🧠 Translating Logic: From Python to Declarative MeTTa

This guide walks through a three-step translation pipeline to convert typical Python logic into fully declarative, symbolic MeTTa — a language designed for higher-order reasoning and unification-based pattern matching.

Our example comes from the ARC (Abstraction and Reasoning Corpus), where solving visual puzzles involves manipulating objects, colors, and spatial transformations.

Along the way, we demonstrate higher-order programming, where functions are passed and composed dynamically — a core strength preserved in the final MeTTa form.

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✅ Step 1: Start with Python

Here's a Python function using functional composition and direct logic:

def solve_ae3edfdc(I):
    objs = objects(I, T, F, T)
    x = replace(replace(I, THREE, ZERO), SEVEN, ZERO)
    filt = lbind(colorfilter, objs)
    apply_grav = chain(lbind(rbind, gravitate), first, filt)
    x7, x8 = apply_grav(TWO), apply_grav(ONE)
    paint1 = mapply(fork(shift, identity, x7), filt(THREE))
    paint2 = mapply(fork(shift, identity, x8), filt(SEVEN))
    return paint(paint(x, paint1), paint2)

📝 This version is tight, but the logic is implicit — intermediate values are opaque (x, x7, etc), and behavior is hard to follow.

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🧩 Step 2: Expand with Meaningful Names

We rewrite the logic using descriptive names. This reveals the modular structure and makes logic pipelines explicit.

def solve_ae3edfdc(I):
    objs = objects(I, T, F, T)

    replaced_3 = replace(I, THREE, ZERO)
    replaced_3_7 = replace(replaced_3, SEVEN, ZERO)

    color_filtered = lbind(colorfilter, objs)

    gravity_applier = chain(lbind(rbind, gravitate), first, color_filtered)

    gravity_vec_2 = gravity_applier(TWO)
    gravity_vec_1 = gravity_applier(ONE)

    color3_objs = color_filtered(THREE)
    color7_objs = color_filtered(SEVEN)

    shift_3 = fork(shift, identity, gravity_vec_2)
    shift_7 = fork(shift, identity, gravity_vec_1)

    moved_3_objs = mapply(shift_3, color3_objs)
    moved_7_objs = mapply(shift_7, color7_objs)

    painted_3 = paint(replaced_3_7, moved_3_objs)
    output = paint(painted_3, moved_7_objs)

    return output

🔍 This version clarifies:

• Object extraction
• Color filtering
• Gravity vector computation
• Object shifting
• Compositional painting

📎 View Source on GitHub

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🧬 Step 3: Convert to Declarative MeTTa

Now we translate the program into MeTTa, a Datalog-inspired symbolic language using S-expressions and logic variables.

(= (solve_ae3edfdc $I $output)
   (match-and &self
     (objects $I T F T $objs)

     (replace $I THREE ZERO $replaced_3)
     (replace $replaced_3 SEVEN ZERO $replaced_3_7)

     (lbind colorfilter $objs $color_filtered)

     (lbind rbind gravitate $grav_func)
     (chain $grav_func first $color_filtered $gravity_applier)
     ($gravity_applier TWO $gravity_vec_2)
     ($gravity_applier ONE $gravity_vec_1)

     ($color_filtered THREE $color3_objs)
     ($color_filtered SEVEN $color7_objs)

     (fork shift identity $gravity_vec_2 $shift_3)
     (fork shift identity $gravity_vec_1 $shift_7)

     (mapply $shift_3 $color3_objs $moved_3_objs)
     (mapply $shift_7 $color7_objs $moved_7_objs)

     (paint $replaced_3_7 $moved_3_objs $painted_3)
     (paint $painted_3 $moved_7_objs $output)))

🎯 Each step is declarative and referentially transparent. Logic is explicit and composable, enabling:

• Backward and forward reasoning
• Symbolic queries
• Program introspection

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🔄 Why This Workflow?

Step	Purpose
🧩 Expand Python	Improve readability and structure
🧬 Convert to MeTTa	Unlock symbolic reasoning and queryability
♻️ Retain Higher-Order	Preserve abstraction and logic pipelines

This supports logic-heavy systems and AI-focused symbolic inference.

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🧠 What MeTTa Unlocks

By translating to MeTTa, we gain:

✅ Bidirectional reasoning — any variable can be an input or a goal

✅ Composable relations — logic can be reused and inverted

✅ Higher-order logic programming — function pipelines as first-class objects

✅ Explainability — every clause is traceable and transparent

✅ Symbolic search — pose abstract questions like "what shift aligns color-3 with color-7?"

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🧰 Integration with ARC DSL

This MeTTa program works with the arc-dsl.metta library, which provides:

• objects, paint, replace
• Combinators like lbind, chain, fork
• Spatial and logical operators

It composes with other ARC solvers to handle complex visual logic declaratively.