Objective:To acquire a comprehensive understanding of the application of grammars and formal language theory to computing languages.Given: Consider the following set of productions: P01: FN → FN–HEAD   FN–BODY P02: FN–HEAD → TYPE   id    (   PARAM–LIST    ) P03: TYPE → char P04: TYPE → int P05: TYPE → real P06: PARAM–LIST → TYPE   id P07: PARAM–LIST → PARAM–LIST    ,    TYPE   id P08: FN–BODY → {    VAR–DECL   STMT    return   (    EXPRESN    )   ;   } P09: VAR–DECL → λ P10: VAR–DECL → TYPE   ID–LIST    ; P11: VAR–DECL → VAR–DECL   TYPE   ID–LIST    ; P12: ID–LIST → id P13: ID–LIST → ID–LIST    ,   id P14: STMT → λ P15: STMT → SIMPLE–STMT P16: STMT → SELECT–STMT P17: STMT → REPEAT–STMT P18: STMT → SEQUENCE–STMT P19: SIMPLE–STMT → ASSIGN–STMT P20: SIMPLE–STMT → FN–CALL–STMT P21: ASSIGN–STMT → var    =    EXPRESN    ; P22: EXPRESN → ARITH–EXP P23: EXPRESN → BOOL–EXP P24: ARITH–EXP → TERM P25: ARITH–EXP → ARITH–EXP   ADD–OP   TERM P26: ADD–OP → + P27: ADD–OP → – P28: TERM → FAC P29: TERM → TERM   MUL–OP   FAC P30: MUL–OP → * P31: MUL–OP → / P32: FAC → (    ARITH–EXP    ) P33: FAC → OPD P34: OPD → var P35: OPD → const P36: BOOL–EXP → RELN–EXP P37: BOOL–EXP → LOGIC–EXP P38: RELN–EXP → OPD   RELN–OPR   OPD P39: RELN–OPR → == P40: RELN–OPR → != P41: RELN–OPR → < P42: RELN–OPR → <= P43: RELN–OPR → > P44: RELN–OPR → >= P45: LOGIC–EXP → OPD   LOGIC–OPR   OPD P46: LOGIC–EXP → LOGIC–OPR   OPD P47: LOGIC–OPR → and P48: LOGIC–OPR → or P49: LOGIC–OPR → not P50: FN–CALL–STMT → id    (   ARG–LIST    )   ; P51: ARG–LIST → λ P52: ARG–LIST → id P53: ARG–LIST → ARG–LIST    ,    id P54: SELECT–STMT → if    CONDITION   STMT    else    STMT P55: CONDITION → (    BOOL–EXP    ) P56: REPEAT–STMT → DO–STMT P57: REPEAT–STMT → WHILE–STMT P58: DO–STMT → do   {    STMT    }   while    CONDITION    ; P59: WHILE–STMT → while    CONDITION    do   {    STMT    }   ; P60: SEQUENCE–STMT → STMT   STMT Instructions: (30 points)    Rewrite the set of productions above in Extended Backus-Naur Form (EBNF). (35 points)    Using a Push Down Automaton (PDA), determine if the following function is valid code according to the given set of productions. int Max ( int x, int y )      {          int z ;          if ( x >y )              z = x ;          else              z = y ;          return ( z ) ;      } (35 points)    Validate your answer in (2) by illustrating it with a derivation tree Deliverable: Submit a paper Times New Roman font, 12 pt., double-space lines).   The project must contain an introduction which includes the purpose of the project.   I attached the answers to 1 and 2 just look to make sure correct and write a paper. .

1. Objective:To acquire a comprehensive understanding of the
application of grammars and formal language theory to
computing languages.Given:
Consider the following set of productions:
P01:
FN
→
FN–HEAD FN–BODY
P02:
FN–HEAD
→
TYPE id
(
PARAM–LIST
)
P03:
TYPE
→
char
P04:
TYPE
→
int
P05:
TYPE
→
real
P06:
PARAM–LIST
→
TYPE id
P07:
PARAM–LIST
→
PARAM–LIST

2. ,
TYPE id
P08:
FN–BODY
→
{
VAR–DECL STMT
return (
EXPRESN
) ; }
P09:
VAR–DECL
→
λ
P10:
VAR–DECL
→
TYPE ID–LIST
;
P11:
VAR–DECL
→
VAR–DECL TYPE ID–LIST
;
P12:
ID–LIST
→
id
P13:
ID–LIST
→
ID–LIST
,
id
P14:
STMT

3. →
λ
P15:
STMT
→
SIMPLE–STMT
P16:
STMT
→
SELECT–STMT
P17:
STMT
→
REPEAT–STMT
P18:
STMT
→
SEQUENCE–STMT
P19:
SIMPLE–STMT
→
ASSIGN–STMT
P20:
SIMPLE–STMT
→
FN–CALL–STMT
P21:
ASSIGN–STMT
→
var
=
EXPRESN
;
P22:
EXPRESN
→

4. ARITH–EXP
P23:
EXPRESN
→
BOOL–EXP
P24:
ARITH–EXP
→
TERM
P25:
ARITH–EXP
→
ARITH–EXP ADD–OP TERM
P26:
ADD–OP
→
+
P27:
ADD–OP
→
–
P28:
TERM
→
FAC
P29:
TERM
→
TERM MUL–OP FAC
P30:
MUL–OP
→
*
P31:
MUL–OP
→

5. /
P32:
FAC
→
(
ARITH–EXP
)
P33:
FAC
→
OPD
P34:
OPD
→
var
P35:
OPD
→
const
P36:
BOOL–EXP
→
RELN–EXP
P37:
BOOL–EXP
→
LOGIC–EXP
P38:
RELN–EXP
→
OPD RELN–OPR OPD
P39:
RELN–OPR
→
==
P40:

6. RELN–OPR
→
!=
P41:
RELN–OPR
→
<
P42:
RELN–OPR
→
<=
P43:
RELN–OPR
→
>
P44:
RELN–OPR
→
>=
P45:
LOGIC–EXP
→
OPD LOGIC–OPR OPD
P46:
LOGIC–EXP
→
LOGIC–OPR OPD
P47:
LOGIC–OPR
→
and
P48:
LOGIC–OPR
→
or
P49:

7. LOGIC–OPR
→
not
P50:
FN–CALL–STMT
→
id
(
ARG–LIST
) ;
P51:
ARG–LIST
→
λ
P52:
ARG–LIST
→
id
P53:
ARG–LIST
→
ARG–LIST
,
id
P54:
SELECT–STMT
→
if
CONDITION STMT
else
STMT
P55:
CONDITION
→
(
BOOL–EXP

8. )
P56:
REPEAT–STMT
→
DO–STMT
P57:
REPEAT–STMT
→
WHILE–STMT
P58:
DO–STMT
→
do {
STMT
} while
CONDITION
;
P59:
WHILE–STMT
→
while
CONDITION
do {
STMT
} ;
P60:
SEQUENCE–STMT
→
STMT STMT
Instructions:
(30 points)
Rewrite the set of productions above in Extended Backus-
Naur Form (EBNF).
(35 points)
Using a Push Down Automaton (PDA), determine if the
following function is valid code according to the given set of

9. productions.
int Max ( int x, int y )
{
int z ;
if ( x >y )
z = x ;
else
z = y ;
return ( z ) ;
}
(35 points)
Validate your answer in (2) by illustrating it with a derivation
tree
Deliverable:
Submit a paper Times New Roman font, 12 pt., double-space
lines). The project must contain an introduction which
includes the purpose of the project.
I attached the answers to 1 and 2 just look to make sure correct
and write a paper.