Safe Haskell | Trustworthy |
---|---|
Language | Haskell2010 |
Data.Constraint.Nat
Description
Utilities for working with KnownNat
constraints.
This module is only available on GHC 8.0 or later.
Documentation
plusAssociates :: forall m n o. Dict (((m + n) + o) ~ (m + (n + o))) Source #
timesAssociates :: forall m n o. Dict (((m * n) * o) ~ (m * (n * o))) Source #
plusCommutes :: forall n m. Dict ((m + n) ~ (n + m)) Source #
timesCommutes :: forall n m. Dict ((m * n) ~ (n * m)) Source #
plusDistributesOverTimes :: forall n m o. Dict ((n * (m + o)) ~ ((n * m) + (n * o))) Source #
timesDistributesOverPow :: forall n m o. Dict ((n ^ (m + o)) ~ ((n ^ m) * (n ^ o))) Source #
minIsIdempotent :: forall n. Dict (Min n n ~ n) Source #
maxIsIdempotent :: forall n. Dict (Max n n ~ n) Source #
lcmIsIdempotent :: forall n. Dict (Lcm n n ~ n) Source #
gcdIsIdempotent :: forall n. Dict (Gcd n n ~ n) Source #
plusIsCancellative :: forall n m o. ((n + m) ~ (n + o)) :- (m ~ o) Source #
timesIsCancellative :: forall n m o. (1 <= n, (n * m) ~ (n * o)) :- (m ~ o) Source #
plusMonotone1 :: forall a b c. (a <= b) :- ((a + c) <= (b + c)) Source #
plusMonotone2 :: forall a b c. (b <= c) :- ((a + b) <= (a + c)) Source #
timesMonotone1 :: forall a b c. (a <= b) :- ((a * c) <= (b * c)) Source #
timesMonotone2 :: forall a b c. (b <= c) :- ((a * b) <= (a * c)) Source #
powMonotone1 :: forall a b c. (a <= b) :- ((a ^ c) <= (b ^ c)) Source #
powMonotone2 :: forall a b c. (b <= c) :- ((a ^ b) <= (a ^ c)) Source #
plusMinusInverse1 :: forall n m. Dict (((m + n) - n) ~ m) Source #
plusMinusInverse2 :: forall n m. (m <= n) :- (((m + n) - m) ~ n) Source #
plusMinusInverse3 :: forall n m. (n <= m) :- (((m - n) + n) ~ m) Source #