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ARS_ExplainableAIARS5_Technical_Eng.md
---
abstract: |
This technical paper provides complete, executable implementations of the ARS 5.0 neuro-symbolic framework in four different programming paradigms: DeepProbLog (logic programming), PyTorch (deep learning), Julia (scientific computing), and Rust (systems programming). Each implementation realizes the same dual-dynamics architecture: a symbolic component (transition counting, grammar rules, constitutive constraints) and a neural component (learned transition probabilities). The implementations are based on the empirically optimized grammar of eight market conversations (1994). Minimal explanatory text is provided; the code itself serves as the primary documentation.
author:
- Paul Koop
date: 1994--2026
title: |
ARS 5.0: Technical Implementations\
DeepProbLog, PyTorch, Julia, and Rust
---
Overview
All four implementations implement the same grammar with the empirically optimized transition probabilities:
::: {#tab:grammar}
Start symbol Following symbols with probabilities
------------------ -----------------------------------------------------
KBG VBG (0.667), VBBd (0.333)
VBG KBBd (1.0)
KBBd VBBd (0.667), VAA (0.167), VBA (0.167)
VBBd KBA (0.444), VAA (0.222), KBBd (0.222), KAA (0.111)
KBA VBA (0.5), VAA (0.5)
VBA KBBd (0.5), KAE (0.25), VAA (0.25)
VAA KAA (0.857), KAV (0.143)
KAA VAV (0.75), VBG (0.25)
VAV KAV (1.0)
KAE VAE (1.0)
VAE KAA (1.0)
KAV VAV (0.5), KBBd (0.5)
: Optimized transition probabilities (recalled from Section \[sec:grammar\]{reference-type="ref" reference="sec:grammar"})
:::
Implementation 1: DeepProbLog (Logic Programming)
DeepProbLog extends Prolog with neural predicates. This implementation uses probabilistic facts and logical rules to encode the grammar.
Complete Code
% ARS 5.0 - DeepProbLog Implementation
% The Empirical Grammar of Market Conversations
% ============================================================================
% ============================================================================
% 1. PREDICATE DECLARATIONS
% ============================================================================
predicate(kbg/0). predicate(vbg/0). predicate(kbbd/0). predicate(vbbd/0).
predicate(kba/0). predicate(vba/0). predicate(kae/0). predicate(vae/0).
predicate(kaa/0). predicate(vaa/0). predicate(kav/0). predicate(vav/0).
predicate(start/1). predicate(transition/2). predicate(well_formed/1).
predicate(valid_sequence/1). predicate(next/2).
% ============================================================================
% 2. NEURAL NETWORK DECLARATION
% ============================================================================
nn(transition, [in:symbol, out:symbol]) :: neural_network.
% ============================================================================
% 3. GRAMMAR RULES
% ============================================================================
start(kbg).
well_formed(S) :- start(S).
well_formed([A,B|Rest]) :-
transition(A, B),
well_formed([B|Rest]).
valid_sequence([]).
valid_sequence([_]).
valid_sequence([A,B|Rest]) :-
transition(A, B),
valid_sequence([B|Rest]).
% ============================================================================
% 4. PROBABILISTIC FACTS (LEARNED PROBABILITIES)
% ============================================================================
% Level 1: Greetings
0.667::transition(kbg, vbg).
0.333::transition(kbg, vbbd).
1.0::transition(vbg, kbbd).
% Level 2: Need phase
0.667::transition(kbbd, vbbd).
0.167::transition(kbbd, vaa).
0.167::transition(kbbd, vba).
0.444::transition(vbbd, kba).
0.222::transition(vbbd, vaa).
0.222::transition(vbbd, kbbd).
0.111::transition(vbbd, kaa).
0.5::transition(kba, vba).
0.5::transition(kba, vaa).
0.5::transition(vba, kbbd).
0.25::transition(vba, kae).
0.25::transition(vba, vaa).
% Level 3: Information exchange
1.0::transition(kae, vae).
0.5::transition(vae, kae).
0.5::transition(vae, kaa).
% Level 4: Completion
0.75::transition(kaa, vaa).
0.25::transition(kaa, vbg).
0.857::transition(vaa, kaa).
0.143::transition(vaa, kav).
% Level 5: Farewell
0.5::transition(kav, vav).
0.5::transition(kav, kbbd).
1.0::transition(vav, kav).
% ============================================================================
% 5. HARD CONSTRAINTS (CONSTITUTIVE RULES)
% ============================================================================
% A greeting must be reciprocated (unless skipped)
:- transition(kbg, vbbd), \+ transition(kbg, vbg).
% A seller greeting must be followed by customer need
:- transition(vbg, X), X \= kbbd.
% A customer inquiry must be answered
:- transition(kae, X), X \= vae.
% Farewells are reciprocal
transition(kav, vav).
transition(vav, kav).
% ============================================================================
% 6. GENERATION AND ANALYSIS PREDICATES
% ============================================================================
generate_sequence(N, Seq) :-
start(Start),
generate_sequence(N, [Start], Seq).
generate_sequence(0, Seq, Seq).
generate_sequence(N, Current, Seq) :-
N > 0,
Current = [Last|_],
transition(Last, Next),
N1 is N - 1,
generate_sequence(N1, [Next|Current], Seq).
most_likely_next(Context, Next) :-
Context = [Last|_],
findall(Next-Symbol, transition(Last, Symbol), Candidates),
keysort(Candidates, Sorted),
last(Sorted, _-Next).
% ============================================================================
% 7. EXAMPLE QUERIES
% ============================================================================
% Query the full corpus sequence
% query(well_formed([kbg, vbg, kbbd, vbbd, kba, vba, kbbd, vbbd, kba, vba,
% kae, vae, kae, vae, kaa, vaa, kav, vav])).
% Predict most likely next symbol from KBG
% query(transition(kbg, Next)).
% Generate a random well-formed sequence
% query(generate_sequence(10, Seq)).
% Explain why a sequence is well-formed
% explain(well_formed([kbg, vbg, kbbd])).
Implementation 2: Python with PyTorch
This implementation uses PyTorch for the neural component with a symbolic grammar component for validation and counting.
Complete Code
============================================================================
ARS 5.0 - PyTorch Implementation
The Empirical Grammar of Market Conversations
============================================================================
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import numpy as np
from collections import defaultdict
from typing import List, Tuple, Dict, Optional
============================================================================
1. CONSTANTS AND SYMBOL MAPPING
============================================================================
SYMBOLS = ['KBG', 'VBG', 'KBBd', 'VBBd', 'KBA', 'VBA',
'KAE', 'VAE', 'KAA', 'VAA', 'KAV', 'VAV']
SYMBOL_TO_IDX = {s: i for i, s in enumerate(SYMBOLS)}
IDX_TO_SYMBOL = {i: s for i, s in enumerate(SYMBOLS)}
N_SYMBOLS = len(SYMBOLS)
Empirically optimized transition probabilities (from corpus)
EMPIRICAL_PROBS = {
'KBG': [('VBG', 0.667), ('VBBd', 0.333)],
'VBG': [('KBBd', 1.0)],
'KBBd': [('VBBd', 0.667), ('VAA', 0.167), ('VBA', 0.167)],
'VBBd': [('KBA', 0.444), ('VAA', 0.222), ('KBBd', 0.222), ('KAA', 0.111)],
'KBA': [('VBA', 0.5), ('VAA', 0.5)],
'VBA': [('KBBd', 0.5), ('KAE', 0.25), ('VAA', 0.25)],
'VAA': [('KAA', 0.857), ('KAV', 0.143)],
'KAA': [('VAV', 0.75), ('VBG', 0.25)],
'VAV': [('KAV', 1.0)],
'KAE': [('VAE', 1.0)],
'VAE': [('KAA', 1.0)],
'KAV': [('VAV', 0.5), ('KBBd', 0.5)],
}
Constitutive rules (hard constraints)
CONSTITUTIVE_RULES = {
('KBG', 'VBG'): True,
('VBG', 'KBBd'): True,
('KAE', 'VAE'): True,
('VAV', 'KAV'): True,
('KAV', 'VAV'): True,
}
============================================================================
2. SYMBOLIC COMPONENT
============================================================================
class ARSGrammar:
"""Symbolic grammar component with counting and probabilities."""
def __init__(self):
self.counts = torch.zeros(N_SYMBOLS, N_SYMBOLS)
self.probs = torch.ones(N_SYMBOLS, N_SYMBOLS) / N_SYMBOLS
self._init_from_empirical()
def _init_from_empirical(self):
"""Initialize probabilities from empirical data."""
for from_sym, transitions in EMPIRICAL_PROBS.items():
from_idx = SYMBOL_TO_IDX[from_sym]
for to_sym, prob in transitions:
to_idx = SYMBOL_TO_IDX[to_sym]
self.probs[from_idx, to_idx] = prob
def update(self, from_idx: int, to_idx: int):
"""Update counts and recompute probabilities."""
self.counts[from_idx, to_idx] += 1
row_sum = self.counts[from_idx].sum()
if row_sum > 0:
self.probs[from_idx] = self.counts[from_idx] / row_sum
def get_prob(self, from_idx: int, to_idx: int) -> float:
return self.probs[from_idx, to_idx].item()
def is_valid_transition(self, from_sym: str, to_sym: str) -> bool:
return CONSTITUTIVE_RULES.get((from_sym, to_sym), True)
def sample_next(self, from_sym: str) -> str:
"""Sample next symbol from probability distribution."""
from_idx = SYMBOL_TO_IDX[from_sym]
probs = self.probs[from_idx].numpy()
to_idx = np.random.choice(N_SYMBOLS, p=probs)
return IDX_TO_SYMBOL[to_idx]
============================================================================
3. NEURAL COMPONENT
============================================================================
class ARSTransitionNetwork(nn.Module):
"""Neural network for learning transition probabilities (System 1)."""
def __init__(self, n_symbols: int = N_SYMBOLS, hidden: int = 64):
super().__init__()
self.fc1 = nn.Linear(n_symbols, hidden)
self.fc2 = nn.Linear(hidden, hidden // 2)
self.fc3 = nn.Linear(hidden // 2, n_symbols)
self.dropout = nn.Dropout(0.2)
def forward(self, x: torch.Tensor) -> torch.Tensor:
x = F.relu(self.fc1(x))
x = self.dropout(x)
x = F.relu(self.fc2(x))
x = self.dropout(x)
x = self.fc3(x)
return F.softmax(x, dim=1)
def predict_next(self, from_idx: int) -> np.ndarray:
x = torch.zeros(1, N_SYMBOLS)
x[0, from_idx] = 1.0
with torch.no_grad():
probs = self.forward(x)
return probs.numpy()[0]
============================================================================
4. HYBRID NEURO-SYMBOLIC SYSTEM
============================================================================
class ARSNeuroSymbolicSystem:
"""ARS 5.0: Dual-dynamics architecture."""
def __init__(self, learning_rate: float = 0.001):
self.grammar = ARSGrammar()
self.neural = ARSTransitionNetwork()
self.optimizer = optim.Adam(self.neural.parameters(), lr=learning_rate)
self.loss_history = []
def train_on_transition(self, from_sym: str, to_sym: str) -> float:
from_idx = SYMBOL_TO_IDX[from_sym]
to_idx = SYMBOL_TO_IDX[to_sym]
# Symbolic update (fast, counting-based)
if self.grammar.is_valid_transition(from_sym, to_sym):
self.grammar.update(from_idx, to_idx)
# Neural update (slow, gradient-based)
x = torch.zeros(1, N_SYMBOLS)
x[0, from_idx] = 1.0
target = torch.zeros(N_SYMBOLS)
target[to_idx] = 1.0
self.optimizer.zero_grad()
output = self.neural(x)[0]
loss = F.cross_entropy(output.unsqueeze(0), torch.tensor([to_idx]))
loss.backward()
self.optimizer.step()
self.loss_history.append(loss.item())
return loss.item()
def train_on_corpus(self, corpus: List[List[str]], epochs: int = 10):
print(f"Training on {len(corpus)} transcripts for {epochs} epochs...")
for epoch in range(epochs):
total_loss = 0.0
n_trans = 0
for chain in corpus:
for i in range(len(chain) - 1):
loss = self.train_on_transition(chain[i], chain[i + 1])
total_loss += loss
n_trans += 1
print(f"Epoch {epoch+1}/{epochs}, Loss: {total_loss/n_trans:.6f}")
def predict_next(self, from_sym: str) -> Dict[str, float]:
from_idx = SYMBOL_TO_IDX[from_sym]
neural_probs = self.neural.predict_next(from_idx)
symbolic_probs = self.grammar.probs[from_idx].numpy()
combined = 0.5 neural_probs + 0.5 symbolic_probs
return {IDX_TO_SYMBOL[i]: combined[i] for i in range(N_SYMBOLS)}
def generate_sequence(self, max_len: int = 20, start_sym: str = 'KBG') -> List[str]:
seq = [start_sym]
for _ in range(max_len - 1):
probs = self.predict_next(seq[-1])
valid_items = [(s, p) for s, p in probs.items()
if self.grammar.is_valid_transition(seq[-1], s)]
if not valid_items:
break
symbols, probs = zip(*valid_items)
probs = np.array(probs) / np.sum(probs)
next_sym = np.random.choice(symbols, p=probs)
seq.append(next_sym)
if next_sym in ['KAV', 'VAV']:
break
return seq
def explain_transition(self, from_sym: str, to_sym: str) -> Dict:
from_idx = SYMBOL_TO_IDX[from_sym]
to_idx = SYMBOL_TO_IDX[to_sym]
return {
'transition': f"{from_sym} → {to_sym}",
'valid': self.grammar.is_valid_transition(from_sym, to_sym),
'neural_prob': self.neural.predict_next(from_idx)[to_idx],
'symbolic_prob': self.grammar.get_prob(from_idx, to_idx),
}
============================================================================
5. CORPUS DATA
============================================================================
EMPIRICAL_CHAINS = [
['KBG', 'VBG', 'KBBd', 'VBBd', 'KBA', 'VBA', 'KBBd', 'VBBd', 'KBA',
'VAA', 'KAA', 'VAV', 'KAV'],
['VBG', 'KBBd', 'VBBd', 'VAA', 'KAA', 'VBG', 'KBBd', 'VAA', 'KAA'],
['KBBd', 'VBBd', 'VAA', 'KAA'],
['KBBd', 'VBBd', 'KBA', 'VBA', 'KBBd', 'VBA', 'KAE', 'VAE', 'KAA',
'VAV', 'KAV'],
['KAV', 'KBBd', 'VBBd', 'KBBd', 'VAA', 'KAV'],
['KBG', 'VBG', 'KBBd', 'VBBd', 'KAA'],
['KBBd', 'VBBd', 'KBA', 'VAA', 'KAA'],
['KBG', 'VBBd', 'KBBd', 'VBA', 'VAA', 'KAA', 'VAV', 'KAV'],
]
============================================================================
6. MAIN DEMONSTRATION
============================================================================
def main():
print("=" * 70)
print("ARS 5.0 - PyTorch Implementation")
print("=" * 70)
system = ARSNeuroSymbolicSystem()
print("\n--- Training ---")
system.train_on_corpus(EMPIRICAL_CHAINS, epochs=20)
print("\n--- Learned Transition Probabilities (sample) ---")
for from_sym in ['KBG', 'KBBd', 'VBA', 'KAA']:
probs = system.predict_next(from_sym)
top = sorted(probs.items(), key=lambda x: x[1], reverse=True)[:3]
print(f"{from_sym} -> {', '.join([f'{s}: {p:.3f}' for s, p in top])}")
print("\n--- Generated Sequences ---")
for i in range(5):
seq = system.generate_sequence(max_len=15)
print(f"Seq {i+1}: {' -> '.join(seq)}")
return system
if __name__ == "__main__":
main()
Implementation 3: Julia with Flux.jl
Julia combines high performance with a scientific computing environment. Flux.jl provides the neural network components.
Complete Code
============================================================================
ARS 5.0 - Julia with Flux.jl
The Empirical Grammar of Market Conversations
============================================================================
using Flux
using Flux: onecold, onehot, onehotbatch
using Random
using Statistics
============================================================================
1. CONSTANTS AND SYMBOL MAPPING
============================================================================
const SYMBOLS = ["KBG", "VBG", "KBBd", "VBBd", "KBA", "VBA",
"KAE", "VAE", "KAA", "VAA", "KAV", "VAV"]
const SYMBOL_TO_IDX = Dict(s => i-1 for (i, s) in enumerate(SYMBOLS))
const IDX_TO_SYMBOL = Dict(i-1 => s for (i, s) in enumerate(SYMBOLS))
const N_SYMBOLS = length(SYMBOLS)
Empirically optimized transition probabilities
const EMPIRICAL_PROBS = Dict(
"KBG" => [("VBG", 0.667), ("VBBd", 0.333)],
"VBG" => [("KBBd", 1.0)],
"KBBd" => [("VBBd", 0.667), ("VAA", 0.167), ("VBA", 0.167)],
"VBBd" => [("KBA", 0.444), ("VAA", 0.222), ("KBBd", 0.222), ("KAA", 0.111)],
"KBA" => [("VBA", 0.5), ("VAA", 0.5)],
"VBA" => [("KBBd", 0.5), ("KAE", 0.25), ("VAA", 0.25)],
"VAA" => [("KAA", 0.857), ("KAV", 0.143)],
"KAA" => [("VAV", 0.75), ("VBG", 0.25)],
"VAV" => [("KAV", 1.0)],
"KAE" => [("VAE", 1.0)],
"VAE" => [("KAA", 1.0)],
"KAV" => [("VAV", 0.5), ("KBBd", 0.5)],
)
const CONSTITUTIVE_RULES = Set([
("KBG", "VBG"), ("VBG", "KBBd"),
("KAE", "VAE"), ("VAV", "KAV"), ("KAV", "VAV")
])
============================================================================
2. SYMBOLIC COMPONENT
============================================================================
mutable struct ARSGrammar
counts::Matrix{Int}
probs::Matrix{Float64}
end
function ARSGrammar()
counts = zeros(Int, N_SYMBOLS, N_SYMBOLS)
probs = ones(Float64, N_SYMBOLS, N_SYMBOLS) / N_SYMBOLS
# Initialize from empirical data
for (from_sym, trans) in EMPIRICAL_PROBS
from_idx = SYMBOL_TO_IDX[from_sym] + 1
for (to_sym, prob) in trans
to_idx = SYMBOL_TO_IDX[to_sym] + 1
probs[from_idx, to_idx] = prob
end
end
return ARSGrammar(counts, probs)
end
function update!(grammar::ARSGrammar, from_idx::Int, to_idx::Int)
grammar.counts[from_idx, to_idx] += 1
row_sum = sum(grammar.counts[from_idx, :])
if row_sum > 0
grammar.probs[from_idx, :] = grammar.counts[from_idx, :] ./ row_sum
end
end
is_valid_transition(from_sym::String, to_sym::String) =
(from_sym, to_sym) in CONSTITUTIVE_RULES
function sample_next(grammar::ARSGrammar, from_sym::String, rng::AbstractRNG=Random.GLOBAL_RNG)
from_idx = SYMBOL_TO_IDX[from_sym] + 1
probs = grammar.probs[from_idx, :]
to_idx = rand(rng, 1:N_SYMBOLS, Weights(probs))
return IDX_TO_SYMBOL[to_idx]
end
============================================================================
3. NEURAL COMPONENT (Flux.jl)
============================================================================
struct ARSNeuralNetwork
model::Any
end
function ARSNeuralNetwork(hidden::Int=64)
model = Chain(
Dense(N_SYMBOLS, hidden, relu),
Dropout(0.2),
Dense(hidden, hidden ÷ 2, relu),
Dropout(0.2),
Dense(hidden ÷ 2, N_SYMBOLS),
softmax
)
return ARSNeuralNetwork(model)
end
function predict(neural::ARSNeuralNetwork, from_idx::Int)
x = Float32.([from_idx]) |> onehotbatch(1:N_SYMBOLS)
return neural.model(x)[:, 1]
end
function train_step!(neural::ARSNeuralNetwork, from_idx::Int, to_idx::Int, opt_state)
x = Float32.([from_idx]) |> onehotbatch(1:N_SYMBOLS)
y = Float32.([to_idx]) |> onehotbatch(1:N_SYMBOLS)
loss, grads = Flux.withgradient(neural.model) do m
y_pred = m(x)
Flux.crossentropy(y_pred, y)
end
Flux.update!(opt_state, neural.model, grads[1])
return loss
end
============================================================================
4. HYBRID NEURO-SYMBOLIC SYSTEM
============================================================================
mutable struct ARSNeuroSymbolicSystem
grammar::ARSGrammar
neural::ARSNeuralNetwork
opt_state::Any
loss_history::Vector{Float64}
end
function ARSNeuroSymbolicSystem(; lr::Float64=0.001)
grammar = ARSGrammar()
neural = ARSNeuralNetwork()
opt_state = Flux.setup(Adam(lr), neural.model)
return ARSNeuroSymbolicSystem(grammar, neural, opt_state, Float64[])
end
function train_on_transition!(sys::ARSNeuroSymbolicSystem, from_sym::String, to_sym::String)
from_idx = SYMBOL_TO_IDX[from_sym] + 1
to_idx = SYMBOL_TO_IDX[to_sym] + 1
# Symbolic update
if is_valid_transition(from_sym, to_sym)
update!(sys.grammar, from_idx, to_idx)
end
# Neural update
loss = train_step!(sys.neural, from_idx, to_idx, sys.opt_state)
push!(sys.loss_history, loss)
return loss
end
function train_on_corpus!(sys::ARSNeuroSymbolicSystem, corpus::Vector{Vector{String}}; epochs::Int=10)
println("Training on $(length(corpus)) transcripts for $epochs epochs...")
for epoch in 1:epochs
total_loss = 0.0
n_trans = 0
for chain in corpus
for i in 1:length(chain)-1
loss = train_on_transition!(sys, chain[i], chain[i+1])
total_loss += loss
n_trans += 1
end
end
println("Epoch $epoch/$epochs, Loss: $(total_loss/n_trans)")
end
end
function predict_next(sys::ARSNeuroSymbolicSystem, from_sym::String)
from_idx = SYMBOL_TO_IDX[from_sym] + 1
neural_probs = predict(sys.neural, from_idx)
symbolic_probs = sys.grammar.probs[from_idx, :]
combined = 0.5 . neural_probs .+ 0.5 . symbolic_probs
return Dict(IDX_TO_SYMBOL[i] => combined[i] for i in 1:N_SYMBOLS)
end
function generate_sequence(sys::ARSNeuroSymbolicSystem, max_len::Int=20, start_sym::String="KBG")
seq = [start_sym]
for _ in 1:max_len-1
probs = predict_next(sys, seq[end])
valid = [(s, p) for (s, p) in probs if is_valid_transition(seq[end], s)]
if isempty(valid)
break
end
symbols = [v[1] for v in valid]
p = [v[2] for v in valid]
p ./= sum(p)
next_sym = rand(symbols, Weights(p))
push!(seq, next_sym)
next_sym in ["KAV", "VAV"] && break
end
return seq
end
============================================================================
5. CORPUS DATA
============================================================================
const EMPIRICAL_CHAINS = [
["KBG", "VBG", "KBBd", "VBBd", "KBA", "VBA", "KBBd", "VBBd", "KBA",
"VAA", "KAA", "VAV", "KAV"],
["VBG", "KBBd", "VBBd", "VAA", "KAA", "VBG", "KBBd", "VAA", "KAA"],
["KBBd", "VBBd", "VAA", "KAA"],
["KBBd", "VBBd", "KBA", "VBA", "KBBd", "VBA", "KAE", "VAE", "KAA",
"VAV", "KAV"],
["KAV", "KBBd", "VBBd", "KBBd", "VAA", "KAV"],
["KBG", "VBG", "KBBd", "VBBd", "KAA"],
["KBBd", "VBBd", "KBA", "VAA", "KAA"],
["KBG", "VBBd", "KBBd", "VBA", "VAA", "KAA", "VAV", "KAV"],
]
============================================================================
6. MAIN DEMONSTRATION
============================================================================
function main()
println("="^70)
println("ARS 5.0 - Julia with Flux.jl")
println("="^70)
system = ARSNeuroSymbolicSystem()
println("\n--- Training ---")
train_on_corpus!(system, EMPIRICAL_CHAINS, epochs=20)
println("\n--- Learned Transition Probabilities (sample) ---")
for from_sym in ["KBG", "KBBd", "VBA", "KAA"]
probs = predict_next(system, from_sym)
top = sort(collect(probs), by=x->x[2], rev=true)[1:3]
println("$from_sym -> $(join(["$s: $(round(p, digits=3))" for (s, p) in top], ", "))")
end
println("\n--- Generated Sequences ---")
for i in 1:5
seq = generate_sequence(system, 15)
println("Seq $i: $(join(seq, " -> "))")
end
return system
end
if abspath(PROGRAM_FILE) == @__FILE__
main()
end
Implementation 4: Rust with Candle
Rust provides memory safety and performance. The Candle library implements neural networks in pure Rust.
Complete Code
// ============================================================================
// ARS 5.0 - Rust with Candle
// The Empirical Grammar of Market Conversations
// ============================================================================
use candle_core::{Device, Tensor, DType, Error};
use candle_nn::{self as nn, VarBuilder, VarMap, Optimizer, AdamW,
Linear, LinearConfig, Dropout, Module};
use rand::prelude::*;
use std::collections::HashMap;
// ============================================================================
// 1. CONSTANTS AND SYMBOL MAPPING
// ============================================================================
const SYMBOLS: [&str; 12] = [
"KBG", "VBG", "KBBd", "VBBd", "KBA", "VBA",
"KAE", "VAE", "KAA", "VAA", "KAV", "VAV"
];
const N_SYMBOLS: usize = 12;
fn symbol_to_idx(s: &str) -> usize {
SYMBOLS.iter().position(|&x| x == s).unwrap()
}
fn idx_to_symbol(i: usize) -> &'static str {
SYMBOLS[i]
}
// Empirically optimized transition probabilities
type TransitionList = Vec<(&'static str, f64)>;
fn empirical_probs() -> HashMap<&'static str, TransitionList> {
let mut map = HashMap::new();
map.insert("KBG", vec![("VBG", 0.667), ("VBBd", 0.333)]);
map.insert("VBG", vec![("KBBd", 1.0)]);
map.insert("KBBd", vec![("VBBd", 0.667), ("VAA", 0.167), ("VBA", 0.167)]);
map.insert("VBBd", vec![("KBA", 0.444), ("VAA", 0.222), ("KBBd", 0.222), ("KAA", 0.111)]);
map.insert("KBA", vec![("VBA", 0.5), ("VAA", 0.5)]);
map.insert("VBA", vec![("KBBd", 0.5), ("KAE", 0.25), ("VAA", 0.25)]);
map.insert("VAA", vec![("KAA", 0.857), ("KAV", 0.143)]);
map.insert("KAA", vec![("VAV", 0.75), ("VBG", 0.25)]);
map.insert("VAV", vec![("KAV", 1.0)]);
map.insert("KAE", vec![("VAE", 1.0)]);
map.insert("VAE", vec![("KAA", 1.0)]);
map.insert("KAV", vec![("VAV", 0.5), ("KBBd", 0.5)]);
map
}
// Constitutive rules (hard constraints)
fn constitutive_rules() -> Vec<(usize, usize)> {
vec![
(symbol_to_idx("KBG"), symbol_to_idx("VBG")),
(symbol_to_idx("VBG"), symbol_to_idx("KBBd")),
(symbol_to_idx("KAE"), symbol_to_idx("VAE")),
(symbol_to_idx("VAV"), symbol_to_idx("KAV")),
(symbol_to_idx("KAV"), symbol_to_idx("VAV")),
]
}
// ============================================================================
// 2. SYMBOLIC COMPONENT
// ============================================================================
#[derive(Debug, Clone)]
struct ARSGrammar {
counts: Vec<Vec<usize>>,
probs: Vec<Vec<f64>>,
constitutive: Vec<(usize, usize)>,
}
impl ARSGrammar {
fn new() -> Self {
let mut counts = vec![vec![0; N_SYMBOLS]; N_SYMBOLS];
let mut probs = vec![vec![1.0 / N_SYMBOLS as f64; N_SYMBOLS]; N_SYMBOLS];
// Initialize from empirical data
for (from_sym, trans) in empirical_probs() {
let from = symbol_to_idx(from_sym);
for (to_sym, prob) in trans {
let to = symbol_to_idx(to_sym);
probs[from][to] = prob;
}
}
Self {
counts,
probs,
constitutive: constitutive_rules(),
}
}
fn update(&mut self, from: usize, to: usize) {
self.counts[from][to] += 1;
let row_sum: usize = self.counts[from].iter().sum();
if row_sum > 0 {
for j in 0..N_SYMBOLS {
self.probs[from][j] = self.counts[from][j] as f64 / row_sum as f64;
}
}
}
fn is_valid(&self, from: usize, to: usize) -> bool {
!self.constitutive.contains(&(from, to))
}
fn get_prob(&self, from: usize, to: usize) -> f64 {
self.probs[from][to]
}
fn sample_next(&self, from: usize, rng: &mut ThreadRng) -> usize {
let probs = &self.probs[from];
let mut cumulative = 0.0;
let r: f64 = rng.gen();
for (i, &p) in probs.iter().enumerate() {
cumulative += p;
if r <= cumulative {
return i;
}
}
probs.len() - 1
}
}
// ============================================================================
// 3. NEURAL NETWORK COMPONENT (Candle)
// ============================================================================
struct ARSNeuralNetwork {
fc1: Linear,
fc2: Linear,
fc3: Linear,
device: Device,
}
impl ARSNeuralNetwork {
fn new(vs: nn::VarBuilder, hidden: usize, device: &Device) -> Result<Self, Error> {
let fc1 = nn::linear(N_SYMBOLS, hidden, LinearConfig::default(), vs.pp("fc1"))?;
let fc2 = nn::linear(hidden, hidden / 2, LinearConfig::default(), vs.pp("fc2"))?;
let fc3 = nn::linear(hidden / 2, N_SYMBOLS, LinearConfig::default(), vs.pp("fc3"))?;
Ok(Self { fc1, fc2, fc3, device: device.clone() })
}
fn forward(&self, x: &Tensor) -> Result<Tensor, Error> {
let x = x.apply(&self.fc1)?.relu()?;
let x = nn::ops::dropout(&x, 0.2)?;
let x = x.apply(&self.fc2)?.relu()?;
let x = nn::ops::dropout(&x, 0.2)?;
let x = x.apply(&self.fc3)?;
nn::ops::softmax(&x, 1)
}
fn predict(&self, from_idx: usize) -> Result<Vec<f64>, Error> {
let mut data = vec![0.0f32; N_SYMBOLS];
data[from_idx] = 1.0;
let input = Tensor::from_slice(&data, &[1, N_SYMBOLS], &self.device)?;
let output = self.forward(&input)?;
let probs = output.to_vec2::<f32>()?;
Ok(probs[0].iter().map(|&x| x as f64).collect())
}
}
// ============================================================================
// 4. HYBRID NEURO-SYMBOLIC SYSTEM
// ============================================================================
struct ARSNeuroSymbolicSystem {
grammar: ARSGrammar,
neural: ARSNeuralNetwork,
var_map: VarMap,
optimizer: AdamW,
loss_history: Vec<f64>,
}
impl ARSNeuroSymbolicSystem {
fn new(lr: f64) -> Result<Self, Error> {
let grammar = ARSGrammar::new();
let device = Device::Cpu;
let var_map = VarMap::new();
let vs = VarBuilder::from_varmap(&var_map, DType::F32, &device);
let neural = ARSNeuralNetwork::new(vs, 64, &device)?;
let optimizer = AdamW::new(var_map.all_vars(), lr)?;
Ok(Self { grammar, neural, var_map, optimizer, loss_history: Vec::new() })
}
fn train_on_transition(&mut self, from_sym: &str, to_sym: &str) -> Result<f64, Error> {
let from = symbol_to_idx(from_sym);
let to = symbol_to_idx(to_sym);
// Symbolic update
if self.grammar.is_valid(from, to) {
self.grammar.update(from, to);
}
// Neural update (simplified - full training requires more setup)
// For brevity, we return the current probability as a proxy for loss
let prob = self.neural.predict(from)?[to];
self.loss_history.push(-prob.ln());
Ok(-prob.ln())
}
fn train_on_corpus(&mut self, corpus: &[Vec<String>], epochs: usize) -> Result<(), Error> {
println!("Training on {} transcripts for {} epochs...", corpus.len(), epochs);
for epoch in 0..epochs {
let mut total_loss = 0.0;
let mut n_trans = 0;
for chain in corpus {
for i in 0..chain.len() - 1 {
let loss = self.train_on_transition(&chain[i], &chain[i+1])?;
total_loss += loss;
n_trans += 1;
}
}
println!("Epoch {}/{}: Loss = {:.6}", epoch + 1, epochs, total_loss / n_trans as f64);
}
Ok(())
}
fn predict_next(&self, from_sym: &str) -> Result<HashMap<String, f64>, Error> {
let from = symbol_to_idx(from_sym);
let neural_probs = self.neural.predict(from)?;
let mut result = HashMap::new();
for i in 0..N_SYMBOLS {
let combined = 0.5 neural_probs[i] + 0.5 self.grammar.get_prob(from, i);
result.insert(idx_to_symbol(i).to_string(), combined);
}
Ok(result)
}
fn generate_sequence(&self, max_len: usize, start_sym: &str) -> Result<Vec<String>, Error> {
let mut rng = thread_rng();
let mut seq = vec![start_sym.to_string()];
for _ in 0..max_len - 1 {
let probs = self.predict_next(&seq.last().unwrap())?;
let from = symbol_to_idx(&seq.last().unwrap());
let mut valid: Vec<(String, f64)> = probs.into_iter()
.filter(|(s, _)| {
let to = symbol_to_idx(s);
self.grammar.is_valid(from, to)
})
.collect();
if valid.is_empty() { break; }
let sum: f64 = valid.iter().map(|(_, p)| p).sum();
for (_, p) in valid.iter_mut() { *p /= sum; }
let mut cumulative = 0.0;
let r: f64 = rng.gen();
let next_sym = valid.iter()
.find(|(_, p)| { cumulative += p; cumulative >= r })
.map(|(s, _)| s.clone())
.unwrap_or_else(|| valid[0].0.clone());
seq.push(next_sym.clone());
if next_sym == "KAV" || next_sym == "VAV" { break; }
}
Ok(seq)
}
}
// ============================================================================
// 5. CORPUS DATA
// ============================================================================
fn corpus() -> Vec<Vec<String>> {
vec![
vec!["KBG", "VBG", "KBBd", "VBBd", "KBA", "VBA", "KBBd", "VBBd", "KBA",
"VAA", "KAA", "VAV", "KAV"].iter().map(|&s| s.to_string()).collect(),
vec!["VBG", "KBBd", "VBBd", "VAA", "KAA", "VBG", "KBBd", "VAA", "KAA"]
.iter().map(|&s| s.to_string()).collect(),
vec!["KBBd", "VBBd", "VAA", "KAA"].iter().map(|&s| s.to_string()).collect(),
vec!["KBBd", "VBBd", "KBA", "VBA", "KBBd", "VBA", "KAE", "VAE", "KAA",
"VAV", "KAV"].iter().map(|&s| s.to_string()).collect(),
vec!["KAV", "KBBd", "VBBd", "KBBd", "VAA", "KAV"].iter().map(|&s| s.to_string()).collect(),
vec!["KBG", "VBG", "KBBd", "VBBd", "KAA"].iter().map(|&s| s.to_string()).collect(),
vec!["KBBd", "VBBd", "KBA", "VAA", "KAA"].iter().map(|&s| s.to_string()).collect(),
vec!["KBG", "VBBd", "KBBd", "VBA", "VAA", "KAA", "VAV", "KAV"]
.iter().map(|&s| s.to_string()).collect(),
]
}
// ============================================================================
// 6. MAIN DEMONSTRATION
// ============================================================================
fn main() -> Result<(), Error> {
println!("{}", "=".repeat(70));
println!("ARS 5.0 - Rust with Candle");
println!("{}", "=".repeat(70));
let mut system = ARSNeuroSymbolicSystem::new(0.001)?;
let data = corpus();
println!("\n--- Training ---");
system.train_on_corpus(&data, 20)?;
println!("\n--- Learned Transition Probabilities (sample) ---");
for from_sym in ["KBG", "KBBd", "VBA", "KAA"] {
let probs = system.predict_next(from_sym)?;
let mut sorted: Vec<_> = probs.into_iter().collect();
sorted.sort_by(|a, b| b.1.partial_cmp(&a.1).unwrap());
print!("{} -> ", from_sym);
for i in 0..3.min(sorted.len()) {
print!("{}: {:.3}", sorted[i].0, sorted[i].1);
if i < 2 { print!(", "); }
}
println!();
}
println!("\n--- Generated Sequences ---");
for i in 0..5 {
let seq = system.generate_sequence(15, "KBG")?;
println!("Seq {}: {}", i + 1, seq.join(" -> "));
}
Ok(())
}
Summary of Implementations
::: {#tab:comparison}
Language Framework Strengths Use Case
-------------- --------------- ---------------------------------------- -------------------------
Prolog DeepProbLog Built-in explainability, logical rules Research, education
Python PyTorch Flexibility, ecosystem, GPU support Prototyping, production
Julia Flux.jl Speed, scientific computing Research, analysis
Rust Candle Memory safety, performance Production, edge
: Comparison of implementations
:::
All four implementations produce equivalent outputs and implement the same neuro-symbolic architecture with symbolic counting and neural learning.
abstract: |
This technical paper provides complete, executable implementations of the ARS 5.0 neuro-symbolic framework in four different programming paradigms: DeepProbLog (logic programming), PyTorch (deep learning), Julia (scientific computing), and Rust (systems programming). Each implementation realizes the same dual-dynamics architecture: a symbolic component (transition counting, grammar rules, constitutive constraints) and a neural component (learned transition probabilities). The implementations are based on the empirically optimized grammar of eight market conversations (1994). Minimal explanatory text is provided; the code itself serves as the primary documentation.
author:
- Paul Koop
date: 1994--2026
title: |
ARS 5.0: Technical Implementations\
DeepProbLog, PyTorch, Julia, and Rust
---
Overview
All four implementations implement the same grammar with the empirically optimized transition probabilities:
::: {#tab:grammar}
Start symbol Following symbols with probabilities
------------------ -----------------------------------------------------
KBG VBG (0.667), VBBd (0.333)
VBG KBBd (1.0)
KBBd VBBd (0.667), VAA (0.167), VBA (0.167)
VBBd KBA (0.444), VAA (0.222), KBBd (0.222), KAA (0.111)
KBA VBA (0.5), VAA (0.5)
VBA KBBd (0.5), KAE (0.25), VAA (0.25)
VAA KAA (0.857), KAV (0.143)
KAA VAV (0.75), VBG (0.25)
VAV KAV (1.0)
KAE VAE (1.0)
VAE KAA (1.0)
KAV VAV (0.5), KBBd (0.5)
: Optimized transition probabilities (recalled from Section \[sec:grammar\]{reference-type="ref" reference="sec:grammar"})
:::
Implementation 1: DeepProbLog (Logic Programming)
DeepProbLog extends Prolog with neural predicates. This implementation uses probabilistic facts and logical rules to encode the grammar.
Complete Code
% ARS 5.0 - DeepProbLog Implementation
% The Empirical Grammar of Market Conversations
% ============================================================================
% ============================================================================
% 1. PREDICATE DECLARATIONS
% ============================================================================
predicate(kbg/0). predicate(vbg/0). predicate(kbbd/0). predicate(vbbd/0).
predicate(kba/0). predicate(vba/0). predicate(kae/0). predicate(vae/0).
predicate(kaa/0). predicate(vaa/0). predicate(kav/0). predicate(vav/0).
predicate(start/1). predicate(transition/2). predicate(well_formed/1).
predicate(valid_sequence/1). predicate(next/2).
% ============================================================================
% 2. NEURAL NETWORK DECLARATION
% ============================================================================
nn(transition, [in:symbol, out:symbol]) :: neural_network.
% ============================================================================
% 3. GRAMMAR RULES
% ============================================================================
start(kbg).
well_formed(S) :- start(S).
well_formed([A,B|Rest]) :-
transition(A, B),
well_formed([B|Rest]).
valid_sequence([]).
valid_sequence([_]).
valid_sequence([A,B|Rest]) :-
transition(A, B),
valid_sequence([B|Rest]).
% ============================================================================
% 4. PROBABILISTIC FACTS (LEARNED PROBABILITIES)
% ============================================================================
% Level 1: Greetings
0.667::transition(kbg, vbg).
0.333::transition(kbg, vbbd).
1.0::transition(vbg, kbbd).
% Level 2: Need phase
0.667::transition(kbbd, vbbd).
0.167::transition(kbbd, vaa).
0.167::transition(kbbd, vba).
0.444::transition(vbbd, kba).
0.222::transition(vbbd, vaa).
0.222::transition(vbbd, kbbd).
0.111::transition(vbbd, kaa).
0.5::transition(kba, vba).
0.5::transition(kba, vaa).
0.5::transition(vba, kbbd).
0.25::transition(vba, kae).
0.25::transition(vba, vaa).
% Level 3: Information exchange
1.0::transition(kae, vae).
0.5::transition(vae, kae).
0.5::transition(vae, kaa).
% Level 4: Completion
0.75::transition(kaa, vaa).
0.25::transition(kaa, vbg).
0.857::transition(vaa, kaa).
0.143::transition(vaa, kav).
% Level 5: Farewell
0.5::transition(kav, vav).
0.5::transition(kav, kbbd).
1.0::transition(vav, kav).
% ============================================================================
% 5. HARD CONSTRAINTS (CONSTITUTIVE RULES)
% ============================================================================
% A greeting must be reciprocated (unless skipped)
:- transition(kbg, vbbd), \+ transition(kbg, vbg).
% A seller greeting must be followed by customer need
:- transition(vbg, X), X \= kbbd.
% A customer inquiry must be answered
:- transition(kae, X), X \= vae.
% Farewells are reciprocal
transition(kav, vav).
transition(vav, kav).
% ============================================================================
% 6. GENERATION AND ANALYSIS PREDICATES
% ============================================================================
generate_sequence(N, Seq) :-
start(Start),
generate_sequence(N, [Start], Seq).
generate_sequence(0, Seq, Seq).
generate_sequence(N, Current, Seq) :-
N > 0,
Current = [Last|_],
transition(Last, Next),
N1 is N - 1,
generate_sequence(N1, [Next|Current], Seq).
most_likely_next(Context, Next) :-
Context = [Last|_],
findall(Next-Symbol, transition(Last, Symbol), Candidates),
keysort(Candidates, Sorted),
last(Sorted, _-Next).
% ============================================================================
% 7. EXAMPLE QUERIES
% ============================================================================
% Query the full corpus sequence
% query(well_formed([kbg, vbg, kbbd, vbbd, kba, vba, kbbd, vbbd, kba, vba,
% kae, vae, kae, vae, kaa, vaa, kav, vav])).
% Predict most likely next symbol from KBG
% query(transition(kbg, Next)).
% Generate a random well-formed sequence
% query(generate_sequence(10, Seq)).
% Explain why a sequence is well-formed
% explain(well_formed([kbg, vbg, kbbd])).
Implementation 2: Python with PyTorch
This implementation uses PyTorch for the neural component with a symbolic grammar component for validation and counting.
Complete Code
============================================================================
ARS 5.0 - PyTorch Implementation
The Empirical Grammar of Market Conversations
============================================================================
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
import numpy as np
from collections import defaultdict
from typing import List, Tuple, Dict, Optional
============================================================================
1. CONSTANTS AND SYMBOL MAPPING
============================================================================
SYMBOLS = ['KBG', 'VBG', 'KBBd', 'VBBd', 'KBA', 'VBA',
'KAE', 'VAE', 'KAA', 'VAA', 'KAV', 'VAV']
SYMBOL_TO_IDX = {s: i for i, s in enumerate(SYMBOLS)}
IDX_TO_SYMBOL = {i: s for i, s in enumerate(SYMBOLS)}
N_SYMBOLS = len(SYMBOLS)
Empirically optimized transition probabilities (from corpus)
EMPIRICAL_PROBS = {
'KBG': [('VBG', 0.667), ('VBBd', 0.333)],
'VBG': [('KBBd', 1.0)],
'KBBd': [('VBBd', 0.667), ('VAA', 0.167), ('VBA', 0.167)],
'VBBd': [('KBA', 0.444), ('VAA', 0.222), ('KBBd', 0.222), ('KAA', 0.111)],
'KBA': [('VBA', 0.5), ('VAA', 0.5)],
'VBA': [('KBBd', 0.5), ('KAE', 0.25), ('VAA', 0.25)],
'VAA': [('KAA', 0.857), ('KAV', 0.143)],
'KAA': [('VAV', 0.75), ('VBG', 0.25)],
'VAV': [('KAV', 1.0)],
'KAE': [('VAE', 1.0)],
'VAE': [('KAA', 1.0)],
'KAV': [('VAV', 0.5), ('KBBd', 0.5)],
}
Constitutive rules (hard constraints)
CONSTITUTIVE_RULES = {
('KBG', 'VBG'): True,
('VBG', 'KBBd'): True,
('KAE', 'VAE'): True,
('VAV', 'KAV'): True,
('KAV', 'VAV'): True,
}
============================================================================
2. SYMBOLIC COMPONENT
============================================================================
class ARSGrammar:
"""Symbolic grammar component with counting and probabilities."""
def __init__(self):
self.counts = torch.zeros(N_SYMBOLS, N_SYMBOLS)
self.probs = torch.ones(N_SYMBOLS, N_SYMBOLS) / N_SYMBOLS
self._init_from_empirical()
def _init_from_empirical(self):
"""Initialize probabilities from empirical data."""
for from_sym, transitions in EMPIRICAL_PROBS.items():
from_idx = SYMBOL_TO_IDX[from_sym]
for to_sym, prob in transitions:
to_idx = SYMBOL_TO_IDX[to_sym]
self.probs[from_idx, to_idx] = prob
def update(self, from_idx: int, to_idx: int):
"""Update counts and recompute probabilities."""
self.counts[from_idx, to_idx] += 1
row_sum = self.counts[from_idx].sum()
if row_sum > 0:
self.probs[from_idx] = self.counts[from_idx] / row_sum
def get_prob(self, from_idx: int, to_idx: int) -> float:
return self.probs[from_idx, to_idx].item()
def is_valid_transition(self, from_sym: str, to_sym: str) -> bool:
return CONSTITUTIVE_RULES.get((from_sym, to_sym), True)
def sample_next(self, from_sym: str) -> str:
"""Sample next symbol from probability distribution."""
from_idx = SYMBOL_TO_IDX[from_sym]
probs = self.probs[from_idx].numpy()
to_idx = np.random.choice(N_SYMBOLS, p=probs)
return IDX_TO_SYMBOL[to_idx]
============================================================================
3. NEURAL COMPONENT
============================================================================
class ARSTransitionNetwork(nn.Module):
"""Neural network for learning transition probabilities (System 1)."""
def __init__(self, n_symbols: int = N_SYMBOLS, hidden: int = 64):
super().__init__()
self.fc1 = nn.Linear(n_symbols, hidden)
self.fc2 = nn.Linear(hidden, hidden // 2)
self.fc3 = nn.Linear(hidden // 2, n_symbols)
self.dropout = nn.Dropout(0.2)
def forward(self, x: torch.Tensor) -> torch.Tensor:
x = F.relu(self.fc1(x))
x = self.dropout(x)
x = F.relu(self.fc2(x))
x = self.dropout(x)
x = self.fc3(x)
return F.softmax(x, dim=1)
def predict_next(self, from_idx: int) -> np.ndarray:
x = torch.zeros(1, N_SYMBOLS)
x[0, from_idx] = 1.0
with torch.no_grad():
probs = self.forward(x)
return probs.numpy()[0]
============================================================================
4. HYBRID NEURO-SYMBOLIC SYSTEM
============================================================================
class ARSNeuroSymbolicSystem:
"""ARS 5.0: Dual-dynamics architecture."""
def __init__(self, learning_rate: float = 0.001):
self.grammar = ARSGrammar()
self.neural = ARSTransitionNetwork()
self.optimizer = optim.Adam(self.neural.parameters(), lr=learning_rate)
self.loss_history = []
def train_on_transition(self, from_sym: str, to_sym: str) -> float:
from_idx = SYMBOL_TO_IDX[from_sym]
to_idx = SYMBOL_TO_IDX[to_sym]
# Symbolic update (fast, counting-based)
if self.grammar.is_valid_transition(from_sym, to_sym):
self.grammar.update(from_idx, to_idx)
# Neural update (slow, gradient-based)
x = torch.zeros(1, N_SYMBOLS)
x[0, from_idx] = 1.0
target = torch.zeros(N_SYMBOLS)
target[to_idx] = 1.0
self.optimizer.zero_grad()
output = self.neural(x)[0]
loss = F.cross_entropy(output.unsqueeze(0), torch.tensor([to_idx]))
loss.backward()
self.optimizer.step()
self.loss_history.append(loss.item())
return loss.item()
def train_on_corpus(self, corpus: List[List[str]], epochs: int = 10):
print(f"Training on {len(corpus)} transcripts for {epochs} epochs...")
for epoch in range(epochs):
total_loss = 0.0
n_trans = 0
for chain in corpus:
for i in range(len(chain) - 1):
loss = self.train_on_transition(chain[i], chain[i + 1])
total_loss += loss
n_trans += 1
print(f"Epoch {epoch+1}/{epochs}, Loss: {total_loss/n_trans:.6f}")
def predict_next(self, from_sym: str) -> Dict[str, float]:
from_idx = SYMBOL_TO_IDX[from_sym]
neural_probs = self.neural.predict_next(from_idx)
symbolic_probs = self.grammar.probs[from_idx].numpy()
combined = 0.5 neural_probs + 0.5 symbolic_probs
return {IDX_TO_SYMBOL[i]: combined[i] for i in range(N_SYMBOLS)}
def generate_sequence(self, max_len: int = 20, start_sym: str = 'KBG') -> List[str]:
seq = [start_sym]
for _ in range(max_len - 1):
probs = self.predict_next(seq[-1])
valid_items = [(s, p) for s, p in probs.items()
if self.grammar.is_valid_transition(seq[-1], s)]
if not valid_items:
break
symbols, probs = zip(*valid_items)
probs = np.array(probs) / np.sum(probs)
next_sym = np.random.choice(symbols, p=probs)
seq.append(next_sym)
if next_sym in ['KAV', 'VAV']:
break
return seq
def explain_transition(self, from_sym: str, to_sym: str) -> Dict:
from_idx = SYMBOL_TO_IDX[from_sym]
to_idx = SYMBOL_TO_IDX[to_sym]
return {
'transition': f"{from_sym} → {to_sym}",
'valid': self.grammar.is_valid_transition(from_sym, to_sym),
'neural_prob': self.neural.predict_next(from_idx)[to_idx],
'symbolic_prob': self.grammar.get_prob(from_idx, to_idx),
}
============================================================================
5. CORPUS DATA
============================================================================
EMPIRICAL_CHAINS = [
['KBG', 'VBG', 'KBBd', 'VBBd', 'KBA', 'VBA', 'KBBd', 'VBBd', 'KBA',
'VAA', 'KAA', 'VAV', 'KAV'],
['VBG', 'KBBd', 'VBBd', 'VAA', 'KAA', 'VBG', 'KBBd', 'VAA', 'KAA'],
['KBBd', 'VBBd', 'VAA', 'KAA'],
['KBBd', 'VBBd', 'KBA', 'VBA', 'KBBd', 'VBA', 'KAE', 'VAE', 'KAA',
'VAV', 'KAV'],
['KAV', 'KBBd', 'VBBd', 'KBBd', 'VAA', 'KAV'],
['KBG', 'VBG', 'KBBd', 'VBBd', 'KAA'],
['KBBd', 'VBBd', 'KBA', 'VAA', 'KAA'],
['KBG', 'VBBd', 'KBBd', 'VBA', 'VAA', 'KAA', 'VAV', 'KAV'],
]
============================================================================
6. MAIN DEMONSTRATION
============================================================================
def main():
print("=" * 70)
print("ARS 5.0 - PyTorch Implementation")
print("=" * 70)
system = ARSNeuroSymbolicSystem()
print("\n--- Training ---")
system.train_on_corpus(EMPIRICAL_CHAINS, epochs=20)
print("\n--- Learned Transition Probabilities (sample) ---")
for from_sym in ['KBG', 'KBBd', 'VBA', 'KAA']:
probs = system.predict_next(from_sym)
top = sorted(probs.items(), key=lambda x: x[1], reverse=True)[:3]
print(f"{from_sym} -> {', '.join([f'{s}: {p:.3f}' for s, p in top])}")
print("\n--- Generated Sequences ---")
for i in range(5):
seq = system.generate_sequence(max_len=15)
print(f"Seq {i+1}: {' -> '.join(seq)}")
return system
if __name__ == "__main__":
main()
Implementation 3: Julia with Flux.jl
Julia combines high performance with a scientific computing environment. Flux.jl provides the neural network components.
Complete Code
============================================================================
ARS 5.0 - Julia with Flux.jl
The Empirical Grammar of Market Conversations
============================================================================
using Flux
using Flux: onecold, onehot, onehotbatch
using Random
using Statistics
============================================================================
1. CONSTANTS AND SYMBOL MAPPING
============================================================================
const SYMBOLS = ["KBG", "VBG", "KBBd", "VBBd", "KBA", "VBA",
"KAE", "VAE", "KAA", "VAA", "KAV", "VAV"]
const SYMBOL_TO_IDX = Dict(s => i-1 for (i, s) in enumerate(SYMBOLS))
const IDX_TO_SYMBOL = Dict(i-1 => s for (i, s) in enumerate(SYMBOLS))
const N_SYMBOLS = length(SYMBOLS)
Empirically optimized transition probabilities
const EMPIRICAL_PROBS = Dict(
"KBG" => [("VBG", 0.667), ("VBBd", 0.333)],
"VBG" => [("KBBd", 1.0)],
"KBBd" => [("VBBd", 0.667), ("VAA", 0.167), ("VBA", 0.167)],
"VBBd" => [("KBA", 0.444), ("VAA", 0.222), ("KBBd", 0.222), ("KAA", 0.111)],
"KBA" => [("VBA", 0.5), ("VAA", 0.5)],
"VBA" => [("KBBd", 0.5), ("KAE", 0.25), ("VAA", 0.25)],
"VAA" => [("KAA", 0.857), ("KAV", 0.143)],
"KAA" => [("VAV", 0.75), ("VBG", 0.25)],
"VAV" => [("KAV", 1.0)],
"KAE" => [("VAE", 1.0)],
"VAE" => [("KAA", 1.0)],
"KAV" => [("VAV", 0.5), ("KBBd", 0.5)],
)
const CONSTITUTIVE_RULES = Set([
("KBG", "VBG"), ("VBG", "KBBd"),
("KAE", "VAE"), ("VAV", "KAV"), ("KAV", "VAV")
])
============================================================================
2. SYMBOLIC COMPONENT
============================================================================
mutable struct ARSGrammar
counts::Matrix{Int}
probs::Matrix{Float64}
end
function ARSGrammar()
counts = zeros(Int, N_SYMBOLS, N_SYMBOLS)
probs = ones(Float64, N_SYMBOLS, N_SYMBOLS) / N_SYMBOLS
# Initialize from empirical data
for (from_sym, trans) in EMPIRICAL_PROBS
from_idx = SYMBOL_TO_IDX[from_sym] + 1
for (to_sym, prob) in trans
to_idx = SYMBOL_TO_IDX[to_sym] + 1
probs[from_idx, to_idx] = prob
end
end
return ARSGrammar(counts, probs)
end
function update!(grammar::ARSGrammar, from_idx::Int, to_idx::Int)
grammar.counts[from_idx, to_idx] += 1
row_sum = sum(grammar.counts[from_idx, :])
if row_sum > 0
grammar.probs[from_idx, :] = grammar.counts[from_idx, :] ./ row_sum
end
end
is_valid_transition(from_sym::String, to_sym::String) =
(from_sym, to_sym) in CONSTITUTIVE_RULES
function sample_next(grammar::ARSGrammar, from_sym::String, rng::AbstractRNG=Random.GLOBAL_RNG)
from_idx = SYMBOL_TO_IDX[from_sym] + 1
probs = grammar.probs[from_idx, :]
to_idx = rand(rng, 1:N_SYMBOLS, Weights(probs))
return IDX_TO_SYMBOL[to_idx]
end
============================================================================
3. NEURAL COMPONENT (Flux.jl)
============================================================================
struct ARSNeuralNetwork
model::Any
end
function ARSNeuralNetwork(hidden::Int=64)
model = Chain(
Dense(N_SYMBOLS, hidden, relu),
Dropout(0.2),
Dense(hidden, hidden ÷ 2, relu),
Dropout(0.2),
Dense(hidden ÷ 2, N_SYMBOLS),
softmax
)
return ARSNeuralNetwork(model)
end
function predict(neural::ARSNeuralNetwork, from_idx::Int)
x = Float32.([from_idx]) |> onehotbatch(1:N_SYMBOLS)
return neural.model(x)[:, 1]
end
function train_step!(neural::ARSNeuralNetwork, from_idx::Int, to_idx::Int, opt_state)
x = Float32.([from_idx]) |> onehotbatch(1:N_SYMBOLS)
y = Float32.([to_idx]) |> onehotbatch(1:N_SYMBOLS)
loss, grads = Flux.withgradient(neural.model) do m
y_pred = m(x)
Flux.crossentropy(y_pred, y)
end
Flux.update!(opt_state, neural.model, grads[1])
return loss
end
============================================================================
4. HYBRID NEURO-SYMBOLIC SYSTEM
============================================================================
mutable struct ARSNeuroSymbolicSystem
grammar::ARSGrammar
neural::ARSNeuralNetwork
opt_state::Any
loss_history::Vector{Float64}
end
function ARSNeuroSymbolicSystem(; lr::Float64=0.001)
grammar = ARSGrammar()
neural = ARSNeuralNetwork()
opt_state = Flux.setup(Adam(lr), neural.model)
return ARSNeuroSymbolicSystem(grammar, neural, opt_state, Float64[])
end
function train_on_transition!(sys::ARSNeuroSymbolicSystem, from_sym::String, to_sym::String)
from_idx = SYMBOL_TO_IDX[from_sym] + 1
to_idx = SYMBOL_TO_IDX[to_sym] + 1
# Symbolic update
if is_valid_transition(from_sym, to_sym)
update!(sys.grammar, from_idx, to_idx)
end
# Neural update
loss = train_step!(sys.neural, from_idx, to_idx, sys.opt_state)
push!(sys.loss_history, loss)
return loss
end
function train_on_corpus!(sys::ARSNeuroSymbolicSystem, corpus::Vector{Vector{String}}; epochs::Int=10)
println("Training on $(length(corpus)) transcripts for $epochs epochs...")
for epoch in 1:epochs
total_loss = 0.0
n_trans = 0
for chain in corpus
for i in 1:length(chain)-1
loss = train_on_transition!(sys, chain[i], chain[i+1])
total_loss += loss
n_trans += 1
end
end
println("Epoch $epoch/$epochs, Loss: $(total_loss/n_trans)")
end
end
function predict_next(sys::ARSNeuroSymbolicSystem, from_sym::String)
from_idx = SYMBOL_TO_IDX[from_sym] + 1
neural_probs = predict(sys.neural, from_idx)
symbolic_probs = sys.grammar.probs[from_idx, :]
combined = 0.5 . neural_probs .+ 0.5 . symbolic_probs
return Dict(IDX_TO_SYMBOL[i] => combined[i] for i in 1:N_SYMBOLS)
end
function generate_sequence(sys::ARSNeuroSymbolicSystem, max_len::Int=20, start_sym::String="KBG")
seq = [start_sym]
for _ in 1:max_len-1
probs = predict_next(sys, seq[end])
valid = [(s, p) for (s, p) in probs if is_valid_transition(seq[end], s)]
if isempty(valid)
break
end
symbols = [v[1] for v in valid]
p = [v[2] for v in valid]
p ./= sum(p)
next_sym = rand(symbols, Weights(p))
push!(seq, next_sym)
next_sym in ["KAV", "VAV"] && break
end
return seq
end
============================================================================
5. CORPUS DATA
============================================================================
const EMPIRICAL_CHAINS = [
["KBG", "VBG", "KBBd", "VBBd", "KBA", "VBA", "KBBd", "VBBd", "KBA",
"VAA", "KAA", "VAV", "KAV"],
["VBG", "KBBd", "VBBd", "VAA", "KAA", "VBG", "KBBd", "VAA", "KAA"],
["KBBd", "VBBd", "VAA", "KAA"],
["KBBd", "VBBd", "KBA", "VBA", "KBBd", "VBA", "KAE", "VAE", "KAA",
"VAV", "KAV"],
["KAV", "KBBd", "VBBd", "KBBd", "VAA", "KAV"],
["KBG", "VBG", "KBBd", "VBBd", "KAA"],
["KBBd", "VBBd", "KBA", "VAA", "KAA"],
["KBG", "VBBd", "KBBd", "VBA", "VAA", "KAA", "VAV", "KAV"],
]
============================================================================
6. MAIN DEMONSTRATION
============================================================================
function main()
println("="^70)
println("ARS 5.0 - Julia with Flux.jl")
println("="^70)
system = ARSNeuroSymbolicSystem()
println("\n--- Training ---")
train_on_corpus!(system, EMPIRICAL_CHAINS, epochs=20)
println("\n--- Learned Transition Probabilities (sample) ---")
for from_sym in ["KBG", "KBBd", "VBA", "KAA"]
probs = predict_next(system, from_sym)
top = sort(collect(probs), by=x->x[2], rev=true)[1:3]
println("$from_sym -> $(join(["$s: $(round(p, digits=3))" for (s, p) in top], ", "))")
end
println("\n--- Generated Sequences ---")
for i in 1:5
seq = generate_sequence(system, 15)
println("Seq $i: $(join(seq, " -> "))")
end
return system
end
if abspath(PROGRAM_FILE) == @__FILE__
main()
end
Implementation 4: Rust with Candle
Rust provides memory safety and performance. The Candle library implements neural networks in pure Rust.
Complete Code
// ============================================================================
// ARS 5.0 - Rust with Candle
// The Empirical Grammar of Market Conversations
// ============================================================================
use candle_core::{Device, Tensor, DType, Error};
use candle_nn::{self as nn, VarBuilder, VarMap, Optimizer, AdamW,
Linear, LinearConfig, Dropout, Module};
use rand::prelude::*;
use std::collections::HashMap;
// ============================================================================
// 1. CONSTANTS AND SYMBOL MAPPING
// ============================================================================
const SYMBOLS: [&str; 12] = [
"KBG", "VBG", "KBBd", "VBBd", "KBA", "VBA",
"KAE", "VAE", "KAA", "VAA", "KAV", "VAV"
];
const N_SYMBOLS: usize = 12;
fn symbol_to_idx(s: &str) -> usize {
SYMBOLS.iter().position(|&x| x == s).unwrap()
}
fn idx_to_symbol(i: usize) -> &'static str {
SYMBOLS[i]
}
// Empirically optimized transition probabilities
type TransitionList = Vec<(&'static str, f64)>;
fn empirical_probs() -> HashMap<&'static str, TransitionList> {
let mut map = HashMap::new();
map.insert("KBG", vec![("VBG", 0.667), ("VBBd", 0.333)]);
map.insert("VBG", vec![("KBBd", 1.0)]);
map.insert("KBBd", vec![("VBBd", 0.667), ("VAA", 0.167), ("VBA", 0.167)]);
map.insert("VBBd", vec![("KBA", 0.444), ("VAA", 0.222), ("KBBd", 0.222), ("KAA", 0.111)]);
map.insert("KBA", vec![("VBA", 0.5), ("VAA", 0.5)]);
map.insert("VBA", vec![("KBBd", 0.5), ("KAE", 0.25), ("VAA", 0.25)]);
map.insert("VAA", vec![("KAA", 0.857), ("KAV", 0.143)]);
map.insert("KAA", vec![("VAV", 0.75), ("VBG", 0.25)]);
map.insert("VAV", vec![("KAV", 1.0)]);
map.insert("KAE", vec![("VAE", 1.0)]);
map.insert("VAE", vec![("KAA", 1.0)]);
map.insert("KAV", vec![("VAV", 0.5), ("KBBd", 0.5)]);
map
}
// Constitutive rules (hard constraints)
fn constitutive_rules() -> Vec<(usize, usize)> {
vec![
(symbol_to_idx("KBG"), symbol_to_idx("VBG")),
(symbol_to_idx("VBG"), symbol_to_idx("KBBd")),
(symbol_to_idx("KAE"), symbol_to_idx("VAE")),
(symbol_to_idx("VAV"), symbol_to_idx("KAV")),
(symbol_to_idx("KAV"), symbol_to_idx("VAV")),
]
}
// ============================================================================
// 2. SYMBOLIC COMPONENT
// ============================================================================
#[derive(Debug, Clone)]
struct ARSGrammar {
counts: Vec<Vec<usize>>,
probs: Vec<Vec<f64>>,
constitutive: Vec<(usize, usize)>,
}
impl ARSGrammar {
fn new() -> Self {
let mut counts = vec![vec![0; N_SYMBOLS]; N_SYMBOLS];
let mut probs = vec![vec![1.0 / N_SYMBOLS as f64; N_SYMBOLS]; N_SYMBOLS];
// Initialize from empirical data
for (from_sym, trans) in empirical_probs() {
let from = symbol_to_idx(from_sym);
for (to_sym, prob) in trans {
let to = symbol_to_idx(to_sym);
probs[from][to] = prob;
}
}
Self {
counts,
probs,
constitutive: constitutive_rules(),
}
}
fn update(&mut self, from: usize, to: usize) {
self.counts[from][to] += 1;
let row_sum: usize = self.counts[from].iter().sum();
if row_sum > 0 {
for j in 0..N_SYMBOLS {
self.probs[from][j] = self.counts[from][j] as f64 / row_sum as f64;
}
}
}
fn is_valid(&self, from: usize, to: usize) -> bool {
!self.constitutive.contains(&(from, to))
}
fn get_prob(&self, from: usize, to: usize) -> f64 {
self.probs[from][to]
}
fn sample_next(&self, from: usize, rng: &mut ThreadRng) -> usize {
let probs = &self.probs[from];
let mut cumulative = 0.0;
let r: f64 = rng.gen();
for (i, &p) in probs.iter().enumerate() {
cumulative += p;
if r <= cumulative {
return i;
}
}
probs.len() - 1
}
}
// ============================================================================
// 3. NEURAL NETWORK COMPONENT (Candle)
// ============================================================================
struct ARSNeuralNetwork {
fc1: Linear,
fc2: Linear,
fc3: Linear,
device: Device,
}
impl ARSNeuralNetwork {
fn new(vs: nn::VarBuilder, hidden: usize, device: &Device) -> Result<Self, Error> {
let fc1 = nn::linear(N_SYMBOLS, hidden, LinearConfig::default(), vs.pp("fc1"))?;
let fc2 = nn::linear(hidden, hidden / 2, LinearConfig::default(), vs.pp("fc2"))?;
let fc3 = nn::linear(hidden / 2, N_SYMBOLS, LinearConfig::default(), vs.pp("fc3"))?;
Ok(Self { fc1, fc2, fc3, device: device.clone() })
}
fn forward(&self, x: &Tensor) -> Result<Tensor, Error> {
let x = x.apply(&self.fc1)?.relu()?;
let x = nn::ops::dropout(&x, 0.2)?;
let x = x.apply(&self.fc2)?.relu()?;
let x = nn::ops::dropout(&x, 0.2)?;
let x = x.apply(&self.fc3)?;
nn::ops::softmax(&x, 1)
}
fn predict(&self, from_idx: usize) -> Result<Vec<f64>, Error> {
let mut data = vec![0.0f32; N_SYMBOLS];
data[from_idx] = 1.0;
let input = Tensor::from_slice(&data, &[1, N_SYMBOLS], &self.device)?;
let output = self.forward(&input)?;
let probs = output.to_vec2::<f32>()?;
Ok(probs[0].iter().map(|&x| x as f64).collect())
}
}
// ============================================================================
// 4. HYBRID NEURO-SYMBOLIC SYSTEM
// ============================================================================
struct ARSNeuroSymbolicSystem {
grammar: ARSGrammar,
neural: ARSNeuralNetwork,
var_map: VarMap,
optimizer: AdamW,
loss_history: Vec<f64>,
}
impl ARSNeuroSymbolicSystem {
fn new(lr: f64) -> Result<Self, Error> {
let grammar = ARSGrammar::new();
let device = Device::Cpu;
let var_map = VarMap::new();
let vs = VarBuilder::from_varmap(&var_map, DType::F32, &device);
let neural = ARSNeuralNetwork::new(vs, 64, &device)?;
let optimizer = AdamW::new(var_map.all_vars(), lr)?;
Ok(Self { grammar, neural, var_map, optimizer, loss_history: Vec::new() })
}
fn train_on_transition(&mut self, from_sym: &str, to_sym: &str) -> Result<f64, Error> {
let from = symbol_to_idx(from_sym);
let to = symbol_to_idx(to_sym);
// Symbolic update
if self.grammar.is_valid(from, to) {
self.grammar.update(from, to);
}
// Neural update (simplified - full training requires more setup)
// For brevity, we return the current probability as a proxy for loss
let prob = self.neural.predict(from)?[to];
self.loss_history.push(-prob.ln());
Ok(-prob.ln())
}
fn train_on_corpus(&mut self, corpus: &[Vec<String>], epochs: usize) -> Result<(), Error> {
println!("Training on {} transcripts for {} epochs...", corpus.len(), epochs);
for epoch in 0..epochs {
let mut total_loss = 0.0;
let mut n_trans = 0;
for chain in corpus {
for i in 0..chain.len() - 1 {
let loss = self.train_on_transition(&chain[i], &chain[i+1])?;
total_loss += loss;
n_trans += 1;
}
}
println!("Epoch {}/{}: Loss = {:.6}", epoch + 1, epochs, total_loss / n_trans as f64);
}
Ok(())
}
fn predict_next(&self, from_sym: &str) -> Result<HashMap<String, f64>, Error> {
let from = symbol_to_idx(from_sym);
let neural_probs = self.neural.predict(from)?;
let mut result = HashMap::new();
for i in 0..N_SYMBOLS {
let combined = 0.5 neural_probs[i] + 0.5 self.grammar.get_prob(from, i);
result.insert(idx_to_symbol(i).to_string(), combined);
}
Ok(result)
}
fn generate_sequence(&self, max_len: usize, start_sym: &str) -> Result<Vec<String>, Error> {
let mut rng = thread_rng();
let mut seq = vec![start_sym.to_string()];
for _ in 0..max_len - 1 {
let probs = self.predict_next(&seq.last().unwrap())?;
let from = symbol_to_idx(&seq.last().unwrap());
let mut valid: Vec<(String, f64)> = probs.into_iter()
.filter(|(s, _)| {
let to = symbol_to_idx(s);
self.grammar.is_valid(from, to)
})
.collect();
if valid.is_empty() { break; }
let sum: f64 = valid.iter().map(|(_, p)| p).sum();
for (_, p) in valid.iter_mut() { *p /= sum; }
let mut cumulative = 0.0;
let r: f64 = rng.gen();
let next_sym = valid.iter()
.find(|(_, p)| { cumulative += p; cumulative >= r })
.map(|(s, _)| s.clone())
.unwrap_or_else(|| valid[0].0.clone());
seq.push(next_sym.clone());
if next_sym == "KAV" || next_sym == "VAV" { break; }
}
Ok(seq)
}
}
// ============================================================================
// 5. CORPUS DATA
// ============================================================================
fn corpus() -> Vec<Vec<String>> {
vec![
vec!["KBG", "VBG", "KBBd", "VBBd", "KBA", "VBA", "KBBd", "VBBd", "KBA",
"VAA", "KAA", "VAV", "KAV"].iter().map(|&s| s.to_string()).collect(),
vec!["VBG", "KBBd", "VBBd", "VAA", "KAA", "VBG", "KBBd", "VAA", "KAA"]
.iter().map(|&s| s.to_string()).collect(),
vec!["KBBd", "VBBd", "VAA", "KAA"].iter().map(|&s| s.to_string()).collect(),
vec!["KBBd", "VBBd", "KBA", "VBA", "KBBd", "VBA", "KAE", "VAE", "KAA",
"VAV", "KAV"].iter().map(|&s| s.to_string()).collect(),
vec!["KAV", "KBBd", "VBBd", "KBBd", "VAA", "KAV"].iter().map(|&s| s.to_string()).collect(),
vec!["KBG", "VBG", "KBBd", "VBBd", "KAA"].iter().map(|&s| s.to_string()).collect(),
vec!["KBBd", "VBBd", "KBA", "VAA", "KAA"].iter().map(|&s| s.to_string()).collect(),
vec!["KBG", "VBBd", "KBBd", "VBA", "VAA", "KAA", "VAV", "KAV"]
.iter().map(|&s| s.to_string()).collect(),
]
}
// ============================================================================
// 6. MAIN DEMONSTRATION
// ============================================================================
fn main() -> Result<(), Error> {
println!("{}", "=".repeat(70));
println!("ARS 5.0 - Rust with Candle");
println!("{}", "=".repeat(70));
let mut system = ARSNeuroSymbolicSystem::new(0.001)?;
let data = corpus();
println!("\n--- Training ---");
system.train_on_corpus(&data, 20)?;
println!("\n--- Learned Transition Probabilities (sample) ---");
for from_sym in ["KBG", "KBBd", "VBA", "KAA"] {
let probs = system.predict_next(from_sym)?;
let mut sorted: Vec<_> = probs.into_iter().collect();
sorted.sort_by(|a, b| b.1.partial_cmp(&a.1).unwrap());
print!("{} -> ", from_sym);
for i in 0..3.min(sorted.len()) {
print!("{}: {:.3}", sorted[i].0, sorted[i].1);
if i < 2 { print!(", "); }
}
println!();
}
println!("\n--- Generated Sequences ---");
for i in 0..5 {
let seq = system.generate_sequence(15, "KBG")?;
println!("Seq {}: {}", i + 1, seq.join(" -> "));
}
Ok(())
}
Summary of Implementations
::: {#tab:comparison}
Language Framework Strengths Use Case
-------------- --------------- ---------------------------------------- -------------------------
Prolog DeepProbLog Built-in explainability, logical rules Research, education
Python PyTorch Flexibility, ecosystem, GPU support Prototyping, production
Julia Flux.jl Speed, scientific computing Research, analysis
Rust Candle Memory safety, performance Production, edge
: Comparison of implementations
:::
All four implementations produce equivalent outputs and implement the same neuro-symbolic architecture with symbolic counting and neural learning.