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|
(* $Id$ *)
Require Export fast_integer.
Require Export zarith_aux.
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 : constr :=
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 $c) ]
with expr : constr :=
expr_plus [ expr($p) "+" expr($c) ] -> [ (Zplus $p $c) ]
| expr_minus [ expr($p) "-" expr($c) ] -> [ (Zminus $p $c) ]
| expr2 [ expr2($e) ] -> [$e]
with expr2 : constr :=
expr_mult [ expr2($p) "*" expr2($c) ] -> [ (Zmult $p $c) ]
| expr1 [ expr1($e) ] -> [$e]
with expr1 : constr :=
expr_abs [ "|" expr($c) "|" ] -> [ (Zabs $c) ]
| expr0 [ expr0($e) ] -> [$e]
with expr0 : constr :=
expr_id [ constr:global($c) ] -> [ $c ]
| expr_com [ "[" constr:constr($c) "]" ] -> [$c]
| expr_appl [ "(" application($a) ")" ] -> [$a]
| expr_num [ number($s) ] -> [$s ]
| expr_negnum [ "-" negnumber($n) ] -> [ $n ]
| expr_inv [ "-" expr0($c) ] -> [ (Zopp $c) ]
with application : constr :=
apply [ application($p) expr($c1) ] -> [ ($p $c1) ]
| pair [ expr($p) "," expr($c) ] -> [ ($p, $c) ]
| appl0 [ expr($a) ] -> [$a]
.
Grammar constr constr0 :=
z_in_com [ "`" znatural:formula($c) "`" ] -> [$c].
Grammar constr pattern :=
z_in_pattern [ "`" znatural:number($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"].
|
