Specifications of a simple type checker

The type of each identifier must be declared before the identifier is used. The type checker is a translation scheme that synthesizes the type of each expression from the type of its sub-expressions.

P --> D; E

D--> D; D | id: T

T--> char | integer | array[num] of T | * T

E--> literal | num | id | E mod E | E[E] | E*

Base Types: char, integer, type-error

Translation Scheme

P --> D; E

D--> D;D

D--> id :T { addtype(id.entry,T.type);}

T--> char {T.type= char;}

T--> integer {T.type=integer;}

T-->*T_1 {T.type=pointer(T_1.type);}

T--> array[num] of T_1 { T.type =array(1..num.val,T_1.type); }

Type Checking of Expressions

E--> literal { E.type=char;}

E--> num { E.type =integer;}

E--> id { E.type =lookup(id.entry);}

E--> E_1 mod E_2 { E.type =If (E_1.type ==integer)  if (E_2. Type ==integer) integer; else type-error;

E--> E_1[E_2] { E.type=if ((E_2.type==integer)&& (E_1.type==array(s,t)) t; else type-error;}

E--> *E_1 { E.type = if (E_1.type ==pointer(t)) t else type-error;

Type Checking for Statements

S--> id=E { if (id.type==E.type) void; else type-error;}

S--> if E then S { if (E.type==boolean) S_1.type; else type-error;}

S--> While E do S { if (E.type==boolean) S_1.type; else type-error; 

S--> S; S; { if (S_1.type==void) if (S_2.type ==void) void; else type-error;}

Type Checking of Functions

E--> E(E)

T--> T ‘->’ T { T.type = T1.type -> T2.type}

E--> E(E) {E.type = I f ((E_2.type ==s) && (E_1.type == s--> t)) t; else type-error;