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-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
-(*i $Id: Rsyntax.v,v 1.1.2.1 2004/07/16 19:31:35 herbelin Exp $ i*)
-
-Require Export Rdefinitions.
-
-Axiom NRplus : R->R.
-Axiom NRmult : R->R.
-
-V7only[
-Grammar rnatural ident :=
- nat_id [ prim:var($id) ] -> [$id]
-
-with rnegnumber : constr :=
- neg_expr [ "-" rnumber ($c) ] -> [ (Ropp $c) ]
-
-with rnumber :=
-
-with rformula : constr :=
- form_expr [ rexpr($p) ] -> [ $p ]
-(* | form_eq [ rexpr($p) "==" rexpr($c) ] -> [ (eqT R $p $c) ] *)
-| form_eq [ rexpr($p) "==" rexpr($c) ] -> [ (eqT ? $p $c) ]
-| form_eq2 [ rexpr($p) "=" rexpr($c) ] -> [ (eqT ? $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 $c1) ]
-*)
-| form_eq_eq [ rexpr($p) "==" rexpr($c) "==" rexpr($c1) ]
- -> [ (eqT ? $p $c)/\(eqT ? $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 ? $p $c) ]
-
-with rexpr : constr :=
- expr_plus [ rexpr($p) "+" rexpr($c) ] -> [ (Rplus $p $c) ]
-| expr_minus [ rexpr($p) "-" rexpr($c) ] -> [ (Rminus $p $c) ]
-| rexpr2 [ rexpr2($e) ] -> [ $e ]
-
-with rexpr2 : constr :=
- expr_mult [ rexpr2($p) "*" rexpr2($c) ] -> [ (Rmult $p $c) ]
-| rexpr0 [ rexpr0($e) ] -> [ $e ]
-
-
-with rexpr0 : constr :=
- expr_id [ constr:global($c) ] -> [ $c ]
-| expr_com [ "[" constr:constr($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 $c) ]
-| expr_inv [ "/" rexpr0($c) ] -> [ (Rinv $c) ]
-| expr_meta [ meta($m) ] -> [ $m ]
-
-with meta :=
-| rimpl [ "?" ] -> [ ? ]
-| rmeta0 [ "?" "0" ] -> [ ?0 ]
-| rmeta1 [ "?" "1" ] -> [ ?1 ]
-| rmeta2 [ "?" "2" ] -> [ ?2 ]
-| rmeta3 [ "?" "3" ] -> [ ?3 ]
-| rmeta4 [ "?" "4" ] -> [ ?4 ]
-| rmeta5 [ "?" "5" ] -> [ ?5 ]
-
-with rapplication : constr :=
- apply [ rapplication($p) rexpr($c1) ] -> [ ($p $c1) ]
-| pair [ rexpr($p) "," rexpr($c) ] -> [ ($p, $c) ]
-| appl0 [ rexpr($a) ] -> [ $a ].
-
-Grammar constr constr0 :=
- r_in_com [ "``" rnatural:rformula($c) "``" ] -> [ $c ].
-
-Grammar constr atomic_pattern :=
- r_in_pattern [ "``" rnatural:rnumber($c) "``" ] -> [ $c ].
-
-(*i* pp **)
-
-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 "``"] ]
- | Rodd_outside [(Rplus R1 $r)] -> [ $r:"r_printer_odd_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 "``"] ]
- | Reven_outside [ (Rmult (Rplus R1 R1) $r) ] -> [ $r:"r_printer_even_outside"]
- | 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> "``" "/"(REXPR $n1):E "``"] ]
- ;
-
- level 0:
- rescape_inside [<< (REXPR $r) >>] -> [ "[" $r:E "]" ]
- ;
-
- level 4:
- Rappl_inside [<<(REXPR (APPLIST $h ($LIST $t)))>>]
- -> [ [<hov 0> "("(REXPR $h):E [1 0] (RAPPLINSIDETAIL ($LIST $t)):E ")"] ]
- | Rappl_inside_tail [<<(RAPPLINSIDETAIL $h ($LIST $t))>>]
- -> [(REXPR $h):E [1 0] (RAPPLINSIDETAIL ($LIST $t)):E]
- | Rappl_inside_one [<<(RAPPLINSIDETAIL $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]
- | rsecvar_inside [<<(REXPR (SECVAR $i))>>] -> [(SECVAR $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 $r)>>)>>] -> [ "(" "1" "+" (REXPR $r):L ")"]
- ;
-
- level 6:
- Rmult_inside
- [<<(REXPR <<(Rmult $n1 $n2)>>)>>]
- -> [ (REXPR $n1):E "*" (REXPR $n2):L ]
- | NRmult_inside
- [<<(REXPR <<(NRmult $r)>>)>>] -> [ "(" "2" "*" (REXPR $r):L ")"]
- ;
-
- level 5:
- Ropp_inside [<<(REXPR <<(Ropp $n1)>>)>>] -> [ " -" (REXPR $n1):E ]
- | Rinv_inside [<<(REXPR <<(Rinv $n1)>>)>>] -> [ "/" (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"]
- | Rodd_inside [<<(REXPR <<(Rplus R1 $r)>>)>>] -> [ $r:"r_printer_odd" ]
- | Reven_inside [<<(REXPR <<(Rmult (Rplus R1 R1) $r)>>)>>] -> [ $r:"r_printer_even" ]
-.
-
-(* For parsing/printing based on scopes *)
-Module R_scope.
-
-Infix "<=" Rle (at level 5, no associativity) : R_scope V8only.
-Infix "<" Rlt (at level 5, no associativity) : R_scope V8only.
-Infix ">=" Rge (at level 5, no associativity) : R_scope V8only.
-Infix ">" Rgt (at level 5, no associativity) : R_scope V8only.
-Infix "+" Rplus (at level 4) : R_scope V8only.
-Infix "-" Rminus (at level 4) : R_scope V8only.
-Infix "*" Rmult (at level 3) : R_scope V8only.
-Infix "/" Rdiv (at level 3) : R_scope V8only.
-Notation "- x" := (Ropp x) (at level 0) : R_scope V8only.
-Notation "x == y == z" := (eqT R x y)/\(eqT R y z)
- (at level 5, y at level 4, no associtivity): R_scope.
-Notation "x <= y <= z" := (Rle x y)/\(Rle y z)
- (at level 5, y at level 4) : R_scope
- V8only.
-Notation "x <= y < z" := (Rle x y)/\(Rlt y z)
- (at level 5, y at level 4) : R_scope
- V8only.
-Notation "x < y < z" := (Rlt x y)/\(Rlt y z)
- (at level 5, y at level 4) : R_scope
- V8only.
-Notation "x < y <= z" := (Rlt x y)/\(Rle y z)
- (at level 5, y at level 4) : R_scope
- V8only.
-Notation "/ x" := (Rinv x) (at level 0): R_scope
- V8only.
-
-Open Local Scope R_scope.
-End R_scope.
-].
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