Reasoning about effect interaction by fusion

Effect handlers can be composed by applying them sequentially, each handling some operations and leaving other uninterpreted in the syntax tree. However, semantics of subtle---it is well known that different orders composing lead to drastically semantics. Determining correct order composition a non-trivial task. To alleviate this problem, paper presents systematic way deriving sufficient conditions on for their composite correctly handle combinations, such as sum tensor, effect theories separately handled. These are solely characterised clauses relevant handlers, derived fusing two into one using form fold/build fusion continuation-passing style transformation. As case studies, technique applied commutative distributive interaction obtain series results about common handlers: (a) equations respected handler preserved after composition; (b) mutable state before any gives rise which with from latter handler; (c) writer either combination these theories.