Tutorial 4

Step 1: Meta-Transformations

Creating higher-order operators that manipulate other transformations:

metaTransform(T) = {
    compose: (T₁ ⊕ T₂) ⇒ T₁ ∘ T₂,
    invert: (T⁻¹)(x) ⇒ λ(x) → original(T(x))
}

Step 2: Context-Driven Rules

Applying conditional logic to transformation pipelines:

contextAware(β, σ) = 
    if (σ ∈ {A,B,C}) then
        β ⊗ γ
    else
        β⁻¹ ⊗ σ

Step 3: Dynamic Evaluation

Use the interactive evaluator to process expressions with dynamic rules:

evaluate(α(x)) with {
    x → { value: 42, context: "B" }
}