Definitions 1 Definitions 2 Definitions 3 Circularity and self-reference 1 Circularity and self-reference 2 Circularity and self-reference 3 Two semantical techniques 1 Two semantical techniques 2 Two semantical techniques 3 Fixed point theorems Tarski fixed point theorems Recursion, induction, and all that 1 Recursion, induction, and all that 2 Examples 1 Examples 2 Induction Co-inductive types 1 Co-inductive types 2 Co-inductive types 3 Co-inductive types 4 The categorical perspective