1. Lecture # 21 Chapter 6 Uptill 6.4

2. Type System A type system is a collection of rules for assigning type expressions to the various parts of the program. A Type Checker implements a Type System

3. Type checking of Expressions E  char {E.type=char} E  int {E.type=int} E  id {E.type= lookup (id.entry)} E  E1 mod E2 { E.type= if E1.type= integer and E2.type=integer then integer else error } E  E1[E2] {E.type= if E2.type= integer and E1.type= lookup(E1.type) then E1.type else error }

4. Type Checking of Statements S  id := E { S.type := if id.type = E.type then void else type_error } S  if E then S { S.type := if E.type = boolean then S 1.type else type_error } S  while E do S 1 { S.type := if E.type = boolean then S 1.type else type_error } S  S 1 ; S 2 { S.type := if S 1.type = void and S 2.type = void then void else type_error }

5. Testing the Type Equivalence of Expressions Public bool sequiv (s,t) { if s and t are the same basic type return true else if s=array(s1,s2) and t= array(t1,t2) then return sequiv(s1,t1) and sequiv(s2,t2) else if s=s1*s2 and t=t1* t2 then return sequiv(s1,t1) and sequiv(s2,t2) else return false }

6. Encoding of Type Expressions The expressions can be encoded in bits to check their type equivalence Type Constructor Encoding pointer01 array10 freturns11

7. Basic TypesEncoding boolean 0000 char 0001 integer 0010 real 0011

8. Example Type Encoding Type Expression Char 000000 0001 Freturns(char)000011 0001 Pointer(Freturns(char)) 000111 0001 Array(Pointer(Freturns(char))) 100111 0001