(* $Id$ *)

Require Export Logic.

(* Parsing of things in Logic.v *)

Grammar constr constr1 :=
  conj [ "<" lconstr($l1) "," lconstr($c2) ">" "{" constr($c3) ","
        constr($c4) "}" ] -> [<<(conj $l1 $c2 $c3 $c4)>>]
| proj1 [ "<" lconstr($l1) "," lconstr($c2) ">" "Fst" "{"
        lconstr($l) "}" ] -> [<<(proj1 $l1 $c2 $l)>>]
| proj2 [ "<" lconstr($l1) "," lconstr($c2) ">" "Snd" "{"
        lconstr($l) "}" ] -> [<<(proj2 $l1 $c2 $l)>>]
| IF [ "either" constr($c) "and_then" constr($t) "or_else" constr($e) ] ->
       [<<(IF $c $t $e)>>]
| all [ "<" lconstr($l1) ">" "All" "(" lconstr($l2) ")" ] ->
       [<<(all $l1 $l2)>>]
| eq_expl [ "<" lconstr($l1) ">" constr0($c1) "=" constr0($c2) ] ->
            [<<(eq $l1 $c1 $c2)>>]
| eq_impl [ constr0($c) "=" constr0($c2) ] -> [<<(eq ? $c $c2)>>]

with constr2 :=
  not [ "~" constr2($c) ] -> [<<(not $c)>>]

with constr6 :=
  and [ constr5($c1) "/\\" constr6($c2) ] -> [<<(and $c1 $c2)>>]

with constr7 :=
  or [ constr6($c1) "\\/" constr7($c2) ] -> [<<(or $c1 $c2)>>]

with constr8 :=
  iff [ constr7($c1) "<->" constr8($c2) ] -> [<<(iff $c1 $c2)>>]

with constr10 :=
  allexplicit [ "ALL" ident($x) ":" constr($t) "|" constr($p) ]
                          -> [<<(all $t [$x : $t]$p)>>]
| allimplicit [ "ALL" ident($x) "|" constr($p) ]
                          -> [<<(all ? [$x]$p)>>]
| exexplicit [ "EX" ident($v) ":" constr($t) "|" constr($c1) ]
                          -> [<<(ex $t [$v : $t]$c1)>>]
| eximplicit [ "EX" ident($v) "|" constr($c1) ] 
                          -> [<<(ex ? [$v]$c1)>>]
| ex2explicit [ "EX" ident($v) ":" constr($t) "|" constr($c1) "&"
           constr($c2) ] -> [<<(ex2 $t [$v : $t]$c1 [$v : $t]$c2)>>]
| ex2implicit [ "EX" ident($v) "|" constr($c1) "&" 
           constr($c2) ] -> [<<(ex2 ? [$v]$c1 [$v]$c2)>>].


(* Pretty-printing of things in Logic.v *)

Syntax constr
  level 1:
    equal [<<(eq $_  $t1  $t2)>>] -> [ [<hov 0> $t1:E [0 1]  "=" $t2:E ] ]
  | conj [<<(conj $t1 $t2 $t3 $t4)>>]
      -> [ [<hov 1> [<hov 1> "<" $t1:L "," [0 0] $t2:L ">" ] [0 0]
                    [<hov 1> "{" $t3:L "," [0 0] $t4:L "}"] ] ]
  | IF [<< either $c and_then $t or_else $e >>]
      -> [ [<hov 0> "either" [1 1] $c:E
                [<hov 0> [1 1] "and_then" [1 1] $t:E ]
                [<hov 0> [1 1] "or_else" [1 1] $e:E ]] ]
  ;

  level 2:
    not [<< ~ $t1 >>] -> [ [<hov 0> "~" $t1:E ] ]
  ;

  level 6:
    and [<< $t1 /\ $t2 >>] -> [ [<hov 0> $t1:L [0 0] "/\\" $t2:E ] ]
  ;

  level 7:
    or [<< $t1 \/ $t2 >>] -> [ [<hov 0> $t1:L [0 0]  "\\/" $t2:E ] ]
  ;

  level 8:
    iff [<< $t1 <-> $t2 >>] -> [ [<hov 0> $t1:L [0 0] "<->" $t2:E ] ]
  ;

  level 10:
    all_pred [<<(all $_ $p)>>] -> [ [<hov 4> "All " $p:L ] ]
  | all_imp [<<(all $_ [$x : $T]$t)>>]
       -> [ [<hov 3> "ALL " $x ":" $T:L " |" [1 0] $t:L ] ]

  | ex_pred [<<(ex $_ $p)>>] -> [ [<hov 0> "Ex " $p:L ] ]
  | ex [<<(ex $_ [$x : $T]$P)>>] 
       -> [ [<hov 2> "EX " $x ":" $T:L " |" [1 0] $P:L ] ]

  | ex2_pred [<<(ex2 $_ $p1 $p2)>>]
       -> [ [<hov 3> "Ex2 " $p1:L [1 0] $p2:L ] ]
  | ex2 [<<(ex2 $_ [$x : T]$P1 [$x : $T]$P2)>>] 
       -> [ [<hov 2> "EX " $x ":" $T:L " |" [1 2] $P1:L [1 0] "& " $P2:L] ].