1  Program Architecture and Primitives

This document outlines the complete technical specification of the Monist program architecture and demonstrates how to build primitives, tests, and programs on top of it.

The fundamental architectural breakthrough of this system is its fluid computational pipeline. It refuses to stay confined to a single paradigm, instead creating a hybrid synthesis that shifts the computation to whatever physical or mathematical domain is most optimal for the current step.

1.1 The Hybrid Synthetic Pipeline

Here is exactly how that hybrid synthetic pipeline flows:

graph TD
    A[Natural Deduction<br>The Human Interface] -->|Semantics| B[CPU & System Memory<br>The Geometry Layer]
    B -->|Topological Matrix<br>Bellman-Ford| C[Graph Reduction<br>The Compiler]
    C -->|Untyped S,K,I Combinators| D[GPU VRAM<br>The Physics Engine]
    D -->|Continuous Data Superposition| E[The Holographic Co-processor<br>Continuous Math]
    E -.->|10k-dim Phase Space Cancellation| B

1.1.1 1. Natural Deduction (The Human Interface)

The user writes high-level logical constraints and employs interactive tactics (intro, apply, rewrite). This is the semantic layer. It serves as the initial boundary where human intent is mathematically captured before spatial abstraction begins.

1.1.2 2. CPU & System Memory (The Geometry Layer)

The CPU strips away the human semantics, turning the logic into a pure topological matrix (a Bellman-Ford directed graph). By tracing paths through RAM, it calculates typestate friction and dynamically intercepts paradoxes or loops before they can explode. This step guarantees topological acyclicity even in unstratified structures.

1.1.3 3. Graph Reduction (The Compiler)

Once the topology is verified as safe (or stabilized via the \(T\)-functor), the engine completely abandons traditional variable substitution. It compiles the logic down into pure, untyped Interaction Nets (\(S, K, I\) combinators). This breaks structural dependencies and localizes the computation.

1.1.4 4. GPU VRAM (The Physics Engine)

These combinator graphs are handed off to WGPU compute shaders. Because interaction combinators are strictly local, the GPU doesn’t need locks, mutexes, or a Garbage Collector. It just lets the nodes physically collide and annihilate each other in parallel across millions of lock-free cycles.

1.1.5 5. The Holographic Co-processor (Continuous Math)

When the system encounters massive datasets (like cybersecurity telemetry), it bypasses discrete graph reduction entirely. It superposes the data into 10,000-dimensional continuous wave functions on the GPU (utilizing Vector Symbolic Architectures / HDC). This uses destructive interference to physically cancel out noise in \(O(1)\) time before snapping it back to discrete logic. (See tools/monist-examples/src/bin/holographic_cyber_oracle.rs for the implemented working demo).

1.2 Building Primitives and Programs

To utilize this architecture, developers follow a specific sequence that aligns with the engine’s compilation limits:

  1. Define Axioms and Geometry: Start by declaring constraints via Natural Deduction in the CLI or through direct Rust macros.

    assume Quine_Flatness forall x y. typestate(Q(x,y)) == max(typestate(x), typestate(y))

  2. Topological Handoff (monist-core): Once the primitives are built, feed the logic through eval or the check_strat commands to ensure Bellman-Ford bounds are respected. If dense recursive structures form, rely on the engine’s automated \(T\)-operator injection (\(x \mapsto \iota"x\)).

  3. Deploy via monist-comb: Execute the validated structures locally using the interaction net compiler. The nodes are encoded into 32-bit pointers and dispatched autonomously to WGSL compute shaders.

  4. Integration Testing (monist-examples): Tests should strictly check the engine’s ability to halt negative-weight cycles (e.g. Specker’s Refutation) and safely navigate \(K\)-Iteration depth boundaries. The outputs are verified by streaming standard SMT-LIB witnesses to Lean 4, establishing differential testing confidence.