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Held Friday, April 9
Summary
Contents
Handouts
::=
for productions.
->
for productions.
::=
to separate the two parts of a rule.
Program ::= 'program' identifier '(' Identifier-List ')' Declaration-List Compound-Statement '.'
Compound-Statement ::= 'begin' Statement-List 'end'
Statement-List ::= Statement Statement-List ::= Statement ';' Statement-List
Statement ::= Assignment-Statement Statement ::= Compound-Statement ... Assignment-Statement ::= identifier '=' Expression ...
Rock Anything Hardplace ::= Rock Hardplace
Exp ::= number
Exp ::= identifier
Exp ::= UnOp Exp
UnOp ::= '+' UnOp ::= '-'
Exp := Exp BinOp Exp
BinOp ::= '+' | '-' | '*' | '/'
Exp ::= '(' Exp ')'
a+b*2
is an expression? First,
we observe that the
lexer converts this to
identifier + identifier * number
Exp => // Exp ::= Exp BinOp Exp Exp BinOp Exp => // Exp ::= identifier identifier BinOp Exp => // BinOp ::= '+' identifier + Exp => // Exp ::= Exp BinOp Exp identifier + Exp BinOp Exp => // Exp ::= number identifier + Exp BinOp number => // Exp ::= identifier identifier + identifier BinOp number => identifier + identifier * number
Exp
rather than the
first in Exp BinOp Exp
.
Exp / | \ / | \ Exp BinOp Exp------ / | | \ \ / | | \ \ identifier + Exp BinOp Exp / | | / | | identifier * number
num + num * num
.
num - num - num
might be parsed with
two different trees.
Term
.
Term
? Something that may include
multiplication but does not include no unparenthesized addition.
AddExp
Term
.
Term
.
Factor
.
Term
s.
Term ::= Term MulOp Term MulOp ::= '*' | '/'
Term
s? Those that don't include
multiplication. We've already called those Factor
s.
Term ::= Factor
Factor ::= '(' + Exp + ')' Factor ::= num Factor ::= id
Term
, we can separate them into those that do and
those that don't.
Exp ::= Exp AddOp Exp Exp ::= Term AddOp ::= '+' | '-'
History
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