CAS.Dumb

Symbolic manipulation

(&~:) :: (Eq s⁰, Eq s¹, Eq s²) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> CAS s² s¹ s⁰ infixl 1

expr &~: pat :=: rep replaces every occurence of pat within expr with rep.

For example, 𝑎·𝑏 − 𝑐·𝑑 &~: ㄅ·ㄘ :=: ㄘ·ㄅ yields 𝑏·𝑎 − 𝑑·𝑐.

(&~?) :: (Eq s⁰, Eq s¹, Eq s²) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> [CAS s² s¹ s⁰] infixl 1

expr &~? pat :=: rep gives every possible way pat can be replaced exactly once within expr.

For example, 𝑎·𝑏 − 𝑐·𝑑 &~? ㄅ·ㄘ :=: ㄘ·ㄅ yields [𝑏·𝑎 − 𝑐·𝑑, 𝑎·𝑏 − 𝑑·𝑐].

(&~!) :: (Eq s⁰, Eq s¹, Eq s², Show (CAS s² s¹ s⁰), Show (CAS' GapId s² s¹ s⁰)) => CAS s² s¹ s⁰ -> Eqspattern s² s¹ s⁰ -> CAS s² s¹ s⁰ infixl 1

expr &~! pat :=: rep replaces pat exactly once in expr. If this is not possible, an error is raised. If multiple occurences match, the leftmost is preferred.

(&~~!) :: (Eq l, Eq (Encapsulation l), SymbolClass σ, SCConstraint σ l, Show (AlgebraExpr σ l), Show (AlgebraPattern σ l)) => AlgebraExpr σ l -> [AlgebraPattern σ l] -> AlgebraExpr σ l infixl 1

Apply a sequence of pattern-transformations and yield the result concatenated to the original via the corresponding chain-operator. Because only the rightmost expression in a chain is processed, this can be iterated, giving a chain of intermediate results.

If one of the patterns does not match, this manipulator will raise an error.

(&~~:) :: (Eq l, Eq (Encapsulation l), SymbolClass σ, SCConstraint σ l, Show (AlgebraExpr σ l), Show (AlgebraPattern σ l)) => AlgebraExpr σ l -> [AlgebraPattern σ l] -> AlgebraExpr σ l infixl 1

Apply a sequence of pattern-transformations, each in every spot possible, and yield the result concatenated to the original via the corresponding chain-operator. Because only the rightmost expression in a chain is processed, this can be iterated, giving a chain of intermediate results.

continueExpr

Arguments

:: (Eq l, Monoid l)

=> (AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l)

Combinator to use for chaining the new expression to the old ones

-> (AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l)

Transformation to apply to the rightmost expression in the previous chain

-> AlgebraExpr' γ σ l -> AlgebraExpr' γ σ l

Transformation which appends the result.

Constructing equality axioms

data Equality' γ s² s¹ s⁰

Constructors

(:=:) !(CAS' γ s² s¹ s⁰) !(CAS' γ s² s¹ s⁰) infixr 4

Variable-symbols

(%$>) :: forall σ c c' γ s² s¹. (SymbolClass σ, SCConstraint σ c) => (c -> c') -> CAS' γ s² s¹ (SymbolD σ c) -> CAS' γ s² s¹ (SymbolD σ c') infixl 4

Transform the symbols of an expression, in their underlying representation.

(map succ%$> 𝑎+𝑝) * 𝑥  ≡  (𝑏+𝑞) * 𝑥

module CAS.Dumb.Symbols.Unicode.MathLatin_RomanGreek__BopomofoGaps

Debugging

showStructure :: CAS' γ s² s¹ s⁰ -> String

throwStructure :: CAS' γ s² s¹ s⁰ -> CAS' γ s² s¹ s⁰