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Type Checking Dr. Nguyen Hua Phung Faculty of CSE HCMUT Outline • Type systems – Type expressions – Static and dynamic type checking • Equivalence of type expressions • Type conversions CSE - HCMUT Type Checking 2 Type Expressions • A basic type is a type expression. – boolean, char, integer, float, void, subrange. • A type name is a type expression. • A type constructor applied to type expressions is a type expression. Including: – Arrays: array(I,T) where I: index type, T:element type – Products: T 1 × T 2 – Records: record((name 1 × T 1 ) × (name 2 × T 2 ) ×…) – Pointers: pointer(T) – Functions: T 1 → T 2 • A type variable is a type expression. CSE - HCMUT Type Checking 3 Example • typedef int siso; ⇒ siso • int t[10]; ⇒ array(0 9,int) • int foo(int a,float b) ⇒ (int × float) → int • struct {int a;int b} ⇒ record((a × int) × (b × int)) • int *p ⇒ pointer(int) • template <class T> struct vd {T a; T b[3];} ⇒ record((a × T) × (b × array(0 2,T))) CSE - HCMUT Type Checking 4 Type Checking • Static type checking – is perfomed by the compiler – applied to typed language • Dynamic type checking – is done when the target program runs – target code needs to carry the type of an element CSE - HCMUT Type Checking 5 Equivalence of Type Expressions • Name equivalence • Structural equivalence • Structural equivalence under naming rec1 = record a : integer; b : real; end; rec2 = record c : real; d : integer; end; rec3 = record c : integer; d : real; end; rec4 = record a : integer; b : real; end; rec1 and rec4 are structural equivalence under naming rec1 and rec3 are structural equivalence CSE - HCMUT Type Checking 6 Static Type Checking for Structural Equivalence function sequiv(Type s,Type t):boolean begin if (s and t are the same basic type) then 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 if (s = pointer(s1) and t = pointer(t1)) then return sequiv(s1,t1); else if (s = s1 → s2 and t = t1 → t2) then return sequiv(s1,t1) ; else return false; CSE - HCMUT Type Checking 7 Object-Oriented Approach Type CSE - HCMUT Type Checking 8 BasicType NumericType BooleanType PointerType ProductType FunctionType ArrayType RangeType array(I,T) IntType FloatType class ArrayType extends Type { RangeType index; Type element; } Object-Oriented Approach (cont’d) abstract class Type { abstract boolean isLeftCompatibleTo(Type t) ; } abstract class BasicType extends Type { boolean isLeftCompatibleTo(Type t) { if (this.getClass().equals(t.getClass())) return true; return false; } } class FloatType extends NumericType { boolean isLeftCompatibleTo(Type t) { if (t instanceof NumericType) return true; return false; } } CSE - HCMUT Type Checking 9 Object-Oriented Approach (cont’d) class ArrayType { RangeType index; Type element; boolean isLeftCompatibleTo(Type t) { if (t instanceof ArrayType) { ArrayType at=(ArrayType) t; return index.isLeftCompatibleTo(at.index) && element.isLeftCompatibleTo(at.element); } else return false; } } CSE - HCMUT Type Checking 10 . → s2 and t = t1 → t2) then return sequiv(s1,t1) ; else return false; CSE - HCMUT Type Checking 7 Object-Oriented Approach Type CSE - HCMUT Type Checking 8 BasicType NumericType BooleanType PointerType ProductType FunctionType ArrayType RangeType array(I,T) IntType