Type Checking Biswapati Jana Vidyasagar University Type Checking

Type Checking Biswapati Jana Vidyasagar University

Type Checking • A compiler has to do semantic checks in addition to syntactic checks. • Semantic Checks – Static – done during compilation – Dynamic – done during run-time • Type checking is one of these static checking operations. – we may not do all type checking at compile-time. – Some systems also use dynamic type checking too. • A type system is a collection of rules for assigning type expressions to the parts of a program. • A type checker implements a type system. • A sound type system eliminates run-time type checking for type errors. • A programming language is strongly-typed – In practice, some of type checking operations are done at run-time (so, most of the programming languages are not strongly-typed). – Ex: int x[100]; … x[i] most of the compilers cannot guarantee that i will be between 0 and 99

Static Type Checking Static checking examples: Type checks. Report an error if an operator is applied to an incompatible operand Flow-of-control checks. Statements that causes flow of control to leave a construct must have some place to which to transfer the flow of control Uniqueness checks. There are situations where an object must be defined exactly once. labels, identifiers Name-related checks. Sometimes the same names may be appeared two or more times. Beginning and end of a construct

Type Expression • The type of a language construct is denoted by a type expression. • A type expression can be: – A basic type • a primitive data type such as integer, real, char, boolean, … • type-error to signal a type error • void : no type – A type name • a name can be used to denote a type expression. – A type constructor applies to other type expressions. • arrays: If T is a type expression, then array(I, T) is a type expression where I denotes index range. Ex: array(0. . 99, int) • products: If T 1 and T 2 are type expressions, then their cartesian product T 1 x T 2 is a type expression. Ex: int x int • pointers: If T is a type expression, then pointer(T) is a type expression. Ex: pointer(int)

Type Expression • functions: We may treat functions in a programming language as mapping from a domain type D to a range type R. So, the type of a function can be denoted by the type expression D→R where D are R type expressions. Ex: int→int represents the type of a function which takes an int value as parameter, and its return type is also int. – Function f(a, b: integer) : integer » Integer integer → pointer(integer) • Records: The record type constructor will be applied to a tuple formed from field names and field types. Type row = record address : integer; lexeme: array[1. . 15] of char end; Var table: array[1. . 101] of row; Declares the type name row representing the type expression record( (address integer) (lexeme array(1. . 15, char) )

A Simple Type Checking System P → D; E D → D; D D → id: T { addtype(id. entry, T. type) } T → char { T. type=char } T → int { T. type=int } T → real { T. type=real } T → ↑T 1 { T. type=pointer(T 1. type) } T → array[intnum] of T 1 { T. type=array(1. . intnum. val, T 1. type) } Parts of translation scheme that saves the type of an identifier

Type Checking of Expressions E → id { E. type=lookup(id. entry) } E → literal { E. type=char } E → intliteral { E. type=int } E → realliteral { E. type=real } E → E 1 + E 2 { if (E 1. type=int and E 2. type=int) then E. type=int else if (E 1. type=int and E 2. type=real) then E. type=real else if (E 1. type=real and E 2. type=int) then E. type=real else if (E 1. type=real and E 2. type=real) then E. type=real else E. type=type-error } E → E 1 [E 2] { if (E 2. type=int and E 1. type=array(s, t)) then E. type=t else E. type=type-error } E → E 1 ↑ { if (E 1. type=pointer(t)) then E. type=t else E. type=type-error }

Type Checking of Statements S id = E { if (id. type=E. type then S. type=void else S. type=type-error } S if E then S 1 { if (E. type=boolean then S. type=S 1. type else S. type=type-error } S while E do S 1 { if (E. type=boolean then S. type=S 1. type else S. type=type-error }

Type Checking of Functions E E 1 ( E 2 ) Ex: { if (E 2. type=s and E 1. type=s t) then E. type=t else E. type=type-error } int f(double x, char y) {. . . } f: double x char int argument types return type function root (function f(real): real; x : real) : real Root: (real real) real