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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: Zsyntax.v,v 1.1.2.1 2004/07/16 19:31:44 herbelin Exp $ i*)
-
-Require Export BinInt.
-
-V7only[
-
-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 $c) ]*)
-| form_eq [ expr($p) "=" expr($c) ] -> [ (Coq.Init.Logic.eq ? $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 $c1) ]*)
-| form_eq_eq [ expr($p) "=" expr($c) "=" expr($c1) ]
- -> [ (Coq.Init.Logic.eq ? $p $c)/\(Coq.Init.Logic.eq ? $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) ] -> [ ~(Coq.Init.Logic.eq Z $p $c) ]*)
-| form_neq [ expr($p) "<>" expr($c) ] -> [ ~(Coq.Init.Logic.eq ? $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 $c) ]
-| expr_meta [ zmeta($m) ] -> [ $m ]
-
-with zmeta :=
-| rimpl [ "?" ] -> [ ? ]
-| rmeta0 [ "?" "0" ] -> [ ?0 ]
-| rmeta1 [ "?" "1" ] -> [ ?1 ]
-| rmeta2 [ "?" "2" ] -> [ ?2 ]
-| rmeta3 [ "?" "3" ] -> [ ?3 ]
-| rmeta4 [ "?" "4" ] -> [ ?4 ]
-| rmeta5 [ "?" "5" ] -> [ ?5 ]
-
-with application : constr :=
- apply [ application($p) expr($c1) ] -> [ ($p $c1) ]
-| apply_inject_nat [ "inject_nat" constr:constr($c1) ] -> [ (inject_nat $c1) ]
-| pair [ expr($p) "," expr($c) ] -> [ ($p, $c) ]
-| appl0 [ expr($a) ] -> [$a]
-.
-
-Grammar constr constr0 :=
- z_in_com [ "`" znatural:formula($c) "`" ] -> [$c].
-
-Grammar constr pattern :=
- z_in_pattern [ "`" prim:bigint($c) "`" ] -> [ 'Z: $c ' ].
-
-(* The symbols "`" "`" must be printed just once at the top of the expressions,
- 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), which is printed like \$subexpr
- 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:
- 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_v7 [ ZERO ] -> [ "`0`" ]
- | ZPos_v7 [ (POS $r) ] -> [$r:"positive_printer":9]
- | ZNeg_v7 [ (NEG $r) ] -> [$r:"negative_printer":9]
- ;
-
- 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 $h):E [1 0] (ZAPPLINSIDETAIL ($LIST $t)):E ")"] ]
- | Zappl_inject_nat [ << (ZEXPR (APPLIST <<inject_nat>> $n)) >> ]
- -> [ [<hov 0> "(inject_nat" [1 1] $n:L ")"] ]
- | Zappl_inside_tail [ << (ZAPPLINSIDETAIL $h ($LIST $t)) >> ]
- -> [(ZEXPR $h):E [1 0] (ZAPPLINSIDETAIL ($LIST $t)):E]
- | Zappl_inside_one [ << (ZAPPLINSIDETAIL $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]
- | secvar_inside [ << (ZEXPR (SECVAR $i)) >> ] -> [(SECVAR $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 $c3) ]
-
- | O_inside [ << (ZEXPR << O >>) >> ] -> [ "O" ] (* To shunt Arith printer *)
-
- (* Added by JCF, 9/3/98; updated HH, 11/9/01 *)
- | implicit_head_inside [ << (ZEXPR (APPLISTEXPL ($LIST $c))) >> ]
- -> [ (APPLIST ($LIST $c)) ]
- | implicit_arg_inside [ << (ZEXPR (EXPL "!" $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":9]
- | ZNeg_inside [ << (ZEXPR <<(NEG $p)>>) >>] ->
- [$p:"negative_printer_inside":9]
-.
-].
-
-V7only[
-(* For parsing/printing based on scopes *)
-Module Z_scope.
-
-Infix LEFTA 4 "+" Zplus : Z_scope.
-Infix LEFTA 4 "-" Zminus : Z_scope.
-Infix LEFTA 3 "*" Zmult : Z_scope.
-Notation "- x" := (Zopp x) (at level 0): Z_scope V8only.
-Infix NONA 5 "<=" Zle : Z_scope.
-Infix NONA 5 "<" Zlt : Z_scope.
-Infix NONA 5 ">=" Zge : Z_scope.
-Infix NONA 5 ">" Zgt : Z_scope.
-Infix NONA 5 "?=" Zcompare : Z_scope.
-Notation "x <= y <= z" := (Zle x y)/\(Zle y z)
- (at level 5, y at level 4):Z_scope
- V8only (at level 70, y at next level).
-Notation "x <= y < z" := (Zle x y)/\(Zlt y z)
- (at level 5, y at level 4):Z_scope
- V8only (at level 70, y at next level).
-Notation "x < y < z" := (Zlt x y)/\(Zlt y z)
- (at level 5, y at level 4):Z_scope
- V8only (at level 70, y at next level).
-Notation "x < y <= z" := (Zlt x y)/\(Zle y z)
- (at level 5, y at level 4):Z_scope
- V8only (at level 70, y at next level).
-Notation "x = y = z" := x=y/\y=z : Z_scope
- V8only (at level 70, y at next level).
-
-(* Now a polymorphic notation
-Notation "x <> y" := ~(eq Z x y) (at level 5, no associativity) : Z_scope.
-*)
-
-(* Notation "| x |" (Zabs x) : Z_scope.(* "|" conflicts with THENS *)*)
-
-(* Overwrite the printing of "`x = y`" *)
-Syntax constr level 0:
- Zeq [ (eq Z $n1 $n2) ] -> [[<hov 0> $n1 [1 0] "= " $n2 ]].
-
-Open Scope Z_scope.
-
-End Z_scope.
-].
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