UniqueLogic.ST.Expression

Documentation

data T w s a

An expression is defined by a set of equations and the variable at the top-level. The value of the expression equals the value of the top variable.

Instances

(C w, C a, Fractional a) => Num (T w s a)

Defined in UniqueLogic.ST.Expression

Methods

(+) :: T w s a -> T w s a -> T w s a

(-) :: T w s a -> T w s a -> T w s a

(*) :: T w s a -> T w s a -> T w s a

negate :: T w s a -> T w s a

abs :: T w s a -> T w s a

signum :: T w s a -> T w s a

fromInteger :: Integer -> T w s a

(C w, C a, Fractional a) => Fractional (T w s a)

Defined in UniqueLogic.ST.Expression

Methods

(/) :: T w s a -> T w s a -> T w s a

recip :: T w s a -> T w s a

fromRational :: Rational -> T w s a

Construct primitive expressions

constant :: (C w, C a) => a -> T w s a

Make a constant expression of a simple numeric value.

fromVariable :: Variable w s a -> T w s a

Operators from rules with small numbers of arguments

fromRule1 :: (C w, C a) => (Variable w s a -> T w s ()) -> T w s a

fromRule2 :: (C w, C b) => (Variable w s a -> Variable w s b -> T w s ()) -> T w s a -> T w s b

fromRule3 :: (C w, C c) => (Variable w s a -> Variable w s b -> Variable w s c -> T w s ()) -> T w s a -> T w s b -> T w s c

Operators from rules with any number of arguments

data Apply w s f

Instances

Applicative (Apply w s)

Defined in UniqueLogic.ST.Expression

Methods

pure :: a -> Apply w s a

(<*>) :: Apply w s (a -> b) -> Apply w s a -> Apply w s b

liftA2 :: (a -> b -> c) -> Apply w s a -> Apply w s b -> Apply w s c

(*>) :: Apply w s a -> Apply w s b -> Apply w s b

(<*) :: Apply w s a -> Apply w s b -> Apply w s a

Functor (Apply w s)

Defined in UniqueLogic.ST.Expression

Methods

fmap :: (a -> b) -> Apply w s a -> Apply w s b

(<$) :: a -> Apply w s b -> Apply w s a

arg :: T w s a -> Apply w s (Variable w s a)

This function allows to generalize fromRule2 and fromRule3 to more arguments using Applicative combinators.

Example:

fromRule3 rule x y
   = runApply $ liftA2 rule (arg x) (arg y)
   = runApply $ pure rule <*> arg x <*> arg y

Building rules with arg provides more granularity than using auxiliary pair rules!

runApply :: (C w, C a) => Apply w s (Variable w s a -> T w s ()) -> T w s a

Predicates on expressions

(=:=) :: C w => T w s a -> T w s a -> T w s () infix 0

Common operators (see also Num and Fractional instances)

(=!=) :: C w => T w s a -> T w s a -> T w s a infixl 4

sqr :: (C w, C a, Floating a) => T w s a -> T w s a

sqrt :: (C w, C a, Floating a) => T w s a -> T w s a

max :: (C w, Ord a, C a) => T w s a -> T w s a -> T w s a

We are not able to implement a full Ord instance including Eq superclass and comparisons, but we need to compute maxima.

maximum :: (C w, Ord a, C a) => [T w s a] -> T w s a

pair :: (C w, C a, C b) => T w s a -> T w s b -> T w s (a, b)

Construct or decompose a pair.