Data.Rel

Definitions

Rel : Vect n Type -> Type

  Build an n-ary relation type from a Vect of Types

Totality: total
Visibility: public export

All : (ts : Vect n Type) -> Rel ts -> Type

  Universal quantification of a n-ary Relation over its
  arguments to build a (function) type from a `Rel` type
  
  ```
  λ> All [Nat,Nat] LTE
  (x : Nat) -> (x : Nat) -> LTE x x
  ```

Totality: total
Visibility: public export

Ex : (ts : Vect n Type) -> Rel ts -> Type

  Existential quantification of a n-ary relation over its
  arguments to build a dependent pair (eg. Sigma type).
  
  Given a (type of) relation `p : [t_1, t_2 ... t_n] x r` where `t_i` and `r` are
  types, `Ex` builds the type `Σ (x_1 : t_1). Σ (x_2 : t_2) ... . r`
  For example:
  ```
  λ> Ex [Nat,Nat] LTE
  (x : Nat ** (x : Nat ** LTE x x))
  ```
  Which is the type of a pair of natural numbers along with a proof that the first
  is smaller or equal than the second.

Totality: total
Visibility: public export

liftRel : (ts : Vect n Type) -> Rel ts -> (Type -> Type) -> Type

  Map a type-level function over the co-domain of a n-ary Relation

Totality: total
Visibility: public export