Idris2Doc : Data.Prim.Int16

Data.Prim.Int16

(source)
Reexports
import public Algebra.Ring
import public Control.Order
import public Control.Relation
import public Control.Relation.ReflexiveClosure
import public Control.Relation.Trichotomy
import public Control.WellFounded
import public Data.Maybe0
Definitions
data (<) : Int16 -> Int16 -> Type
  Witness that `m < n === True`.

  Totality: total
  Visibility: export
  Constructor: 
LT : (0 _ : m < n = True) -> m < n

  Hints:
  
(0 _ : m < n = True) -> m < n
  
Transitive Int16 (<)
  
Trichotomous Int16 (<)

  Fixity Declaration: infix operator, level 6
unerase : (0 _ : m < n) -> m < n
  Makes a compile-time proof of `x < y` available at runtime.
  
  Heads up: `(<)` is not supposed to be used or even needed at runtime,
  as it will be erased anymay. However, this function is sometimes
  required, for instance when implementing interface `Connex`.

  Totality: total
  Visibility: export
0 mkLT : (0 _ : m < n = True) -> m < n
  Contructor for `(<)`.
  
  This can only be used in an erased context.

  Totality: total
  Visibility: export
0 runLT : m < n -> m < n = True
  Extractor for `(<)`.
  
  This can only be used in an erased context.

  Totality: total
  Visibility: export
strictLT : (0 _ : m < n) -> Lazy c -> c
  We don't trust values of type `(<)` too much,
  so we use this when creating magical results.

  Totality: total
  Visibility: export
0 (>) : Int16 -> Int16 -> Type
  Flipped version of `(<)`.

  Totality: total
  Visibility: public export
  Fixity Declaration: infix operator, level 6
0 (<=) : Int16 -> Int16 -> Type
  Alias for `ReflexiveClosure (<) m n`

  Totality: total
  Visibility: public export
  Fixity Declaration: infix operator, level 6
lt : (x : Int16) -> (y : Int16) -> Maybe0 (x < y)
  Totality: total
  Visibility: public export
lte : (x : Int16) -> (y : Int16) -> Maybe0 (x <= y)
  Totality: total
  Visibility: public export
comp : (m : Int16) -> (n : Int16) -> Trichotomy (<) m n
  Totality: total
  Visibility: export
MinInt16 : Int16
  Lower bound of `Int16`

  Totality: total
  Visibility: public export
MaxInt16 : Int16
  Upper bound of `Int16`

  Totality: total
  Visibility: public export
0 GTE_MinInt16 : (m : Int16) -> MinInt16 <= m
  `m >= 0` for all `m` of type `Int16`.

  Totality: total
  Visibility: export
0 Not_LT_MinInt16 : m < MinInt16 -> Void
  Not value of type `Int16` is less than zero.

  Totality: total
  Visibility: export
0 LTE_MaxInt16 : (m : Int16) -> m <= MaxInt16
  `m <= MaxInt16` for all `m` of type `Int16`.

  Totality: total
  Visibility: export
0 Not_GT_MaxInt16 : m > MaxInt16 -> Void
  Not value of type `Int16` is greater than `MaxInt16`.

  Totality: total
  Visibility: export
accessLT : (m : Int16) -> Accessible (<) m
  Every value of type `Int16` is accessible with relation
  to `(<)`.

  Totality: total
  Visibility: export
accessGT : (m : Int16) -> Accessible (>) m
  Every value of type `Int16` is accessible with relation
  to `(>)`.

  Totality: total
  Visibility: export