(****************************************************************************)
(*                 The Calculus of Inductive Constructions                  *)
(*                                                                          *)
(*                                Projet Coq                                *)
(*                                                                          *)
(*                     INRIA        LRI-CNRS        ENS-CNRS                *)
(*              Rocquencourt         Orsay          Lyon                    *)
(*                                                                          *)
(*                                 Coq V6.3                                 *)
(*                               July 1st 1999                              *)
(*                                                                          *)
(****************************************************************************)
(*                                 Zsyntax.v                                *)
(****************************************************************************)

Require Export fast_integer.
Require Export zarith_aux.

Declare ML Module "g_zsyntax".


Axiom My_special_variable0 : positive->positive.
Axiom My_special_variable1 : positive->positive.

Grammar znatural ident :=
  nat_id [ prim:var($id) ] -> [$id]

with number :=

with negnumber := 

with formula :=
  form_expr [ expr($p) ] -> [$p]
| form_eq [ expr($p) "=" expr($c) ] -> [<<(eq Z $p $c)>>]
| form_le [ expr($p) "<=" expr($c) ] -> [<<(Zle $p $c)>>]
| form_lt [ expr($p) "<" expr($c) ] -> [<<(Zlt $p $c)>>]
| form_ge [ expr($p) ">=" expr($c) ] -> [<<(Zge $p $c)>>]
| form_gt [ expr($p) ">" expr($c) ] -> [<<(Zgt $p $c)>>]
| form_eq_eq [ expr($p) "=" expr($c) "=" expr($c1) ]
              -> [<<(eq Z $p $c)/\(eq Z $c $c1)>>]
| form_le_le [ expr($p) "<=" expr($c) "<=" expr($c1) ]
              -> [<<(Zle $p $c)/\(Zle $c $c1)>>]
| form_le_lt [ expr($p) "<=" expr($c) "<" expr($c1) ]
              -> [<<(Zle $p $c)/\(Zlt $c $c1)>>]
| form_lt_le [ expr($p) "<" expr($c) "<=" expr($c1) ]
              -> [<<(Zlt $p $c)/\(Zle $c $c1)>>]
| form_lt_lt [ expr($p) "<" expr($c) "<" expr($c1) ]
              -> [<<(Zlt $p $c)/\(Zlt $c $c1)>>]
| form_neq  [ expr($p) "<>" expr($c) ] -> [<<~(eq Z $p $c)>>]
| form_comp [ expr($p) "?" "=" expr($c) ] -> [<<(Zcompare $p $c)>>]

with expr :=
  expr_plus [ expr($p) "+" expr($c) ] -> [<<(Zplus $p $c)>>]
| expr_minus [ expr($p) "-" expr($c) ] -> [<<(Zminus $p $c)>>]
| expr2 [ expr2($e) ] -> [$e]

with expr2 :=
  expr_mult [ expr2($p) "*" expr2($c) ] -> [<<(Zmult $p $c)>>]
| expr1 [ expr1($e) ] -> [$e]

with expr1 :=
  expr_abs [ "|" expr($c) "|" ] -> [<<(Zabs $c)>>]
| expr0 [ expr0($e) ] -> [$e]

with expr0 :=
  expr_id [ ident($c) ] -> [$c]
| expr_com [ "[" command:command($c) "]" ] -> [$c]
| expr_appl [ "(" application($a) ")" ] -> [$a]
| expr_num [ number($s) ] -> [$s ]
| expr_negnum [ "-" negnumber($n) ] -> [ $n ]
| expr_inv [ "-" expr0($c) ] -> [<<(Zopp $c)>>] 

with application :=
  apply [ application($p) expr($c1) ] -> [<<($p $c1)>>]
| pair [ expr($p) "," expr($c) ] -> [<<($p,$c)>>]
| appl0 [ expr($a) ] -> [$a]
.

Grammar command command0 :=
  z_in_com [ "`" znatural:formula($c) "`" ] -> [$c].

Grammar command atomic_pattern :=
  z_in_pattern [ "`" znatural:number($c) "`" ] -> [$c].   

(* The symbols "`" "`" must be printed just once at the top of the expession,
  to avoid printings like |``x` + `y`` < `45`| 
  for |x + y < 45|.
  So when a Z-expression is to be printed, its sub-expresssions are
  enclosed into an ast (ZEXPR $subexpr). (ZEXPR $s) is printed like $s
  but without symbols "`" "`" around. *)

(* There is just one problem: NEG and Zopp have the same printing rules.
   If Zopp is opaque, we may not be able to solve a goal like
    ` -5 = -5 ` by reflexivity. (In fact, this precise Goal is solved
  by the Reflexivity tactic, but more complex problems may arise *)
(* SOLUTION : Print (Zopp 5) for constants and -x for variables *)

Syntax constr
  level 0:
    My_special_variable0 [<< My_special_variable0 >>] -> [ "POS" ]
  | My_special_variable1 [<< My_special_variable1 >>] -> [ "NEG" ] 
  | Zle [<<(Zle $n1 $n2)>>] -> 
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "<= " (ZEXPR $n2) "`"]]
  | Zlt [<<(Zlt $n1 $n2)>>] -> 
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "< "(ZEXPR $n2) "`" ]]
  | Zge [<<(Zge $n1 $n2)>>] -> 
      [[<hov 0> "`" (ZEXPR $n1) [1 0] ">= "(ZEXPR $n2) "`" ]]
  | Zgt [<<(Zgt $n1 $n2)>>] -> 
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "> "(ZEXPR $n2) "`" ]]
  | Zcompare [<<(Zcompare $n1 $n2)>>] ->
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "?= " (ZEXPR $n2) "`" ]]
  | Zeq [<<(eq Z $n1 $n2)>>] -> 
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "= "(ZEXPR $n2)"`"]]
  | Zneq [<<~(eq Z $n1 $n2)>>] ->
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "<> "(ZEXPR $n2) "`"]]
  | Zle_Zle [<<(Zle $n1 $n2)/\(Zle $n2 $n3)>>] ->
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "<= " (ZEXPR $n2)
                                [1 0] "<= " (ZEXPR $n3) "`"]]
  | Zle_Zlt [<<(Zle $n1 $n2)/\(Zlt $n2 $n3)>>] ->
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "<= "(ZEXPR $n2)
                                [1 0] "< " (ZEXPR $n3) "`"]]
  | Zlt_Zle [<<(Zlt $n1 $n2)/\(Zle $n2 $n3)>>] ->
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "< " (ZEXPR $n2)
                                [1 0] "<= " (ZEXPR $n3) "`"]]
  | Zlt_Zlt [<<(Zlt $n1 $n2)/\(Zlt $n2 $n3)>>] ->
      [[<hov 0> "`" (ZEXPR $n1) [1 0] "< " (ZEXPR $n2)
                                [1 0] "< " (ZEXPR $n3) "`"]]
  | ZZero [<<ZERO>>] -> ["`0`"]
  | ZPos [<<(POS $r)>>] -> [$r:"positive_printer"]
  | ZNeg [<<(NEG $r)>>] -> [$r:"negative_printer"]
  ;

  level 7:
    Zplus [<<(Zplus $n1 $n2)>>]
      -> [ [<hov 0> "`"(ZEXPR $n1):E "+"  [0 0] (ZEXPR $n2):L "`"] ]
  | Zminus [<<(Zminus $n1 $n2)>>]
      -> [ [<hov 0> "`"(ZEXPR $n1):E "-" [0 0] (ZEXPR $n2):L "`"] ]
  ;

  level 6:
    Zmult [<<(Zmult $n1 $n2)>>]
      -> [ [<hov 0> "`"(ZEXPR $n1):E "*" [0 0] (ZEXPR $n2):L "`"] ]
  ;

  level 8:
    Zopp [<<(Zopp $n1)>>] -> [ [<hov 0> "`" "-"(ZEXPR $n1):E "`"] ]
  | Zopp_POS [<<(Zopp (POS $r))>>] -> 
         [ [<hov 0> "`(" "Zopp" [1 0] $r:"positive_printer_inside"  ")`"] ]
  | Zopp_ZERO [<<(Zopp ZERO)>>] -> [ [<hov 0> "`(" "Zopp" [1 0] "0" ")`"] ]
  | Zopp_NEG [<<(Zopp (NEG $r))>>] ->  
         [ [<hov 0> "`(" "Zopp" [1 0] "(" $r:"negative_printer_inside" "))`"] ]
  ;

  level 4:
    Zabs [<<(Zabs $n1)>>] -> [  [<hov 0> "`|"(ZEXPR $n1):E "|`"] ]
  ;

  level 0:
    escape_inside [(ZEXPR $r)] -> [ "[" $r:E "]" ]
  ;

  level 4:
    Zappl_inside [(ZEXPR (APPLIST $h ($LIST $t)))]
      -> [ [<hov 0> "("(ZEXPR $h):E [1 0] (APPLINSIDETAIL ($LIST $t)):E ")"] ]
  | Zappl_inside_tail [(APPLINSIDETAIL $h ($LIST $t))]
      -> [(ZEXPR $h):E [1 0] (APPLINSIDETAIL ($LIST $t)):E] 
  | Zappl_inside_one [(APPLINSIDETAIL $e)] ->[(ZEXPR $e):E]
  | pair_inside [(ZEXPR <<(pair $s1 $s2 $z1 $z2)>>)] 
      -> [ [<hov 0> "("(ZEXPR $z1):E "," [1 0] (ZEXPR $z2):E ")"] ]
  ;

 level 3:
    var_inside [(ZEXPR ($VAR $i))] -> [$i]
  | const_inside [(ZEXPR (CONST $c))] -> [(CONST $c)]
  | mutind_inside [(ZEXPR (MUTIND $i $n))] 
      -> [(MUTIND $i $n)]
  | mutconstruct_inside [(ZEXPR (MUTCONSTRUCT $c1 $c2 $c3))]
      -> [ (MUTCONSTRUCT $c1 $c2 $c3) ]
  (* Added by JCF, 9/3/98 *)
  | implicit_head_inside [(ZEXPR (XTRA "!" $c))] -> [ $c ]
  | implicit_arg_inside  [(ZEXPR (XTRA "!" $n $c))] -> [ ]

  ;

  level 7:
    Zplus_inside
      [(ZEXPR <<(Zplus $n1 $n2)>>)]
      	 -> [ (ZEXPR $n1):E "+" [0 0] (ZEXPR $n2):L ]
  | Zminus_inside
      [(ZEXPR <<(Zminus $n1 $n2)>>)]
      	 -> [ (ZEXPR $n1):E "-" [0 0] (ZEXPR $n2):L ]
  ;

  level 6:
    Zmult_inside
      [(ZEXPR <<(Zmult $n1 $n2)>>)]
      	 -> [ (ZEXPR $n1):E "*" [0 0] (ZEXPR $n2):L ]
  ;

  level 5:
    Zopp_inside [(ZEXPR <<(Zopp $n1)>>)] -> [ "(-" (ZEXPR $n1):E ")" ]
  ;  

  level 10:
    Zopp_POS_inside [(ZEXPR <<(Zopp (POS $r))>>)] -> 
      	 [ [<hov 0> "Zopp" [1 0] $r:"positive_printer_inside" ] ]
  | Zopp_ZERO_inside [(ZEXPR <<(Zopp ZERO)>>)] -> 
      	 [ [<hov 0> "Zopp" [1 0] "0"] ]
  | Zopp_NEG_inside [(ZEXPR <<(Zopp (NEG $r))>>)] ->  
      	 [ [<hov 0> "Zopp" [1 0] $r:"negative_printer_inside" ] ]
  ;

  level 4:
    Zabs_inside [(ZEXPR <<(Zabs $n1)>>)] -> [ "|" (ZEXPR $n1) "|"]
  ;

  level 0:
    ZZero_inside [(ZEXPR <<ZERO>>)] -> ["0"]
  | ZPos_inside [(ZEXPR <<(POS $p)>>)] -> [$p:"positive_printer_inside"]
  | ZNeg_inside [(ZEXPR <<(NEG $p)>>)] -> 
      	       	       	  [$p:"negative_printer_inside"].



(* $Id: Zsyntax.v,v 1.28 1999/12/07 22:49:44 herbelin Exp $ *)
