Download Syntax and Semantics of Context-Free Grammar in Programming Languages - Prof. Laura Dillon and more Exams Programming Languages in PDF only on Docsity!
L. Dillon CSE 452, Fall 2008
1
− “... the rules and principles that govern the sentence structure of any individual language ” -- Wikipedia − Standard:base a programming language syntax on a context free grammar
− “ the meaning or relationship of meanings of a sign or set of signs ” -- Merriam-Webster Dictionary −Standards for defining semantics vary
Foundations: program definition
L. Dillon CSE 452, Fall 2008
2
- Nonterminal symbols for
key syntactic categories
(a nonterminal)
- Terminal symbols, which
appear in “sentences”
- Productions , rules show-
ing how symbols compose
to form sentences
Context free grammar
3
3
- Nonterminal symbols for
key syntactic categories
(a nonterminal)
- Terminal symbols, which
appear in “sentences”
- Productions , rules show-
ing how symbols compose
to form sentences
Context free grammar
- Example nonterminals: P - programs # start S - statements e - expressions
Example terminals:
0 3.14 15 ‘a’ “hi” ... literals if then else end... keywords x y time len ... identifiers < => + * / ... operators
Our examples will use:
num - for numeric literals id - for identifiers op - for operators
Context free grammar
4
4
- Nonterminal symbols for
key syntactic categories
(a nonterminal)
- Terminal symbols, which
appear in “sentences”
- Productions , rules show-
ing how symbols compose
to form sentences
Context free grammar
Example productions
e ::= num | id | e op e | ( e ) S ::= read id | write e | id := e | S ; S | if e then S else S | while e do S | { S } P ::= prog S end
L. Dillon CSE 452, Fall 2008
5
A sequence of replacement steps, starting from the start symbol and producing a string of nonterminals
P $ prog S end $ prog S ; S end $ prog read x; S end $ prog read x; if e then S else S end $ prog read x; if e > e then S else S end $ prog read x; if x > e then S else S end $ prog read x; if x > 0 then S else S end $... $ prog read x; if x > 0 then write 0 else write 1 end
Derivation
L. Dillon CSE 452, Fall 2008
6
A sequence of replacement steps, starting from the start symbol and producing a string of nonterminals
P $ prog S end $ prog S ; S end $ prog read x; S end $ prog read x; if e then S else S end $ prog read x; if e > e then S else S end $ prog read x; if x > e then S else S end $ prog read x; if x > 0 then S else S end $... $ prog read x; if x > 0 then write 0 else write 1 end
Derivation
P ::= prog S end
7
7
A sequence of replacement steps, starting from the start symbol and producing a string of nonterminals
P $ prog S end $ prog S ; S end $ prog read x; S end $ prog read x; if e then S else S end $ prog read x; if e > e then S else S end $ prog read x; if x > e then S else S end $ prog read x; if x > 0 then S else S end $... $ prog read x; if x > 0 then write 0 else write 1 end
Derivation
S ::= S ; S
8
8
A sequence of replacement steps, starting from the start symbol and producing a string of nonterminals
P $ prog S end $ prog S ; S end $ prog read x; S end $ prog read x; if e then S else S end $ prog read x; if e > e then S else S end $ prog read x; if x > e then S else S end $ prog read x; if x > 0 then S else S end $... $ prog read x; if x > 0 then write 0 else write 1 end
Derivation
S ::= read id
L. Dillon CSE 452, Fall 2008
13
Some syntax is not expressed in CFG
- More convenient/efficient not to use CFG for some pur-
poses, e.g.
− Precedence/associativity rules for operators − Regular expressions for “syntax” of classes of terminals, such as integers, floating point numbers, characters, strings, etc.
- CFG not sufficiently expressive for some purposes, e.g. − Scoping constraints − Typing constraints - Static semantics refers to the syntax of a programming
language that is not expressed in CFG
− contrast this with dynamic semantics , which is generally what we mean by “semantics”
L. Dillon CSE 452, Fall 2008
14
Defining (dynamic) semantics
Much more difficult than defining syntax
- Typically done informally or, at best, semi-formally
- Formal approaches have influenced designs of modern program- ming languages −Denotational semantics – HO functions, continuations, ... − Operational semantics – documentation, typing rules, ... − Axiomatic semantics – program assertions, contracts, ...
15
15
Code Data
Program Counter
Translation to an abstract machine model
Very simple machine model:
- codememory: −array of machine instructions − contents is static
- datamemory: −array of data values − contents change during execu- tion
- programcounter (PC): contains label (index) of the next instruc- tion
- machinecycle: fetch-incre- ment-decode-execute
Example: Operational semantics
16
16
Code Data
Program Counter
Machine instructions:
• I/O
− put mi − get mj
- Assignments − mi := num − mi := mj − mi := mj op mk
- Branches − goto li − ifz mi goto lj
Here, mi , mj , mk denote data references; li , lj denote labels
mj :
li :
Machine instructions
L. Dillon CSE 452, Fall 2008
17
ei
e (^) j op e (^) k
code for ej code for ek m (^) i := m (^) j op mk
e (^) i
num
m (^) i := m (^) j
ei
( ej )
code for e (^) j mi := mj
ei
id j
Rules for translating expressions Convention: m (^) j is a unique memory reference for the expression e (^) j / variable id j
m (^) i := num
computes ej & stores the value in m (^) j
L. Dillon CSE 452, Fall 2008
18
ei
ej op e (^) k
code for e (^) j code for ek m (^) i := mj op mk
ei
num
mi := mj
ei
( e (^) j )
code for e (^) j mi := mj
ei
id j
Rules for translating expressions Convention: m (^) j is a unique memory reference for the expression e (^) j / variable id j
m (^) i := num
computes ek & stores the value in m (^) k
19
19
ei
e (^) j op e (^) k
code for ej code for ek m (^) i := m (^) j op mk
e (^) i
num
m (^) i := m (^) j
ei
( ej )
code for e (^) j mi := mj
ei
id j
Rules for translating expressions Convention: m (^) j is a unique memory reference for the expression e (^) j / variable id j
m (^) i := num
computes ei & stores the value in m (^) i
20
20
Example: translating expressions
2 ***** ( a - b )
a b
e
e e
e
e e
L. Dillon CSE 452, Fall 2008
25
Example: translating expressions
a 6 b 7
e 3
e 4 e 5
e 2
e 0
e (^1)
- Associate a unique memory reference (mi ) with each ex- pression (ej ) and each variable ( id j ) - Apply translation rules (left-to-right, bottom up)
e (^) i
id j
m (^) i := mj
L. Dillon CSE 452, Fall 2008
26
Example: translating expressions
a 6 b 7
e 3
e 4 e 5
e 2
e 0
e 1
- Associate a unique memory reference (mi ) with each ex- pression (ej ) and each variable ( id j ) - Apply translation rules (left-to-right, bottom up)
ei
id j
m (^) i := mj
27
27
Example: translating expressions
a 6 b 7
e 3
e 4 e 5
e 2
e 0
e (^1)
- Associate a unique memory reference (mi ) with each ex- pression (ej ) and each variable ( id j ) - Apply translation rules (left-to-right, bottom up)
e (^) i
id j
m (^) i := mj
28
28
Example: translating expressions
a 6 b 7
e 3
e 4 e 5
e 2
e 0
e 1
- Associate a unique memory reference (mi ) with each ex- pression (ej ) and each variable ( id j ) - Apply translation rules (left-to-right, bottom up)
e (^) i
ej op ek
code for e (^) j code for e (^) k mi := mj op mk
L. Dillon CSE 452, Fall 2008
29
Example: translating expressions
a 6 b 7
e 3
e 4 e 5
e 2
e 0
e (^1)
- Associate a unique memory reference (mi ) with each ex- pression (ej ) and each variable ( id j ) - Apply translation rules (left-to-right, bottom up)
e (^) i
ej op ek
code for ej code for e (^) k mi := mj op mk
L. Dillon CSE 452, Fall 2008
30
Example: translating expressions
a 6 b 7
e 3
e 4 e 5
e 2
e 0
e 1
- Associate a unique memory reference (mi ) with each ex- pression (ej ) and each variable ( id j ) - Apply translation rules (left-to-right, bottom up)
31
31
Ambiguity
e 2
e 0
e 1 *****
e 3 - e 4
a b
e 2
e 0
e 1 -
e 3 ***** e (^4)
2 a
b
2 ***** a - b
Suppose a = 5 and b = 1
- what will the code from the left tree calculate for “ 2 ***** a - b”?
- what will the code from the right tree calculate for “ 2 ***** a - b”? How might a compiler resolve such ambiguities?
32
32
Rules for translating statements Conventions:
- lj is a label marking the code for statement Sj
- lbeg & lend are labels marking the start & end of program P
- mj is a reference for expression ej / variable id j
&^ l^ i :^ get^ m^ j
Si
read id j
code for ej put mj
&^ li :
Si
write ej
code for ek mj := m (^) k
l (^) i :
S (^) i
vj := ek
code for Si exit
lbeg:
P
S (^) i
code for Sj code for Sk
li :
Si
Sj ; Sk
&^ li^ :code for^ Sj
S (^) i
{ S (^) j
prog end
lend:
L. Dillon CSE 452, Fall 2008
37
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4 if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
- Associate − a unique label, l (^) j , with each statement, S (^) j − a uniquememory reference, mj , with each expression ej / (distinct) variable, id j
- Determinethe label, nj , of the statement “after” each statement, S (^) j − proceed top-down − based on the production that yields Sj P
prog S^ i end
use: ni = lend
L. Dillon CSE 452, Fall 2008
38
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4 if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
- Associate − a unique label, l (^) j , with each statement, Sj − a uniquememory reference, m (^) j , with each expression ej / (distinct) variable, id j
- Determinethe label, n (^) j , of the statement “after” each statement, Sj − proceed top-down − based on the production that yields S (^) j P
prog Si end
use: ni = lend
39
39
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4
if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
- Associate − a unique label, l (^) j , with each statement, S (^) j − a uniquememory reference, mj , with each expression ej / (distinct) variable, id j
- Determinethe label, nj , of the statement “after” each statement, S (^) j − proceed top-down − based on the production that yields Sj
40
40
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4
if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
- Associate − a unique label, l (^) j , with each statement, Sj − a uniquememory reference, m (^) j , with each expression ej / (distinct) variable, id j
- Determinethe label, n (^) j , of the statement “after” each statement, Sj − proceed top-down − based on the production that yields S (^) j
use: nj = lk n (^) k = ni
Si
S (^) j ; Sk
L. Dillon CSE 452, Fall 2008
41
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4 if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
- Associate − a unique label, l (^) j , with each statement, S (^) j − a uniquememory reference, mj , with each expression ej / (distinct) variable, id j
- Determinethe label, nj , of the statement “after” each statement, S (^) j − proceed top-down − based on the production that yields Sj
L. Dillon CSE 452, Fall 2008
42
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4 if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
- Associate − a unique label, l (^) j , with each statement, Sj − a uniquememory reference, m (^) j , with each expression ej / (distinct) variable, id j
- Determinethe label, n (^) j , of the statement “after” each statement, Sj − proceed top-down − based on the production that yields S (^) j
use: nk = ni nq = ni
S (^) i
if ej then^ S^ k else S^ q
43
43
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4
if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
- Associate − a unique label, l (^) j , with each statement, S (^) j − a uniquememory reference, mj , with each expression ej / (distinct) variable, id j
- Determinethe label, nj , of the statement “after” each statement, S (^) j − proceed top-down − based on the production that yields Sj
- Apply the translation rules (top-down)
44
44
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4
if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
L. Dillon CSE 452, Fall 2008
49
Translating statements
S 2 ; S 3
P
prog S 1 end
read x 4 if e 5 then S 6 else S 7
e 8 > e 9
x 4 0 write
e 10
write
e 11
L. Dillon CSE 452, Fall 2008
50
Foundations: implementation
Compiled languages
Compiler
Real Machine
(CPU, memory, ...)
Source Program
... if (x == 0) { x = x + 1; } ...
Target Program
... cmp (1000), $ bne L add (1000), $ L: ...
Data
Output
Source and target programs have the same semantics.
Target program is in machine or assembly code.
Machine interpreter executes the target program.
Compiler translates the source program into a target program
51
51
Foundations: implementation
Typical compiler:
Source Program
Syntax analyzer (parser)
Lexical analyzer (scanner)
Semantic analyzer (type checker) Intermediate code generator
Code optimizer
Code generator
Target Program
52
52
Foundations: implementation
Interpreted languages
Source Program
Interpreter
Data
Output
Software interpreter “executes” source program instructions, often interactively.
Traditionally: Read - Eval - Print loop
53
Foundations: implementation
Typical interpreter:
Source Program
Data
Output
Compiler
Target Program
Source Language-specific Virtual Machine
54
Java: implementation
Java Compiler
Java Virtual Machine (JVM)
Source Program
... if (x == 0) { x = x + 1; } ...
Target Program
... iload_ iconst_ ifne L inc store_ L:...
Data
Output
Compromise between compilation/interpretation
Important design goals:
_- Portability
- Remote execution
- Safety
- Reliability
- Multithreaded execution
- Simplicity
- Familiarity
- Efficiency_
