Parse EBNF
Create a simple parser for EBNF grammars. Here is an ebnf grammar in itself and a parser for it in php.
- You can use regular expressions for lexing.
- Generate the calculator in Arithmetic evaluation using an EBNF description of the calculator.
Here are simple parser rules for a calculator taken from the antlr tutorial
expr : term ( ( PLUS | MINUS ) term )* ; term : factor ( ( MULT | DIV ) factor )* ; factor : NUMBER ;
PicoLisp
<lang PicoLisp>(de parse (Str)
(let *L (str Str "") (aggr) ) )
(de aggr ()
(let X (prod) (while (member (car *L) '("+" "-")) (setq X (op (if (= "+" (pop '*L)) "PLUS" "MINUS") X (prod))) ) X ) )
(de prod ()
(let X (term) (while (member (car *L) '("*" "/")) (setq X (op (if (= "*" (pop '*L)) "MULT" "DIV") X (term))) ) X ) )
(de term ()
(let X (pop '*L) (cond ((num? X) X) ((= "+" X) (term)) ((= "-" X) (pack "-" (term))) ((= "(" X) (prog1 (aggr) (pop '*L)))) ) ) )
(de op (Op Ex1 Ex2)
(pack Op " " (subx Ex1) " " (subx Ex2)) )
(de subx (Ex)
(if (sub? " " Ex) (pack "{" Ex "}") Ex) ) )</lang>
Output:
: (parse "1-2 - -3 * (4+5)") -> "MINUS {MINUS 1 2} {MULT -3 {PLUS 4 5}}" : (parse "1-2 - -3 * 4+5") -> "PLUS {MINUS {MINUS 1 2} {MULT -3 4}} 5" : (parse "(1+2+3)*-4/(1+2)") -> "DIV {MULT {PLUS {PLUS 1 2} 3} -4} {PLUS 1 2}"
Tcl
Demonstration lexer and parser. Note that this parser supports parenthesized expressions, making the grammar recursive. <lang tcl>package require Tcl 8.6
- Utilities to make the coroutine easier to use
proc provide args {while {![yield $args]} {yield}} proc next lexer {$lexer 1} proc pushback lexer {$lexer 0}
- Lexical analyzer coroutine core
proc lexer {str} {
yield [info coroutine] set symbols {+ PLUS - MINUS * MULT / DIV ( LPAR ) RPAR} set idx 0 while 1 {
switch -regexp -matchvar m -- $str { {^\s+} { # No special action for whitespace } {^([-+*/()])} { provide [dict get $symbols [lindex $m 1]] [lindex $m 1] $idx } {^(\d+)} { provide NUMBER [lindex $m 1] $idx } {^$} { provide EOT "EOT" $idx return } . { provide PARSE_ERROR [lindex $m 0] $idx } } # Trim the matched string set str [string range $str [string length [lindex $m 0]] end] incr idx [string length [lindex $m 0]]
}
}
- Utility functions to help with making an LL(1) parser; ParseLoop handles
- EBNF looping constructs, ParseSeq handles sequence constructs.
proc ParseLoop {lexer def} {
upvar 1 token token payload payload index index foreach {a b} $def {
if {$b ne "-"} {set b [list set c $b]} lappend m $a $b
} lappend m default {pushback $lexer; break} while 1 {
lassign [next $lexer] token payload index switch -- $token {*}$m if {[set c [catch {uplevel 1 $c} res opt]]} { dict set opt -level [expr {[dict get $opt -level]+1}] return -options $opt $res }
}
} proc ParseSeq {lexer def} {
upvar 1 token token payload payload index index foreach {t s} $def {
lassign [next $lexer] token payload index switch -- $token $t { if {[set c [catch {uplevel 1 $s} res opt]]} { dict set opt -level [expr {[dict get $opt -level]+1}] return -options $opt $res } } EOT { throw SYNTAX "end of text at position $index" } default { throw SYNTAX "\"$payload\" at position $index" }
}
}
- Main parser driver; contains "master" grammar that ensures that the whole
- text is matched and not just a prefix substring. Note also that the parser
- runs the lexer as a coroutine (with a fixed name in this basic demonstration
- code).
proc parse {str} {
set lexer [coroutine l lexer $str] try {
set parsed [parse.expr $lexer] ParseLoop $lexer { EOT { return $parsed } } throw SYNTAX "\"$payload\" at position $index"
} trap SYNTAX msg {
return -code error "syntax error: $msg"
} finally {
catch {rename $lexer ""}
}
}
- Now the descriptions of how to match each production in the grammar...
proc parse.expr {lexer} {
set expr [parse.term $lexer] ParseLoop $lexer {
PLUS - MINUS { set expr [list $token $expr [parse.term $lexer]] }
} return $expr
} proc parse.term {lexer} {
set term [parse.factor $lexer] ParseLoop $lexer {
MULT - DIV { set term [list $token $term [parse.factor $lexer]] }
} return $term
} proc parse.factor {lexer} {
ParseLoop $lexer {
NUMBER { return $payload } MINUS { ParseSeq $lexer { NUMBER {return -$payload} } } LPAR { set result [parse.expr $lexer] ParseSeq $lexer { RPAR {return $result} } break } EOT { throw SYNTAX "end of text at position $index" }
} throw SYNTAX "\"$payload\" at position $index"
}</lang>
<lang tcl># Demonstration code puts [parse "1 - 2 - -3 * 4 + 5"] puts [parse "1 - 2 - -3 * (4 + 5)"]</lang> Output:
PLUS {MINUS {MINUS 1 2} {MULT -3 4}} 5 MINUS {MINUS 1 2} {MULT -3 {PLUS 4 5}}