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|
(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(* $Id$ *)
Require Export Rdefinitions.
Axiom NRplus : R->R->R.
Grammar rnatural ident :=
nat_id [ prim:var($id) ] -> [$id]
with rnegnumber :=
neg_expr [ "-" rnumber ($c) ] -> [<<(Ropp $c)>>]
with rnumber :=
with rformula :=
form_expr [ rexpr($p) ] -> [$p]
| form_eq [ rexpr($p) "==" rexpr($c) ] -> [<<(eqT R $p $c)>>]
| form_le [ rexpr($p) "<=" rexpr($c) ] -> [<<(Rle $p $c)>>]
| form_lt [ rexpr($p) "<" rexpr($c) ] -> [<<(Rlt $p $c)>>]
| form_ge [ rexpr($p) ">=" rexpr($c) ] -> [<<(Rge $p $c)>>]
| form_gt [ rexpr($p) ">" rexpr($c) ] -> [<<(Rgt $p $c)>>]
| form_eq_eq [ rexpr($p) "==" rexpr($c) "==" rexpr($c1) ]
-> [<<(eqT R $p $c)/\(eqT R $c $c1)>>]
| form_le_le [ rexpr($p) "<=" rexpr($c) "<=" rexpr($c1) ]
-> [<<(Rle $p $c)/\(Rle $c $c1)>>]
| form_le_lt [ rexpr($p) "<=" rexpr($c) "<" rexpr($c1) ]
-> [<<(Rle $p $c)/\(Rlt $c $c1)>>]
| form_lt_le [ rexpr($p) "<" rexpr($c) "<=" rexpr($c1) ]
-> [<<(Rlt $p $c)/\(Rle $c $c1)>>]
| form_lt_lt [ rexpr($p) "<" rexpr($c) "<" rexpr($c1) ]
-> [<<(Rlt $p $c)/\(Rlt $c $c1)>>]
| form_neq [ rexpr($p) "<>" rexpr($c) ] -> [<< ~(eqT R $p $c)>>]
with rexpr :=
expr_plus [ rexpr($p) "+" rexpr($c) ] -> [<<(Rplus $p $c)>>]
| expr_minus [ rexpr($p) "-" rexpr($c) ] -> [<<(Rminus $p $c)>>]
| rexpr2 [ rexpr2($e) ] -> [$e]
with rexpr2 :=
expr_mult [ rexpr2($p) "*" rexpr2($c) ] -> [<<(Rmult $p $c)>>]
| rexpr0 [ rexpr0($e) ] -> [$e]
with rexpr0 :=
expr_id [ constr:global($c) ] -> [$c]
| expr_hole [ "?" ] -> [<< ? >>]
| expr_com [ "[" constr:constr($c) "]" ] -> [$c]
| expr_appl [ "(" rapplication($a) ")" ] -> [$a]
| expr_num [ rnumber($s) ] -> [$s ]
| expr_negnum [ "-" rnegnumber($n) ] -> [ $n ]
| expr_div [ rexpr0($p) "/" rexpr0($c) ] -> [<<(Rdiv $p $c)>>]
| expr_opp [ "-" rexpr0($c) ] -> [<<(Ropp $c)>>]
| expr_inv [ "1" "/" rexpr0($c) ] -> [<<(Rinv $c)>>]
with rapplication :=
apply [ rapplication($p) rexpr($c1) ] -> [<<($p $c1)>>]
| pair [ rexpr($p) "," rexpr($c) ] -> [<<($p, $c)>>]
| appl0 [ rexpr($a) ] -> [$a].
Grammar command command0 :=
r_in_com [ "``" rnatural:rformula($c) "``" ] -> [$c].
Grammar command atomic_pattern :=
r_in_pattern [ "``" rnatural:rnumber($c) "``" ] -> [$c].
(** pp **)
(* pb: on rajoute des () lorsque les constantes terminent par 1 lors de
l'appel avec NRplus *)
Syntax constr
level 0:
Rle [ (Rle $n1 $n2) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "<= " (REXPR $n2) "``"]]
| Rlt [ (Rlt $n1 $n2) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "< "(REXPR $n2) "``" ]]
| Rge [ (Rge $n1 $n2) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] ">= "(REXPR $n2) "``" ]]
| Rgt [ (Rgt $n1 $n2) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "> "(REXPR $n2) "``" ]]
| Req [ (eqT R $n1 $n2) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "== "(REXPR $n2)"``"]]
| Rneq [ ~(eqT R $n1 $n2) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "<> "(REXPR $n2) "``"]]
| Rle_Rle [ (Rle $n1 $n2)/\(Rle $n2 $n3) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "<= " (REXPR $n2)
[1 0] "<= " (REXPR $n3) "``"]]
| Rle_Rlt [ (Rle $n1 $n2)/\(Rlt $n2 $n3) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "<= "(REXPR $n2)
[1 0] "< " (REXPR $n3) "``"]]
| Rlt_Rle [ (Rlt $n1 $n2)/\(Rle $n2 $n3) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "< " (REXPR $n2)
[1 0] "<= " (REXPR $n3) "``"]]
| Rlt_Rlt [ (Rlt $n1 $n2)/\(Rlt $n2 $n3) ] ->
[[<hov 0> "``" (REXPR $n1) [1 0] "< " (REXPR $n2)
[1 0] "< " (REXPR $n3) "``"]]
| Rzero [ R0 ] -> ["``0``"]
| Rone [ R1 ] -> ["``1``"]
;
level 7:
Rplus [ (Rplus $n1 $n2) ]
-> [ [<hov 0> "``"(REXPR $n1):E "+" [0 0] (REXPR $n2):L "``"] ]
| Rconst [(Rplus $r R1)] -> [$r:"r_printer_outside"]
| Rminus [ (Rminus $n1 $n2) ]
-> [ [<hov 0> "``"(REXPR $n1):E "-" [0 0] (REXPR $n2):L "``"] ]
;
level 6:
Rmult [ (Rmult $n1 $n2) ]
-> [ [<hov 0> "``"(REXPR $n1):E "*" [0 0] (REXPR $n2):L "``"] ]
|Rdiv [ (Rdiv $n1 $n2) ]
-> [ [<hov 0> "``"(REXPR $n1):E "/" [0 0] (REXPR $n2):L "``"] ]
;
level 8:
Ropp [(Ropp $n1)] -> [ [<hov 0> "``" "-"(REXPR $n1):E "``"] ]
|Rinv [(Rinv $n1)] -> [ [<hov 0> "``" "1""/"(REXPR $n1):E "``"] ]
;
level 0:
rescape_inside [<< (REXPR $r) >>] -> [ "[" $r:E "]" ]
;
level 4:
Rappl_inside [<<(REXPR (APPLIST $h ($LIST $t)))>>]
-> [ [<hov 0> "("(REXPR $h):E [1 0] (APPLINSIDETAIL ($LIST $t)):E ")"] ]
| Rappl_inside_tail [<<(APPLINSIDETAIL $h ($LIST $t))>>]
-> [(REXPR $h):E [1 0] (APPLINSIDETAIL ($LIST $t)):E]
| Rappl_inside_one [<<(APPLINSIDETAIL $e)>>] ->[(REXPR $e):E]
| rpair_inside [<<(REXPR <<(pair $s1 $s2 $r1 $r2)>>)>>]
-> [ [<hov 0> "("(REXPR $r1):E "," [1 0] (REXPR $r2):E ")"] ]
;
level 3:
rvar_inside [<<(REXPR ($VAR $i))>>] -> [$i]
| rconst_inside [<<(REXPR (CONST $c))>>] -> [(CONST $c)]
| rmutind_inside [<<(REXPR (MUTIND $i $n))>>]
-> [(MUTIND $i $n)]
| rmutconstruct_inside [<<(REXPR (MUTCONSTRUCT $c1 $c2 $c3))>>]
-> [ (MUTCONSTRUCT $c1 $c2 $c3) ]
| rimplicit_head_inside [<<(REXPR (XTRA "!" $c))>>] -> [ $c ]
| rimplicit_arg_inside [<<(REXPR (XTRA "!" $n $c))>>] -> [ ]
;
level 7:
Rplus_inside
[<<(REXPR <<(Rplus $n1 $n2)>>)>>]
-> [ (REXPR $n1):E "+" [0 0] (REXPR $n2):L ]
| Rminus_inside
[<<(REXPR <<(Rminus $n1 $n2)>>)>>]
-> [ (REXPR $n1):E "-" [0 0] (REXPR $n2):L ]
| NRplus_inside
[<<(REXPR <<(NRplus $n1 $n2)>>)>>]
-> ["(" (REXPR $n1):E "+" [0 0] (REXPR $n2):L ")"]
;
level 6:
Rmult_inside
[<<(REXPR <<(Rmult $n1 $n2)>>)>>]
-> [ (REXPR $n1):E "*" [0 0] (REXPR $n2):L ]
;
level 5:
Ropp_inside [<<(REXPR <<(Ropp $n1)>>)>>] -> [ " -" (REXPR $n1):E ]
|Rinv_inside [<<(REXPR <<(Rinv $n1)>>)>>] -> [ "1""/" (REXPR $n1):E ]
|Rdiv_inside
[<<(REXPR <<(Rdiv $n1 $n2)>>)>>]
-> [ (REXPR $n1):E "/" [0 0] (REXPR $n2):L ]
;
level 0:
Rzero_inside [<<(REXPR <<R0>>)>>] -> ["0"]
| Rone_inside [<<(REXPR <<R1>>)>>] -> ["1"]
| Rconst_inside [<<(REXPR <<(Rplus R1 $r)>>)>>] -> [$r:"r_printer"].
|
