Source code is compiled using a multi-stage compiler that includes a tokenizer, a type checker, and a composer. The tokenizer segments source code into a sequence of tagged segments. The source code includes at least one instruction that composes a first abstraction and a second abstraction with a selected composition operator. The parser builds a tree using the sequence of tagged segments. The type checker performs a first pass of the tree to determine whether abstractions on the tree are well typed. The composer reduces the at least one instruction composing the first and the second abstractions on the tree to a third abstraction. The composer substitutes the first and the second abstractions on the tree with the third abstraction, wherein the type checker performs a second pass of the tree to determine whether the third abstraction is well typed.