1. seminář 51 Seminář 5

2. seminář 52 The system λμ It is the system of recursive types. The recursive types come together with an equivalence relation. The type assignment rules consist of the rules of and the following rule

3. seminář 53 The set T=Type(λμ), trees of types of λμ. (i) The set of types of λμ, T = Type(λμ), is defined by the following abstract grammar. where V is the set of type variables.

4. seminář 54 (ii) Let be a type. The tree of σ, T(σ) is defined by induction on the structure of σ as follows: if is a type variable If for some else

5. seminář 55 (iii) The equivalence relation on trees is defined as follows: Exercises. (a) Assume then

6. seminář 56 (b) Assume then

7. seminář 57 (c) (d) for all σ, even if α.

8. seminář 58 (start rule)

9. seminář 59  |- K : α  α  |- (λx. (λy.x)) : α  α