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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.
+].
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-19 00:02:10 +0000