Takmela: Parsing arithmetic expression example (more complicated and with ambiguity)

An aritmetic expression grammar that is both more complicated than 1+2, and has a deliberate (and useless) ambiguity, to show how the more interesting parts of Takmela work.

// Arithmetic expressions with deliberate ambiguity
// to see how Takmela handles it
// e.g 1+a(3) -> [1+a](3) or 1 + [a(3)]

expr :   expr '+' term
       | term ;
term : 
      ID 
    | NUM
    | expr '(' expr ')';
    
ID: [a-zA-Z] [a-zA-Z0-9]*;

NUM: [0-9]+;

WS skip: [ \r\n\t]*;

12 + f(13)

Hint: Hovering over a graph expands it

Trace appears confusing? This might help

Call start nonterminal
	#0: Called e/0 at the top level (will process) Processing e/0 codePos e → • e `+` t inputPos 0 Calling: e/0 with Cont e/0 ; e → e• `+` t ; e [already processed] Processing e/0 codePos e → • t inputPos 0 Calling: t/0 with Cont e/0 ; e → t• ; e [will process] Processing t/0 codePos t → • ID inputPos 0 Match ID to 12, fail Processing t/0 codePos t → • NUM inputPos 0 Match NUM to 12, matched; inputPos now 1 Reached end of rule, success! t/0 → 1 Processing t/0 codePos t → • e `(` e `)` inputPos 0 Calling: e/0 with Cont t/0 ; t → e• `(` e `)` ; t [already processed] New continuations: e/0 → t/0 ; t → e• `(` e `)` e/0 → e/0 ; e → e• `+` t t/0 → e/0 ; e → t•
t/0 → 1, t('12')
Iteration 0
Worklist - successes jS t/0 → 1 木t('12') Worklist - continuations nJ e/0 → t/0 ; t → e• `(` e `)` ; t nJ e/0 → e/0 ; e → e• `+` t ; e S⤚ t/0 → e/0 ; e → t• ; e
	#1: JoinS: t/0 → 1 木t('12') will resume cont: e/0 ; e → t• ; e Processing e/0 codePos e → t• inputPos 1 Reached end of rule, success! e/0 → 1
t/0 → 1, t('12') e/0 → 1, e(t('12'))
Iteration 1
Worklist - successes jS e/0 → 1 木e(t('12')) Worklist - continuations
	#2: JoinS: e/0 → 1 木e(t('12')) will resume cont: t/0 ; t → e• `(` e `)` ; t Processing t/0 codePos t → e• `(` e `)` inputPos 1 Match `(` to +, fail
t/0 → 1, t('12') e/0 → 1, e(t('12'))
	#3: JoinS: e/0 → 1 木e(t('12')) will resume cont: e/0 ; e → e• `+` t ; e Processing e/0 codePos e → e• `+` t inputPos 1 Match + to +, matched; inputPos now 2 Calling: t/2 with Cont e/0 ; e → e `+` t• ; e(e(t('12')), '+') [will process] Processing t/2 codePos t → • ID inputPos 2 Match ID to f, matched; inputPos now 3 Reached end of rule, success! t/2 → 3 Processing t/2 codePos t → • NUM inputPos 2 Match NUM to f, fail Processing t/2 codePos t → • e `(` e `)` inputPos 2 Calling: e/2 with Cont t/2 ; t → e• `(` e `)` ; t [will process] Processing e/2 codePos e → • e `+` t inputPos 2 Calling: e/2 with Cont e/2 ; e → e• `+` t ; e [already processed] Processing e/2 codePos e → • t inputPos 2 Calling: t/2 with Cont e/2 ; e → t• ; e [already processed] New continuations: e/2 → t/2 ; t → e• `(` e `)` e/2 → e/2 ; e → e• `+` t t/2 → e/2 ; e → t• t/2 → e/0 ; e → e `+` t•
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f')
	#4: JoinS: e/0 → 1 木e(t('12')) will resume cont: Root/0 ; Root → e• ; Root ×Didn't reach end of input, not a successful parse
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f')
Iteration 2
Worklist - successes jS t/2 → 3 木t('f') Worklist - continuations nJ e/2 → t/2 ; t → e• `(` e `)` ; t nJ e/2 → e/2 ; e → e• `+` t ; e S⤚ t/2 → e/2 ; e → t• ; e S⤚ t/2 → e/0 ; e → e `+` t• ; e(e(t('12')), '+')
	#5: JoinS: t/2 → 3 木t('f') will resume cont: e/2 ; e → t• ; e Processing e/2 codePos e → t• inputPos 3 Reached end of rule, success! e/2 → 3
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f'))
	#6: JoinS: t/2 → 3 木t('f') will resume cont: e/0 ; e → e `+` t• ; e(e(t('12')), '+') Processing e/0 codePos e → e `+` t• inputPos 3 Reached end of rule, success! e/0 → 3
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f'))
Iteration 3
Worklist - successes jS e/0 → 3 木e(e(t('12')),'+',t('f')) jS e/2 → 3 木e(t('f')) Worklist - continuations
	#7: JoinS: e/0 → 3 木e(e(t('12')),'+',t('f')) will resume cont: t/0 ; t → e• `(` e `)` ; t Processing t/0 codePos t → e• `(` e `)` inputPos 3 Match ( to (, matched; inputPos now 4 Calling: e/4 with Cont t/0 ; t → e `(` e• `)` ; t(e(e(t('12')), '+', t('f')), '(') [will process] Processing e/4 codePos e → • e `+` t inputPos 4 Calling: e/4 with Cont e/4 ; e → e• `+` t ; e [already processed] Processing e/4 codePos e → • t inputPos 4 Calling: t/4 with Cont e/4 ; e → t• ; e [will process] Processing t/4 codePos t → • ID inputPos 4 Match ID to 13, fail Processing t/4 codePos t → • NUM inputPos 4 Match NUM to 13, matched; inputPos now 5 Reached end of rule, success! t/4 → 5 Processing t/4 codePos t → • e `(` e `)` inputPos 4 Calling: e/4 with Cont t/4 ; t → e• `(` e `)` ; t [already processed] New continuations: e/4 → t/0 ; t → e `(` e• `)` e/4 → t/4 ; t → e• `(` e `)` e/4 → e/4 ; e → e• `+` t t/4 → e/4 ; e → t•
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13')
	#8: JoinS: e/0 → 3 木e(e(t('12')),'+',t('f')) will resume cont: e/0 ; e → e• `+` t ; e Processing e/0 codePos e → e• `+` t inputPos 3 Match `+` to (, fail
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13')
	#9: JoinS: e/0 → 3 木e(e(t('12')),'+',t('f')) will resume cont: Root/0 ; Root → e• ; Root ×Didn't reach end of input, not a successful parse
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13')
	#10: JoinS: e/2 → 3 木e(t('f')) will resume cont: t/2 ; t → e• `(` e `)` ; t Processing t/2 codePos t → e• `(` e `)` inputPos 3 Match ( to (, matched; inputPos now 4 Calling: e/4 with Cont t/2 ; t → e `(` e• `)` ; t(e(t('f')), '(') [already processed] New continuations: e/4 → t/2 ; t → e `(` e• `)`
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13')
	#11: JoinS: e/2 → 3 木e(t('f')) will resume cont: e/2 ; e → e• `+` t ; e Processing e/2 codePos e → e• `+` t inputPos 3 Match `+` to (, fail
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13')
Iteration 4
Worklist - successes jS t/4 → 5 木t('13') Worklist - continuations nJ e/4 → t/0 ; t → e `(` e• `)` ; t(e(e(t('12')), '+', t('f')), '(') nJ e/4 → t/2 ; t → e `(` e• `)` ; t(e(t('f')), '(') nJ e/4 → t/4 ; t → e• `(` e `)` ; t nJ e/4 → e/4 ; e → e• `+` t ; e S⤚ t/4 → e/4 ; e → t• ; e
	#12: JoinS: t/4 → 5 木t('13') will resume cont: e/4 ; e → t• ; e Processing e/4 codePos e → t• inputPos 5 Reached end of rule, success! e/4 → 5
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13'))
Iteration 5
Worklist - successes jS e/4 → 5 木e(t('13')) Worklist - continuations
	#13: JoinS: e/4 → 5 木e(t('13')) will resume cont: t/0 ; t → e `(` e• `)` ; t(e(e(t('12')), '+', t('f')), '(') Processing t/0 codePos t → e `(` e• `)` inputPos 5 Match ) to ), matched; inputPos now 6 Reached end of rule, success! t/0 → 6
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')
	#14: JoinS: e/4 → 5 木e(t('13')) will resume cont: t/2 ; t → e `(` e• `)` ; t(e(t('f')), '(') Processing t/2 codePos t → e `(` e• `)` inputPos 5 Match ) to ), matched; inputPos now 6 Reached end of rule, success! t/2 → 6
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')')
	#15: JoinS: e/4 → 5 木e(t('13')) will resume cont: t/4 ; t → e• `(` e `)` ; t Processing t/4 codePos t → e• `(` e `)` inputPos 5 Match `(` to ), fail
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')')
	#16: JoinS: e/4 → 5 木e(t('13')) will resume cont: e/4 ; e → e• `+` t ; e Processing e/4 codePos e → e• `+` t inputPos 5 Match `+` to ), fail
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')')
Iteration 6
Worklist - successes jS t/0 → 6 木t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') jS t/2 → 6 木t(e(t('f')),'(',e(t('13')),')') Worklist - continuations
	#17: JoinS: t/0 → 6 木t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') will resume cont: e/0 ; e → t• ; e Processing e/0 codePos e → t• inputPos 6 Reached end of rule, success! e/0 → 6
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')') e/0 → 6, e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')'))
	#18: JoinS: t/2 → 6 木t(e(t('f')),'(',e(t('13')),')') will resume cont: e/2 ; e → t• ; e Processing e/2 codePos e → t• inputPos 6 Reached end of rule, success! e/2 → 6
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')') e/0 → 6, e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) e/2 → 6, e(t(e(t('f')),'(',e(t('13')),')'))
	#19: JoinS: t/2 → 6 木t(e(t('f')),'(',e(t('13')),')') will resume cont: e/0 ; e → e `+` t• ; e(e(t('12')), '+') Processing e/0 codePos e → e `+` t• inputPos 6 Reached end of rule, success! e/0 → 6
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')') e/0 → 6, e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) e/2 → 6, e(t(e(t('f')),'(',e(t('13')),')')) e/0 → 6, e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')'))
Iteration 7
Worklist - successes jS e/0 → 6 木e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')'))木e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) jS e/2 → 6 木e(t(e(t('f')),'(',e(t('13')),')')) Worklist - continuations
	#20: JoinS: e/0 → 6 木e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')'))木e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) will resume cont: t/0 ; t → e• `(` e `)` ; t Processing t/0 codePos t → e• `(` e `)` inputPos 6 Match `(` to (eof), fail Processing t/0 codePos t → e• `(` e `)` inputPos 6 Match `(` to (eof), fail
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')') e/0 → 6, e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) e/2 → 6, e(t(e(t('f')),'(',e(t('13')),')')) e/0 → 6, e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')'))
	#21: JoinS: e/0 → 6 木e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')'))木e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) will resume cont: e/0 ; e → e• `+` t ; e Processing e/0 codePos e → e• `+` t inputPos 6 Match `+` to (eof), fail Processing e/0 codePos e → e• `+` t inputPos 6 Match `+` to (eof), fail
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')') e/0 → 6, e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) e/2 → 6, e(t(e(t('f')),'(',e(t('13')),')')) e/0 → 6, e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')'))
	#22: JoinS: e/0 → 6 木e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')'))木e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) will resume cont: Root/0 ; Root → e• ; Root ✓Reached end of input, successful parse!
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')') e/0 → 6, e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) e/2 → 6, e(t(e(t('f')),'(',e(t('13')),')')) e/0 → 6, e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')')) Root/0 → 6, Root(e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')))✓ Root/0 → 6, Root(e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')')))✓
	#23: JoinS: e/2 → 6 木e(t(e(t('f')),'(',e(t('13')),')')) will resume cont: t/2 ; t → e• `(` e `)` ; t Processing t/2 codePos t → e• `(` e `)` inputPos 6 Match `(` to (eof), fail
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')') e/0 → 6, e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) e/2 → 6, e(t(e(t('f')),'(',e(t('13')),')')) e/0 → 6, e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')')) Root/0 → 6, Root(e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')))✓ Root/0 → 6, Root(e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')')))✓
	#24: JoinS: e/2 → 6 木e(t(e(t('f')),'(',e(t('13')),')')) will resume cont: e/2 ; e → e• `+` t ; e Processing e/2 codePos e → e• `+` t inputPos 6 Match `+` to (eof), fail
t/0 → 1, t('12') e/0 → 1, e(t('12')) t/2 → 3, t('f') e/2 → 3, e(t('f')) e/0 → 3, e(e(t('12')),'+',t('f')) t/4 → 5, t('13') e/4 → 5, e(t('13')) t/0 → 6, t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')') t/2 → 6, t(e(t('f')),'(',e(t('13')),')') e/0 → 6, e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')) e/2 → 6, e(t(e(t('f')),'(',e(t('13')),')')) e/0 → 6, e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')')) Root/0 → 6, Root(e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')))✓ Root/0 → 6, Root(e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')')))✓
Iteration 8
Worklist - successes nJ Root/0 → 6 木Root(e(t(e(e(t('12')),'+',t('f')),'(',e(t('13')),')')))木Root(e(e(t('12')),'+',t(e(t('f')),'(',e(t('13')),')'))) Worklist - continuations
(No new calls or successes that can be further processed)
Iteration 9 [Fixed point reached]