Start of FORM5 Interpreter for a Formula v5.frm at Sun Apr 22 18:28:46 2001


Scanner started

Input program:

# odd ( #i# x _{ #i# a , #i# a } : #i# a \in V( #i# G ) ) #

Scanned program:

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Identifiers:x, a, G;

Scanner ended

Parser started


Stack & Word # <•odd( #i# x _{ #i# a , #i# a } : #i# a \in V( #i# G ) ) #

Stack & Word # <•odd <•(#i# x _{ #i# a , #i# a } : #i# a \in V( #i# G ) ) #


Stack & Word # <•odd =•prefpar#i# x _{ #i# a , #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

prefpar
(


Stack & Word # <•odd =•prefpar <•#i#_{ #i# a , #i# a } : #i# a \in V( #i# G ) ) #


Stack & Word # <•odd =•prefpar <•logvar_{ #i# a , #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

logvar
x


Stack & Word # <•odd =•prefpar <•logvar =•_{#i# a , #i# a } : #i# a \in V( #i# G ) ) #

Stack & Word # <•odd =•prefpar <•logvar =•_{ <•#i#, #i# a } : #i# a \in V( #i# G ) ) #


Stack & Word # <•odd =•prefpar <•logvar =•_{ <•metavariable, #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

metavariable
a



P=48 `metavariables1' -> `metavariable'

Stack & Word # <•odd =•prefpar <•logvar =•_{ <•primary, #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•factor, #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•term, #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•expression1, #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

expression1
term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•expression, #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

expression
expression1
term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index, #i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

index
expression
expression1
term
factor
primary
metavariable
a


Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index <•,#i# a } : #i# a \in V( #i# G ) ) #


Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma#i# a } : #i# a \in V( #i# G ) ) #

Parsing tree

indexkoma
,


Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma <•#i#} : #i# a \in V( #i# G ) ) #


Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma <•metavariable} : #i# a \in V( #i# G ) ) #

Parsing tree

metavariable
a



P=48 `metavariables1' -> `metavariable'

Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma <•primary} : #i# a \in V( #i# G ) ) #

Parsing tree

primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma <•factor} : #i# a \in V( #i# G ) ) #

Parsing tree

factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma <•term} : #i# a \in V( #i# G ) ) #

Parsing tree

term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma <•expression1} : #i# a \in V( #i# G ) ) #

Parsing tree

expression1
term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma <•expression} : #i# a \in V( #i# G ) ) #

Parsing tree

expression
expression1
term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma <•index} : #i# a \in V( #i# G ) ) #

Parsing tree

index
expression
expression1
term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•index =•indexkoma =•indexes1} : #i# a \in V( #i# G ) ) #

Parsing tree

indexes1
index
expression
expression1
term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ <•indexes1} : #i# a \in V( #i# G ) ) #

Parsing tree

indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a



Stack & Word # <•odd =•prefpar <•logvar =•_{ =•indexes} : #i# a \in V( #i# G ) ) #

Parsing tree

indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a


Stack & Word # <•odd =•prefpar <•logvar =•_{ =•indexes =•}: #i# a \in V( #i# G ) ) #


Stack & Word # <•odd =•prefpar <•literal: #i# a \in V( #i# G ) ) #

Parsing tree

literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}



Stack & Word # <•odd =•prefpar <•logterm: #i# a \in V( #i# G ) ) #

Parsing tree

logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}



Stack & Word # <•odd =•prefpar <•clause: #i# a \in V( #i# G ) ) #

Parsing tree

clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}



Stack & Word # <•odd =•prefpar <•leftpart: #i# a \in V( #i# G ) ) #

Parsing tree

leftpart
clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}



Stack & Word # <•odd =•prefpar <•formula: #i# a \in V( #i# G ) ) #

Parsing tree

formula
leftpart
clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}



Stack & Word # <•odd =•prefpar <•bigformula: #i# a \in V( #i# G ) ) #

Parsing tree

bigformula
formula
leftpart
clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}



P=30 `bigformula1' -> `bigformula'

Stack & Word # <•odd =•prefpar =•bigformula1: #i# a \in V( #i# G ) ) #

Parsing tree

bigformula1
bigformula
formula
leftpart
clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}


Stack & Word # <•odd =•prefpar =•bigformula1 =•:#i# a \in V( #i# G ) ) #

Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•#i#\in V( #i# G ) ) #


Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariable\in V( #i# G ) ) #

Parsing tree

metavariable
a



P=48 `metavariables1' -> `metavariable'

Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariables1\in V( #i# G ) ) #

Parsing tree

metavariables1
metavariable
a



Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariables\in V( #i# G ) ) #

Parsing tree

metavariables
metavariables1
metavariable
a


Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariables =•\inV( #i# G ) ) #

Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariables =•\in =•V(#i# G ) ) #

Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariables =•\in =•V( <•#i#) ) #


Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariables =•\in =•V( <•graphname) ) #

Parsing tree

graphname
G



Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariables =•\in =•V( =•graphname1) ) #

Parsing tree

graphname1
graphname
G


Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•metavariables =•\in =•V( =•graphname1 =•)) #


Stack & Word # <•odd =•prefpar =•bigformula1 =•: <•limit) #

Parsing tree

limit
metavariables
metavariables1
metavariable
a
\inV(graphname1
graphname
G
)



Stack & Word # <•odd =•prefpar =•bigformula1 =•: =•limits) #

Parsing tree

limits
limit
metavariables
metavariables1
metavariable
a
\inV(graphname1
graphname
G
)


Stack & Word # <•odd =•prefpar =•bigformula1 =•: =•limits =•)#


P=16 `bigformula' -> \bigvee_{ `limits' `lbra' `bigformula'

P=19 `bigformula' -> odd `prefpar' `bigformula1' : `limits' )

Stack & Word # <•bigformula#

Parsing tree

bigformula
oddprefpar
(
bigformula1
bigformula
formula
leftpart
clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}
:limits
limit
metavariables
metavariables1
metavariable
a
\inV(graphname1
graphname
G
)
)



P=30 `bigformula1' -> `bigformula'

Stack & Word # <•metaformula#

Parsing tree

metaformula
bigformula
oddprefpar
(
bigformula1
bigformula
formula
leftpart
clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}
:limits
limit
metavariables
metavariables1
metavariable
a
\inV(graphname1
graphname
G
)
)



P=2 `family' -> `metaformula'

Stack & Word # =•family#

Parsing tree

family
metaformula
bigformula
oddprefpar
(
bigformula1
bigformula
formula
leftpart
clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}
:limits
limit
metavariables
metavariables1
metavariable
a
\inV(graphname1
graphname
G
)
)

the parsing is completed

Parsing tree

family
metaformula
bigformula
oddprefpar
(
bigformula1
bigformula
formula
leftpart
clause
logterm
literal
logvar
x
_{indexes
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
indexkoma
,
indexes1
index
expression
expression1
term
factor
primary
metavariable
a
}
:limits
limit
metavariables
metavariables1
metavariable
a
\inV(graphname1
graphname
G
)
)

Table of identifiers

i1=xi2=ai3=G

Parser ended

Interpreter ended at Sun Apr 22 18:28:46 2001