Contents

1. Two Quick Examples
   • Constraints help you abstract over structure
   • Arbitrary Arity Zips
2. Pre Requisites
3. Usage
   1. Church Encoding of Booleans
      • Conjunction
      • Disjunction
      • Negation
      • Exclusive Or
      • Material Implication
      • Equivalence
      • Value Conversion
   2. Peano Numbers
      • Addition
      • Multiplication
      • Exponentiation
      • Factorial
      • Comparators
      • Subtraction
      • Value Conversion
   3. Dense Numbers
      • Increment
      • Decrement
      • Left Shift
      • Right Shift
      • Addition
      • Multiplication
      • Exponentiation
      • Comparators
      • Subtraction
      • Value Representation
   4. Type Sets
      • Include
      • Contains
      • Remove
      • Union
      • Size
      • Equivalence
   5. Type Maps
      • Add
      • Contains
      • Get
      • Remove
      • Union
      • Keyset
      • Size.
   6. Natural Transformations
      • Construction
      • Composition
      • Conversion to monomorphic function values
   7. Type-Unions and Exclusions
      • Type Unions
      • Type Exclusions
      • Type Hierarchy Unions
      • Type Hierarchy Exclusions
   8. Singleton Types for Literals
   9. Covariant Heterogenous Lists
      • Covariance
      • You can concatenate them
      • You can reverse them
      • They support value level length
      • You can select an element using an integer index
      • You can drop elements.
      • You can take elements.
      • You can update individual elements
      • You can remove an element
      • You can map an element
      • You can flatmap an element
      • You can insert an element.
      • You can insert a hlist.
      • You can split at an index
      • You can index an hlist with a type.
      • You can zip two hlists together.
      • If each element of a hlist is a tuple2, you can unzip it
      • You can apply natural transformations on hlists
      • You can down convert an hlist
      • You can apply an hlist of functions to a hlist of arguments.
      • You can perform arbitrary arity zips and zipwiths with hlists
      • Common View Operations
      • They can be converted to regular lists
   10. Tuple Ops
       • You can cons an element onto a tuple.
       • You can append two tuples.
       • You can reverse tuples.
       • You can get an integer representation of its arity.
       • You can select an element using an integer index.
       • You can drop elements.
       • You can take elements.
       • You can update individual elements
       • You can remove an element
       • You can map an element
       • You can flatmap an element
       • You can insert an element.
       • You can insert a tuple.
       • You can split at an index
       • You can zip two tuples together.
       • If each element of a tuple is a Tuple2 , you can unzip it
       • You can apply natural transformations on tuples
       • You can down convert tuples
       • You can apply a tuple of functions to a tuple of arguments
       • You can perform arbitrary arity zips and zipwiths
       • Common View
       • They can be converted to regular lists
   11. Sized Vectors
       • Construction
       • Value at an index
       • Update
       • Length
       • Reverse
       • Drop
       • Take
       • Slice
       • Map
       • Sorting
       • Split
       • Flattening
       • Zip and Unzip
       • Access to the backing vector
   12. String Indexed Collections
       • Construction
       • Value corresponding to an index
       • Updates
       • Size
       • Conversion to maps
   13. Records
       • Construction
       • Value corresponding to an index
       • Updates
       • Size
       • Conversion to maps
       • Conversion from classes
   14. Understanding Constraints
4. Contents in Depth
5. Combined Pages