (x,b,t1,t2)
| _ -> raise DestKO
let isLetIn c = match kind_of_term c with LetIn _ -> true | _ -> false
(* Destructs an application *)
let destApp c = match kind_of_term c with
| App (f,a) -> (f, a)
| _ -> raise DestKO
let destApplication = destApp
let isApp c = match kind_of_term c with App _ -> true | _ -> false
(* Destructs a constant *)
let destConst c = match kind_of_term c with
| Const kn -> kn
| _ -> raise DestKO
let isConst c = match kind_of_term c with Const _ -> true | _ -> false
(* Destructs an existential variable *)
let destEvar c = match kind_of_term c with
| Evar (kn, a as r) -> r
| _ -> raise DestKO
(* Destructs a (co)inductive type named kn *)
let destInd c = match kind_of_term c with
| Ind (kn, a as r) -> r
| _ -> raise DestKO
(* Destructs a constructor *)
let destConstruct c = match kind_of_term c with
| Construct (kn, a as r) -> r
| _ -> raise DestKO
let isConstruct c = match kind_of_term c with Construct _ -> true | _ -> false
(* Destructs a term <p>Case c of lc1 | lc2 .. | lcn end *)
let destCase c = match kind_of_term c with
| Case (ci,p,c,v) -> (ci,p,c,v)
| _ -> raise DestKO
let isCase c = match kind_of_term c with Case _ -> true | _ -> false
let isProj c = match kind_of_term c with Proj _ -> true | _ -> false
let destProj c = match kind_of_term c with
| Proj (p, c) -> (p, c)
| _ -> raise DestKO
let destFix c = match kind_of_term c with
| Fix fix -> fix
| _ -> raise DestKO
let isFix c = match kind_of_term c with Fix _ -> true | _ -> false
let destCoFix c = match kind_of_term c with
| CoFix cofix -> cofix
| _ -> raise DestKO
let isCoFix c = match kind_of_term c with CoFix _ -> true | _ -> false
(******************************************************************)
(* Cast management *)
(******************************************************************)
let rec strip_outer_cast c = match kind_of_term c with
| Cast (c,_,_) -> strip_outer_cast c
| _ -> c
(* Fonction spéciale qui laisse les cast clés sous les Fix ou les Case *)
let under_outer_cast f c = match kind_of_term c with
| Cast (b,k,t) -> mkCast (f b, k, f t)
| _ -> f c
let rec under_casts f c = match kind_of_term c with
| Cast (c,k,t) -> mkCast (under_casts f c, k, t)
| _ -> f c
(******************************************************************)
(* Flattening and unflattening of embedded applications and casts *)
(******************************************************************)
(* flattens application lists throwing casts in-between *)
let collapse_appl c = match kind_of_term c with
| App (f,cl) ->
let rec collapse_rec f cl2 =
match kind_of_term (strip_outer_cast f) with
| App (g,cl1) -> collapse_rec g (Array.append cl1 cl2)
| _ -> mkApp (f,cl2)
in
collapse_rec f cl
| _ -> c
let decompose_app c =
match kind_of_term c with
| App (f,cl) -> (f, Array.to_list cl)
| _ -> (c,[])
let decompose_appvect c =
match kind_of_term c with
| App (f,cl) -> (f, cl)
| _ -> (c,[||])
(****************************************************************************)
(* Functions for dealing with constr terms *)
(****************************************************************************)
(***************************)
(* Other term constructors *)
(***************************)
let mkNamedProd id typ c = mkProd (Name id, typ, subst_var id c)
let mkNamedLambda id typ c = mkLambda (Name id, typ, subst_var id c)
let mkNamedLetIn id c1 t c2 = mkLetIn (Name id, c1, t, subst_var id c2)
(* Constructs either [(x:t)c] or [[x=b:t]c] *)
let mkProd_or_LetIn (na,body,t) c =
match body with
| None -> mkProd (na, t, c)
| Some b -> mkLetIn (na, b, t, c)
let mkNamedProd_or_LetIn (id,body,t) c =
match body with
| None -> mkNamedProd id t c
| Some b -> mkNamedLetIn id b t c
(* Constructs either [(x:t)c] or [c] where [x] is replaced by [b] *)
let mkProd_wo_LetIn (na,body,t) c =
match body with
| None -> mkProd (na, t, c)
| Some b -> subst1 b c
let mkNamedProd_wo_LetIn (id,body,t) c =
match body with
| None -> mkNamedProd id t c
| Some b -> subst1 b (subst_var id c)
(* non-dependent product t1 -> t2 *)
let mkArrow t1 t2 = mkProd (Anonymous, t1, t2)
(* Constructs either [[x:t]c] or [[x=b:t]c] *)
let mkLambda_or_LetIn (na,body,t) c =
match body with
| None -> mkLambda (na, t, c)
| Some b -> mkLetIn (na, b, t, c)
let mkNamedLambda_or_LetIn (id,body,t) c =
match body with
| None -> mkNamedLambda id t c
| Some b -> mkNamedLetIn id b t c
(* prodn n [xn:Tn;..;x1:T1;Gamma] b = (x1:T1)..(xn:Tn)b *)
let prodn n env b =
let rec prodrec = function
| (0, env, b) -> b
| (n, ((v,t)::l), b) -> prodrec (n-1, l, mkProd (v,t,b))
| _ -> assert false
in
prodrec (n,env,b)
(* compose_prod [xn:Tn;..;x1:T1] b = (x1:T1)..(xn:Tn)b *)
let compose_prod l b = prodn (List.length l) l b
(* lamn n [xn:Tn;..;x1:T1;Gamma] b = [x1:T1]..[xn:Tn]b *)
let lamn n env b =
let rec lamrec = function
| (0, env, b) -> b
| (n, ((v,t)::l), b) -> lamrec (n-1, l, mkLambda (v,t,b))
| _ -> assert false
in
lamrec (n,env,b)
(* compose_lam [xn:Tn;..;x1:T1] b = [x1:T1]..[xn:Tn]b *)
let compose_lam l b = lamn (List.length l) l b
let applist (f,l) = mkApp (f, Array.of_list l)
let applistc f l = mkApp (f, Array.of_list l)
let appvect = mkApp
let appvectc f l = mkApp (f,l)
(* to_lambda n (x1:T1)...(xn:Tn)T =
* [x1:T1]...[xn:Tn]T *)
let rec to_lambda n prod =
if Int.equal n 0 then
prod
else
match kind_of_term prod with
| Prod (na,ty,bd) -> mkLambda (na,ty,to_lambda (n-1) bd)
| Cast (c,_,_) -> to_lambda n c
| _ -> errorlabstrm "to_lambda" (mt ())
let rec to_prod n lam =
if Int.equal n 0 then
lam
else
match kind_of_term lam with
| Lambda (na,ty,bd) -> mkProd (na,ty,to_prod (n-1) bd)
| Cast (c,_,_) -> to_prod n c
| _ -> errorlabstrm "to_prod" (mt ())
(* pseudo-reduction rule:
* [prod_app s (Prod(_,B)) N --> B[N]
* with an strip_outer_cast on the first argument to produce a product *)
let prod_app t n =
match kind_of_term (strip_outer_cast t) with
| Prod (_,_,b) -> subst1 n b
| _ ->
errorlabstrm "prod_app"
(str"Needed a product, but didn't find one" ++ fnl ())
(* prod_appvect T [| a1 ; ... ; an |] -> (T a1 ... an) *)
let prod_appvect t nL = Array.fold_left prod_app t nL
(* prod_applist T [ a1 ; ... ; an ] -> (T a1 ... an) *)
let prod_applist t nL = List.fold_left prod_app t nL
let it_mkProd_or_LetIn = List.fold_left (fun c d -> mkProd_or_LetIn d c)
let it_mkLambda_or_LetIn = List.fold_left (fun c d -> mkLambda_or_LetIn d c)
(*********************************)
(* Other term destructors *)
(*********************************)
(* Transforms a product term (x1:T1)..(xn:Tn)T into the pair
([(xn,Tn);...;(x1,T1)],T), where T is not a product *)
let decompose_prod =
let rec prodec_rec l c = match kind_of_term c with
| Prod (x,t,c) -> prodec_rec ((x,t)::l) c
| Cast (c,_,_) -> prodec_rec l c
| _ -> l,c
in
prodec_rec []
(* Transforms a lambda term [x1:T1]..[xn:Tn]T into the pair
([(xn,Tn);...;(x1,T1)],T), where T is not a lambda *)
let decompose_lam =
let rec lamdec_rec l c = match kind_of_term c with
| Lambda (x,t,c) -> lamdec_rec ((x,t)::l) c
| Cast (c,_,_) -> lamdec_rec l c
| _ -> l,c
in
lamdec_rec []
(* Given a positive integer n, transforms a product term (x1:T1)..(xn:Tn)T
into the pair ([(xn,Tn);...;(x1,T1)],T) *)
let decompose_prod_n n =
if n < 0 then error "decompose_prod_n: integer parameter must be positive";
let rec prodec_rec l n c =
if Int.equal n 0 then l,c
else match kind_of_term c with
| Prod (x,t,c) -> prodec_rec ((x,t)::l) (n-1) c
| Cast (c,_,_) -> prodec_rec l n c
| _ -> error "decompose_prod_n: not enough products"
in
prodec_rec [] n
(* Given a positive integer n, transforms a lambda term [x1:T1]..[xn:Tn]T
into the pair ([(xn,Tn);...;(x1,T1)],T) *)
let decompose_lam_n n =
if n < 0 then error "decompose_lam_n: integer parameter must be positive";
let rec lamdec_rec l n c =
if Int.equal n 0 then l,c
else match kind_of_term c with
| Lambda (x,t,c) -> lamdec_rec ((x,t)::l) (n-1) c
| Cast (c,_,_) -> lamdec_rec l n c
| _ -> error "decompose_lam_n: not enough abstractions"
in
lamdec_rec [] n
(* Transforms a product term (x1:T1)..(xn:Tn)T into the pair
([(xn,Tn);...;(x1,T1)],T), where T is not a product *)
let decompose_prod_assum =
let rec prodec_rec l c =
match kind_of_term c with
| Prod (x,t,c) -> prodec_rec (add_rel_decl (x,None,t) l) c
| LetIn (x,b,t,c) -> prodec_rec (add_rel_decl (x,Some b,t) l) c
| Cast (c,_,_) -> prodec_rec l c
| _ -> l,c
in
prodec_rec empty_rel_context
(* Transforms a lambda term [x1:T1]..[xn:Tn]T into the pair
([(xn,Tn);...;(x1,T1)],T), where T is not a lambda *)
let decompose_lam_assum =
let rec lamdec_rec l c =
match kind_of_term c with
| Lambda (x,t,c) -> lamdec_rec (add_rel_decl (x,None,t) l) c
| LetIn (x,b,t,c) -> lamdec_rec (add_rel_decl (x,Some b,t) l) c
| Cast (c,_,_) -> lamdec_rec l c
| _ -> l,c
in
lamdec_rec empty_rel_context
(* Given a positive integer n, transforms a product term (x1:T1)..(xn:Tn)T
into the pair ([(xn,Tn);...;(x1,T1)],T) *)
let decompose_prod_n_assum n =
if n < 0 then
error "decompose_prod_n_assum: integer parameter must be positive";
let rec prodec_rec l n c =
if Int.equal n 0 then l,c
else match kind_of_term c with
| Prod (x,t,c) -> prodec_rec (add_rel_decl (x,None,t) l) (n-1) c
| LetIn (x,b,t,c) -> prodec_rec (add_rel_decl (x,Some b,t) l) (n-1) c
| Cast (c,_,_) -> prodec_rec l n c
| c -> error "decompose_prod_n_assum: not enough assumptions"
in
prodec_rec empty_rel_context n
(* Given a positive integer n, transforms a lambda term [x1:T1]..[xn:Tn]T
into the pair ([(xn,Tn);...;(x1,T1)],T)
Lets in between are not expanded but turn into local definitions,
but n is the actual number of destructurated lambdas. *)
let decompose_lam_n_assum n =
if n < 0 then
error "decompose_lam_n_assum: integer parameter must be positive";
let rec lamdec_rec l n c =
if Int.equal n 0 then l,c
else match kind_of_term c with
| Lambda (x,t,c) -> lamdec_rec (add_rel_decl (x,None,t) l) (n-1) c
| LetIn (x,b,t,c) -> lamdec_rec (add_rel_decl (x,Some b,t) l) n c
| Cast (c,_,_) -> lamdec_rec l n c
| c -> error "decompose_lam_n_assum: not enough abstractions"
in
lamdec_rec empty_rel_context n
(* (nb_lam [na1:T1]...[nan:Tan]c) where c is not an abstraction
* gives n (casts are ignored) *)
let nb_lam =
let rec nbrec n c = match kind_of_term c with
| Lambda (_,_,c) -> nbrec (n+1) c
| Cast (c,_,_) -> nbrec n c
| _ -> n
in
nbrec 0
(* similar to nb_lam, but gives the number of products instead *)
let nb_prod =
let rec nbrec n c = match kind_of_term c with
| Prod (_,_,c) -> nbrec (n+1) c
| Cast (c,_,_) -> nbrec n c
| _ -> n
in
nbrec 0
let prod_assum t = fst (decompose_prod_assum t)
let prod_n_assum n t = fst (decompose_prod_n_assum n t)
let strip_prod_assum t = snd (decompose_prod_assum t)
let strip_prod t = snd (decompose_prod t)
let strip_prod_n n t = snd (decompose_prod_n n t)
let lam_assum t = fst (decompose_lam_assum t)
let lam_n_assum n t = fst (decompose_lam_n_assum n t)
let strip_lam_assum t = snd (decompose_lam_assum t)
let strip_lam t = snd (decompose_lam t)
let strip_lam_n n t = snd (decompose_lam_n n t)
(***************************)
(* Arities *)
(***************************)
(* An "arity" is a term of the form [[x1:T1]...[xn:Tn]s] with [s] a sort.
Such a term can canonically be seen as the pair of a context of types
and of a sort *)
type arity = rel_context * sorts
let destArity =
let rec prodec_rec l c =
match kind_of_term c with
| Prod (x,t,c) -> prodec_rec ((x,None,t)::l) c
| LetIn (x,b,t,c) -> prodec_rec ((x,Some b,t)::l) c
| Cast (c,_,_) -> prodec_rec l c
| Sort s -> l,s
| _ -> anomaly ~label:"destArity" (Pp.str "not an arity")
in
prodec_rec []
let mkArity (sign,s) = it_mkProd_or_LetIn (mkSort s) sign
let rec isArity c =
match kind_of_term c with
| Prod (_,_,c) -> isArity c
| LetIn (_,b,_,c) -> isArity (subst1 b c)
| Cast (c,_,_) -> isArity c
| Sort _ -> true
| _ -> false
(** Kind of type *)
(* Experimental, used in Presburger contrib *)
type ('constr, 'types) kind_of_type =
| SortType of sorts
| CastType of 'types * 'types
| ProdType of Name.t * 'types * 'types
| LetInType of Name.t * 'constr * 'types * 'types
| AtomicType of 'constr * 'constr array
let kind_of_type t = match kind_of_term t with
| Sort s -> SortType s
| Cast (c,_,t) -> CastType (c, t)
| Prod (na,t,c) -> ProdType (na, t, c)
| LetIn (na,b,t,c) -> LetInType (na, b, t, c)
| App (c,l) -> AtomicType (c, l)
| (Rel _ | Meta _ | Var _ | Evar _ | Const _
| Proj _ | Case _ | Fix _ | CoFix _ | Ind _)
-> AtomicType (t,[||])
| (Lambda _ | Construct _) -> failwith "Not a type"
|