Lab 15

Here’s a simple language of numbers and booleans:

<exp> = <num>

| true

| false

| <exp> + <exp>

| <exp> ^ <exp>

Here’s a simple set of types for this program:

<ty> = bool

| num

Here are some type inference rules:

----------

|- n : num

|- M : num  |- N : num

----------------------

|- M + N : num

---------------

|- false : bool

--------------

|- true : bool

|- M : bool  |- N : bool

------------------------

|- M ^ N : bool

• Develop a define-type for programs.

• Develop a define-type for types.

• Develop the program type-check, that accepts a program and returns its type (if it’s well-typed) or signals an exception (if it’s not).