Type Systems

tags : Programming Languages, Ocaml

One of / Each of/ Maybe (Ocaml) §

The Algebra of Algebraic Data Types - YouTube

• One-of types are more commonly known as sum types
• each-of types as more commonly known as product types.

One of (SUM) §

• Ocaml Variants are like disjoint union
• Aka tagged union
• Variants are also known as Algebraic Data types
• Each value of a variant comes from one of many underlying sets
• Thus far each of those sets is just a single constructor hence has cardinality one
• Disjoint union is indeed sometimes written with a Σ operator.
• OCaml variants actually combine several theoretically independent language features into one: sum types, product types, recursive types, and parameterized (polymorphic) types.
• Resources
  • Sum Types in Postgres - Yurii Rashkovskii

Each of (PRODUCT) §

• Ocaml Tuples/records are like Cartesian product
• Each value of a tuple or record contains a value from each of many underlying sets.
• Cartesian product is usually written with a product operator Π or x

Maybe §

• Ocaml option are maybe types

Resources §

• Hindley–Milner type system - Wikipedia