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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 *)
(************************************************************************)
(*i camlp4deps: "grammar/grammar.cma grammar/q_constr.cmo" i*)
open Pp
open Errors
open Util
open Names
open Term
open Termops
open Inductiveops
open ConstrMatching
open Coqlib
open Declarations
open Tacmach.New
(* I implemented the following functions which test whether a term t
is an inductive but non-recursive type, a general conjuction, a
general disjunction, or a type with no constructors.
They are more general than matching with or_term, and_term, etc,
since they do not depend on the name of the type. Hence, they
also work on ad-hoc disjunctions introduced by the user.
-- Eduardo (6/8/97). *)
type 'a matching_function = constr -> 'a option
type testing_function = constr -> bool
let mkmeta n = Nameops.make_ident "X" (Some n)
let meta1 = mkmeta 1
let meta2 = mkmeta 2
let meta3 = mkmeta 3
let meta4 = mkmeta 4
let op2bool = function Some _ -> true | None -> false
let match_with_non_recursive_type t =
match kind_of_term t with
| App _ ->
let (hdapp,args) = decompose_app t in
(match kind_of_term hdapp with
| Ind (ind,u) ->
if not (Global.lookup_mind (fst ind)).mind_finite then
Some (hdapp,args)
else
None
| _ -> None)
| _ -> None
let is_non_recursive_type t = op2bool (match_with_non_recursive_type t)
(* Test dependencies *)
(* NB: we consider also the let-in case in the following function,
since they may appear in types of inductive constructors (see #2629) *)
let rec has_nodep_prod_after n c =
match kind_of_term c with
| Prod (_,_,b) | LetIn (_,_,_,b) ->
( n>0 || not (dependent (mkRel 1) b))
&& (has_nodep_prod_after (n-1) b)
| _ -> true
let has_nodep_prod = has_nodep_prod_after 0
(* A general conjunctive type is a non-recursive with-no-indices inductive
type with only one constructor and no dependencies between argument;
it is strict if it has the form
"Inductive I A1 ... An := C (_:A1) ... (_:An)" *)
(* style: None = record; Some false = conjunction; Some true = strict conj *)
let is_strict_conjunction = function
| Some true -> true
| _ -> false
let is_lax_conjunction = function
| Some false -> true
| _ -> false
let match_with_one_constructor style onlybinary allow_rec t =
let (hdapp,args) = decompose_app t in
let res = match kind_of_term hdapp with
| Ind ind ->
let (mib,mip) = Global.lookup_inductive (fst ind) in
if Int.equal (Array.length mip.mind_consnames) 1
&& (allow_rec || not (mis_is_recursive (fst ind,mib,mip)))
&& (Int.equal mip.mind_nrealargs 0)
then
if is_strict_conjunction style (* strict conjunction *) then
let ctx =
(prod_assum (snd
(decompose_prod_n_assum mib.mind_nparams mip.mind_nf_lc.(0)))) in
if
List.for_all
(fun (_,b,c) -> Option.is_empty b && isRel c && Int.equal (destRel c) mib.mind_nparams) ctx
then
Some (hdapp,args)
else None
else
let ctyp = prod_applist mip.mind_nf_lc.(0) args in
let cargs = List.map pi3 ((prod_assum ctyp)) in
if not (is_lax_conjunction style) || has_nodep_prod ctyp then
(* Record or non strict conjunction *)
Some (hdapp,List.rev cargs)
else
None
else
None
| _ -> None in
match res with
| Some (hdapp, args) when not onlybinary -> res
| Some (hdapp, [_; _]) -> res
| _ -> None
let match_with_conjunction ?(strict=false) ?(onlybinary=false) t =
match_with_one_constructor (Some strict) onlybinary false t
let match_with_record t =
match_with_one_constructor None false false t
let is_conjunction ?(strict=false) ?(onlybinary=false) t =
op2bool (match_with_conjunction ~strict ~onlybinary t)
let is_record t =
op2bool (match_with_record t)
let match_with_tuple t =
let t = match_with_one_constructor None false true t in
Option.map (fun (hd,l) ->
let ind = destInd hd in
let (mib,mip) = Global.lookup_pinductive ind in
let isrec = mis_is_recursive (fst ind,mib,mip) in
(hd,l,isrec)) t
let is_tuple t =
op2bool (match_with_tuple t)
(* A general disjunction type is a non-recursive with-no-indices inductive
type with of which all constructors have a single argument;
it is strict if it has the form
"Inductive I A1 ... An := C1 (_:A1) | ... | Cn : (_:An)" *)
let test_strict_disjunction n lc =
Array.for_all_i (fun i c ->
match (prod_assum (snd (decompose_prod_n_assum n c))) with
| [_,None,c] -> isRel c && Int.equal (destRel c) (n - i)
| _ -> false) 0 lc
let match_with_disjunction ?(strict=false) ?(onlybinary=false) t =
let (hdapp,args) = decompose_app t in
let res = match kind_of_term hdapp with
| Ind (ind,u) ->
let car = constructors_nrealargs ind in
let (mib,mip) = Global.lookup_inductive ind in
if Array.for_all (fun ar -> Int.equal ar 1) car
&& not (mis_is_recursive (ind,mib,mip))
&& (Int.equal mip.mind_nrealargs 0)
then
if strict then
if test_strict_disjunction mib.mind_nparams mip.mind_nf_lc then
Some (hdapp,args)
else
None
else
let cargs =
Array.map (fun ar -> pi2 (destProd (prod_applist ar args)))
mip.mind_nf_lc in
Some (hdapp,Array.to_list cargs)
else
None
| _ -> None in
match res with
| Some (hdapp,args) when not onlybinary -> res
| Some (hdapp,[_; _]) -> res
| _ -> None
let is_disjunction ?(strict=false) ?(onlybinary=false) t =
op2bool (match_with_disjunction ~strict ~onlybinary t)
(* An empty type is an inductive type, possible with indices, that has no
constructors *)
let match_with_empty_type t =
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind ind ->
let (mib,mip) = Global.lookup_pinductive ind in
let nconstr = Array.length mip.mind_consnames in
if Int.equal nconstr 0 then Some hdapp else None
| _ -> None
let is_empty_type t = op2bool (match_with_empty_type t)
(* This filters inductive types with one constructor with no arguments;
Parameters and indices are allowed *)
let match_with_unit_or_eq_type t =
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind ind ->
let (mib,mip) = Global.lookup_pinductive ind in
let constr_types = mip.mind_nf_lc in
let nconstr = Array.length mip.mind_consnames in
let zero_args c = Int.equal (nb_prod c) mib.mind_nparams in
if Int.equal nconstr 1 && zero_args constr_types.(0) then
Some hdapp
else
None
| _ -> None
let is_unit_or_eq_type t = op2bool (match_with_unit_or_eq_type t)
(* A unit type is an inductive type with no indices but possibly
(useless) parameters, and that has no arguments in its unique
constructor *)
let is_unit_type t =
match match_with_conjunction t with
| Some (_,[]) -> true
| _ -> false
(* Checks if a given term is an application of an
inductive binary relation R, so that R has only one constructor
establishing its reflexivity. *)
type equation_kind =
| MonomorphicLeibnizEq of constr * constr
| PolymorphicLeibnizEq of constr * constr * constr
| HeterogenousEq of constr * constr * constr * constr
exception NoEquationFound
let coq_refl_leibniz1_pattern = PATTERN [ forall x:_, _ x x ]
let coq_refl_leibniz2_pattern = PATTERN [ forall A:_, forall x:A, _ A x x ]
let coq_refl_jm_pattern = PATTERN [ forall A:_, forall x:A, _ A x A x ]
open Globnames
let match_with_equation t =
if not (isApp t) then raise NoEquationFound;
let (hdapp,args) = destApp t in
match kind_of_term hdapp with
| Ind (ind,u) ->
if eq_gr (IndRef ind) glob_eq then
Some (build_coq_eq_data()),hdapp,
PolymorphicLeibnizEq(args.(0),args.(1),args.(2))
else if eq_gr (IndRef ind) glob_identity then
Some (build_coq_identity_data()),hdapp,
PolymorphicLeibnizEq(args.(0),args.(1),args.(2))
else if eq_gr (IndRef ind) glob_jmeq then
Some (build_coq_jmeq_data()),hdapp,
HeterogenousEq(args.(0),args.(1),args.(2),args.(3))
else
let (mib,mip) = Global.lookup_inductive ind in
let constr_types = mip.mind_nf_lc in
let nconstr = Array.length mip.mind_consnames in
if Int.equal nconstr 1 then
if is_matching coq_refl_leibniz1_pattern constr_types.(0) then
None, hdapp, MonomorphicLeibnizEq(args.(0),args.(1))
else if is_matching coq_refl_leibniz2_pattern constr_types.(0) then
None, hdapp, PolymorphicLeibnizEq(args.(0),args.(1),args.(2))
else if is_matching coq_refl_jm_pattern constr_types.(0) then
None, hdapp, HeterogenousEq(args.(0),args.(1),args.(2),args.(3))
else raise NoEquationFound
else raise NoEquationFound
| _ -> raise NoEquationFound
let is_inductive_equality ind =
let (mib,mip) = Global.lookup_inductive ind in
let nconstr = Array.length mip.mind_consnames in
Int.equal nconstr 1 && Int.equal (constructor_nrealargs (ind,1)) 0
let match_with_equality_type t =
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind (ind,_) when is_inductive_equality ind -> Some (hdapp,args)
| _ -> None
let is_equality_type t = op2bool (match_with_equality_type t)
let coq_arrow_pattern = PATTERN [ ?X1 -> ?X2 ]
let match_arrow_pattern t =
let result = matches coq_arrow_pattern t in
match Id.Map.bindings result with
| [(m1,arg);(m2,mind)] ->
assert (Id.equal m1 meta1 && Id.equal m2 meta2); (arg, mind)
| _ -> anomaly (Pp.str "Incorrect pattern matching")
let match_with_nottype t =
try
let (arg,mind) = match_arrow_pattern t in
if is_empty_type mind then Some (mind,arg) else None
with PatternMatchingFailure -> None
let is_nottype t = op2bool (match_with_nottype t)
let match_with_forall_term c=
match kind_of_term c with
| Prod (nam,a,b) -> Some (nam,a,b)
| _ -> None
let is_forall_term c = op2bool (match_with_forall_term c)
let match_with_imp_term c=
match kind_of_term c with
| Prod (_,a,b) when not (dependent (mkRel 1) b) ->Some (a,b)
| _ -> None
let is_imp_term c = op2bool (match_with_imp_term c)
let match_with_nodep_ind t =
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind ind ->
let (mib,mip) = Global.lookup_pinductive ind in
if Array.length (mib.mind_packets)>1 then None else
let nodep_constr = has_nodep_prod_after mib.mind_nparams in
if Array.for_all nodep_constr mip.mind_nf_lc then
let params=
if Int.equal mip.mind_nrealargs 0 then args else
fst (List.chop mib.mind_nparams args) in
Some (hdapp,params,mip.mind_nrealargs)
else
None
| _ -> None
let is_nodep_ind t=op2bool (match_with_nodep_ind t)
let match_with_sigma_type t=
let (hdapp,args) = decompose_app t in
match (kind_of_term hdapp) with
| Ind ind ->
let (mib,mip) = Global.lookup_pinductive ind in
if Int.equal (Array.length (mib.mind_packets)) 1 &&
(Int.equal mip.mind_nrealargs 0) &&
(Int.equal (Array.length mip.mind_consnames)1) &&
has_nodep_prod_after (mib.mind_nparams+1) mip.mind_nf_lc.(0) then
(*allowing only 1 existential*)
Some (hdapp,args)
else
None
| _ -> None
let is_sigma_type t=op2bool (match_with_sigma_type t)
(***** Destructing patterns bound to some theory *)
let rec first_match matcher = function
| [] -> raise PatternMatchingFailure
| (pat,check,build_set)::l when check () ->
(try (build_set (),matcher pat)
with PatternMatchingFailure -> first_match matcher l)
| _::l -> first_match matcher l
(*** Equality *)
(* Patterns "(eq ?1 ?2 ?3)" and "(identity ?1 ?2 ?3)" *)
let coq_eq_pattern_gen eq = lazy PATTERN [ %eq ?X1 ?X2 ?X3 ]
let coq_eq_pattern = coq_eq_pattern_gen coq_eq_ref
let coq_identity_pattern = coq_eq_pattern_gen coq_identity_ref
let coq_jmeq_pattern = lazy PATTERN [ %coq_jmeq_ref ?X1 ?X2 ?X3 ?X4 ]
let match_eq eqn eq_pat =
let pat =
try Lazy.force eq_pat
with e when Errors.noncritical e -> raise PatternMatchingFailure
in
match Id.Map.bindings (matches pat eqn) with
| [(m1,t);(m2,x);(m3,y)] ->
assert (Id.equal m1 meta1 && Id.equal m2 meta2 && Id.equal m3 meta3);
PolymorphicLeibnizEq (t,x,y)
| [(m1,t);(m2,x);(m3,t');(m4,x')] ->
assert (Id.equal m1 meta1 && Id.equal m2 meta2 && Id.equal m3 meta3 && Id.equal m4 meta4);
HeterogenousEq (t,x,t',x')
| _ -> anomaly ~label:"match_eq" (Pp.str "an eq pattern should match 3 or 4 terms")
let no_check () = true
let check_jmeq_loaded () = Library.library_is_loaded Coqlib.jmeq_module
let equalities =
[coq_eq_pattern, no_check, build_coq_eq_data;
coq_jmeq_pattern, check_jmeq_loaded, build_coq_jmeq_data;
coq_identity_pattern, no_check, build_coq_identity_data]
let find_eq_data eqn = (* fails with PatternMatchingFailure *)
let d,k = first_match (match_eq eqn) equalities in
let hd,u = destInd (fst (destApp eqn)) in
d,u,k
let extract_eq_args gl = function
| MonomorphicLeibnizEq (e1,e2) ->
let t = pf_type_of gl e1 in (t,e1,e2)
| PolymorphicLeibnizEq (t,e1,e2) -> (t,e1,e2)
| HeterogenousEq (t1,e1,t2,e2) ->
if pf_conv_x gl t1 t2 then (t1,e1,e2)
else raise PatternMatchingFailure
let find_eq_data_decompose gl eqn =
let (lbeq,u,eq_args) = find_eq_data eqn in
(lbeq,u,extract_eq_args gl eq_args)
let find_this_eq_data_decompose gl eqn =
let (lbeq,u,eq_args) =
try (*first_match (match_eq eqn) inversible_equalities*)
find_eq_data eqn
with PatternMatchingFailure ->
errorlabstrm "" (str "No primitive equality found.") in
let eq_args =
try extract_eq_args gl eq_args
with PatternMatchingFailure ->
error "Don't know what to do with JMeq on arguments not of same type." in
(lbeq,u,eq_args)
let match_eq_nf gls eqn eq_pat =
match Id.Map.bindings (pf_matches gls (Lazy.force eq_pat) eqn) with
| [(m1,t);(m2,x);(m3,y)] ->
assert (Id.equal m1 meta1 && Id.equal m2 meta2 && Id.equal m3 meta3);
(t,pf_whd_betadeltaiota gls x,pf_whd_betadeltaiota gls y)
| _ -> anomaly ~label:"match_eq" (Pp.str "an eq pattern should match 3 terms")
let dest_nf_eq gls eqn =
try
snd (first_match (match_eq_nf gls eqn) equalities)
with PatternMatchingFailure ->
error "Not an equality."
(*** Sigma-types *)
let match_sigma ex =
match kind_of_term ex with
| App (f, [| a; p; car; cdr |]) when is_global (Lazy.force coq_exist_ref) f ->
build_sigma (), (snd (destConstruct f), a, p, car, cdr)
| App (f, [| a; p; car; cdr |]) when is_global (Lazy.force coq_existT_ref) f ->
build_sigma_type (), (snd (destConstruct f), a, p, car, cdr)
| _ -> raise PatternMatchingFailure
let find_sigma_data_decompose ex = (* fails with PatternMatchingFailure *)
match_sigma ex
(* Pattern "(sig ?1 ?2)" *)
let coq_sig_pattern = lazy PATTERN [ %coq_sig_ref ?X1 ?X2 ]
let match_sigma t =
match Id.Map.bindings (matches (Lazy.force coq_sig_pattern) t) with
| [(_,a); (_,p)] -> (a,p)
| _ -> anomaly (Pp.str "Unexpected pattern")
let is_matching_sigma t = is_matching (Lazy.force coq_sig_pattern) t
(*** Decidable equalities *)
(* The expected form of the goal for the tactic Decide Equality *)
(* Pattern "{<?1>x=y}+{~(<?1>x=y)}" *)
(* i.e. "(sumbool (eq ?1 x y) ~(eq ?1 x y))" *)
let coq_eqdec_inf_pattern =
lazy PATTERN [ { ?X2 = ?X3 :> ?X1 } + { ~ ?X2 = ?X3 :> ?X1 } ]
let coq_eqdec_inf_rev_pattern =
lazy PATTERN [ { ~ ?X2 = ?X3 :> ?X1 } + { ?X2 = ?X3 :> ?X1 } ]
let coq_eqdec_pattern =
lazy PATTERN [ %coq_or_ref (?X2 = ?X3 :> ?X1) (~ ?X2 = ?X3 :> ?X1) ]
let coq_eqdec_rev_pattern =
lazy PATTERN [ %coq_or_ref (~ ?X2 = ?X3 :> ?X1) (?X2 = ?X3 :> ?X1) ]
let op_or = coq_or_ref
let op_sum = coq_sumbool_ref
let match_eqdec t =
let eqonleft,op,subst =
try true,op_sum,matches (Lazy.force coq_eqdec_inf_pattern) t
with PatternMatchingFailure ->
try false,op_sum,matches (Lazy.force coq_eqdec_inf_rev_pattern) t
with PatternMatchingFailure ->
try true,op_or,matches (Lazy.force coq_eqdec_pattern) t
with PatternMatchingFailure ->
false,op_or,matches (Lazy.force coq_eqdec_rev_pattern) t in
match Id.Map.bindings subst with
| [(_,typ);(_,c1);(_,c2)] ->
eqonleft, Universes.constr_of_global (Lazy.force op), c1, c2, typ
| _ -> anomaly (Pp.str "Unexpected pattern")
(* Patterns "~ ?" and "? -> False" *)
let coq_not_pattern = lazy PATTERN [ ~ _ ]
let coq_imp_False_pattern = lazy PATTERN [ _ -> %coq_False_ref ]
let is_matching_not t = is_matching (Lazy.force coq_not_pattern) t
let is_matching_imp_False t = is_matching (Lazy.force coq_imp_False_pattern) t
(* Remark: patterns that have references to the standard library must
be evaluated lazily (i.e. at the time they are used, not a the time
coqtop starts) *)
|