Type Checking

Type Checking

1. Type checking is basically the enforcement of a set of rules designed to ensure that only valid operands are provided to the various operations that can be invoked within a program.

   • Type systems are a big topic in programming language design but typically are given little attention in compiler courses and textbooks.

   • The specification of a type system requires:
     • a language/notation for describing types.
     • a set of rules specifying how to associated type descriptions with language constructs (primarily expressions).
     • a set of rules specifying restrictions on the types associated with expressions appearing in various contexts.

2. The description of types in "conventional" languages typically includes:
   • A set of names for primitive types (int, bool, etc.),
   • Constructors for composite types including:
     • pointer( t )
     • array( i, t )
     • record constructor ( id₁:t₁, id₂:t₂, ... )
     • product constructor ( t₁ x t₂ x . . . t_n )
     • function constructor ( t₁ -> t₂ )
   • The ability to bind and use type names.
     • Essential for the description of list, trees and other recursive types.

3. The rules for associating types with expression are typically inextricably intermixed with the rules specifying type constraints. Basically, if a expression violates the constraints, none of the rules for assigning types will apply.

   • For example....

     Given an expression, e, of the form:

     x + y

     where x and y have type "int" then the type of 'e' is "int".

     Given an expression, e, of the form:

     f(x)

     where f has type t₁ rightarrow t₂ and x has type t₁ then e has type t₂.

Type Checking