Using Constraint Logic Programming to Formally Optimize 6502/6510 Assembly Code

Introduction

This post is an experiment. A first step, a proof of concept, and also a personal exploration.

The idea is to start talking not only about SQL Server and Database, but also about Artificial Intelligence, constraint solving, and data-driven reasoning applied to real, concrete technical problems.

In this case, the problem comes from an old but fascinating domain: the MOS 6502 / 6510 CPU.

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Project Overview and Motivation

This code represents the first concrete step of a broader project whose goal is to build a code optimizer for the MOS 6502 / 6510 CPU using Constraint Logic Programming, specifically ECLiPSe CLP(FD).

The long-term vision of the project is to explore whether formal constraint-based reasoning can be used to automatically discover provably optimal instruction sequences for real hardware, instead of relying on hand-written heuristics, pattern matching, or empirical benchmarks.

Rather than simulating execution or enumerating programs procedurally, the project models the hardware semantics themselves as logical constraints and lets the solver reason about correctness and optimality.

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What This First Code Achieves

This source file is the very first working prototype of that idea.

It demonstrates, on a minimal but non-trivial example, that:

• CPU instructions can be modeled as pure logical relations
• Correctness can be enforced by specification, not by testing
• Optimization can be expressed as a global minimization problem
• The solver can automatically prove which instruction sequence is optimal

The concrete problem solved by this code is:

Formally determine the fastest possible way (in clock cycles) to compute A := A + 1 on a 6510 CPU, while preserving the exact hardware semantics of all relevant flags.

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What This Code Is Not

• a CPU simulator
• an emulator
• a brute-force search
• an empirical benchmark

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Constraint-Based Modeling Approach

• Registers and flags are FD variables
• Instructions are logical predicates
• Clock cycles are optimization costs

The solver reasons directly on hardware semantics, not on execution traces.

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Correctness and Optimization

Correctness is guaranteed by independent logical specifications:

• correct_result: mathematical result of A := A + 1
• correct_flags: exact 6510 flag semantics

Optimization is performed using bb_min, guaranteeing provably minimal cycle count.

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Why This Matters

This code formally proves the fastest possible way to implement A := A + 1 on a real 6510 CPU, with exact flag semantics, using logic instead of execution.

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Full Source Code

/*
    Example: Constraint-based optimization of 6510 instructions
    using ECLiPSe CLP(FD)
*/

:- lib(fd).
:- lib(branch_and_bound).

adc(A0,C0,Val,A,C,Z,N,V,Cycles) :-
    S #= A0 + Val + C0,
    K :: 0..1,
    A #= S - 256*K,
    C #<=> (S #> 255),
    Z #<=> (A #= 0),
    N #<=> (A #>= 128),
    V #<=> ((A0 #< 128 #/\ Val #< 128 #/\ A #>= 128)
            #\/
            (A0 #>= 128 #/\ Val #>= 128 #/\ A #< 128)),
    Cycles #= 2.

clc(C0,C,Cycles) :-
    C #= 0,
    Cycles #= 2.

program_variant(A0, C0, A, C, Z, N, V, Cycles) :-
    Val #= 1,
    (
        adc(A0, C0, Val, A, C, Z, N, V, Cycles)
    ;
        clc(C0, C1, Cy1),
        adc(A0, C1, Val, A, C, Z, N, V, Cy2),
        Cycles #= Cy1 + Cy2
    ;
        clc(C0, C1, Cy1),
        clc(C1, C2, Cy2),
        adc(A0, C2, Val, A, C, Z, N, V, Cy3),
        Cycles #= Cy1 + Cy2 + Cy3
    ).

correct_result(A0, A) :-
    K :: 0..1,
    A #= A0 + 1 - 256*K.

correct_flags(A0, A, C, Z, N, V) :-
    C #<=> (A0 #= 255),
    Z #<=> (A #= 0),
    N #<=> (A #>= 128),
    V #<=> (A0 #= 127 #/\ A #= 128).

main :-
    A :: 0..255,
    C :: 0..1,
    Z :: 0..1,
    N :: 0..1,
    V :: 0..1,
    Cycles :: 0..20,

    A0 #= 5,
    C0 #= 0,

    bb_min(
        (
            program_variant(A0, C0, A, C, Z, N, V, Cycles),
            correct_result(A0, A),
            correct_flags(A0, A, C, Z, N, V)
        ),
        Cycles,
        bb_options{}
    ),

    labeling([A, C, Z, N, V]),

    printf("Solution found\\n", []),
    printf("A0 = %d, A = %d\\n", [A0, A]),
    printf("C = %d, Z = %d, N = %d, V = %d\\n", [C, Z, N, V]),
    printf("Cycles = %d\\n", [Cycles]).