Modern processors are marvels of parallel execution. A typical server CPU offers dozens of cores, each capable of executing multiple instructions per cycle through SIMD operations. GPUs push this further with thousands of cores organized in warps and thread blocks. Emerging accelerators like NextSilicon’s Maverick or Graphcore’s IPU reimagine computation entirely. Yet most code fails to harness even a fraction of this power. Why? Because choosing the right parallel execution strategy requires understanding not just what your code does, but what it needs from its environment. This is where coeffects transform compilation.
The Parallelism Predicament
Consider a seemingly simple operation that appears in everything from scientific computing to real-time analytics:
let processDataset (data: float[]) =
data
|> Array.map (fun x -> complexTransform x)
|> Array.filter (fun x -> x > threshold)
|> Array.reduce (+)
How should this compile? The answer depends on context that traditional compilers can’t see:
- Is
complexTransform
a pure mathematical function or does it access external resources? - What’s the size of the data array - does it fit in L3 cache or span gigabytes?
- Are we running on a CPU with strong single-thread performance or a GPU with massive parallelism?
- Does the computation pattern allow for SIMD vectorization or require scalar operations?
Get these decisions wrong and your “parallel” code runs slower than sequential execution. Get them right and you can achieve near-theoretical peak performance. The Fidelity framework uses coeffect analysis to make these decisions automatically and optimally.
Two Paths to Parallelism
At the heart of Fidelity’s approach lies a fundamental choice between two radically different compilation strategies: interaction nets for pure parallelism and delimited continuations for controlled concurrency. Understanding when to use each is the key to efficient execution.
Interaction Nets: When Everything Can Happen at Once
Interaction nets represent computation as a graph where nodes interact through local rewrite rules. When your code has no sequential dependencies or external effects, this model enables maximum parallelism:
// Pure computation - perfect for interaction nets
let matrixMultiply (a: Matrix) (b: Matrix) =
Array2D.init a.Rows b.Cols (fun i j ->
seq { for k in 0 .. a.Cols - 1 -> a.[i,k] * b.[k,j] }
|> Seq.sum)
// Compiles to interaction net:
// - Every element computation is independent
// - Maps directly to GPU thread blocks
// - No synchronization needed until final result
Delimited Continuations: When Order Matters
Delimited continuations capture “the rest of the computation” at specific points, enabling precise control over execution order and resource management:
// Computation with external dependencies - needs delimited continuations
let enrichDataPoints (points: DataPoint[]) = async {
let mutable enriched = []
for point in points do
let! weather = WeatherService.getConditions point.Location
let! traffic = TrafficService.getDensity point.Location
enriched <- { point with
Weather = weather
TrafficDensity = traffic } :: enriched
return List.rev enriched
}
// Compiles to delimited continuations:
// - Must maintain order for external service calls
// - Can optimize service call batching
// - Handles failure/retry gracefully
The key insight: these aren’t just implementation details. The choice between interaction nets and delimited continuations fundamentally determines what optimizations are possible and which hardware can efficiently execute the code.
Coeffects: The Missing Link
This is where coeffects revolutionize compilation. By tracking what code needs from its environment, coeffects provide exactly the information needed to choose between parallel execution strategies:
// Coeffect inference discovers the nature of computation
type ContextRequirement =
| Pure // No external dependencies → Interaction nets
| MemoryAccess of AccessPattern // Data access pattern → Guides parallelization
| ResourceAccess of Resource Set // External resources → Delimited continuations
| Temporal of HistoryDepth // Needs past values → Streaming architecture
The Fidelity compiler will be designed to automatically infer these requirements:
// Example 1: Scientific computation
let runSimulation (grid: float[,]) =
let nextGeneration =
grid |> Array2D.mapi (fun i j cell ->
let neighbors = getNeighbors grid i j
updateCell cell neighbors)
if converged grid nextGeneration then
nextGeneration
else
runSimulation nextGeneration
// Coeffect analysis discovers:
// - Pure computation (no external resources)
// - Regular memory access pattern (stencil)
// - Recursive structure (iterative refinement)
// → Compile to interaction nets on GPU
Real Hardware, Real Decisions
Let’s see how coeffect analysis guides compilation for different processors:
Multi-Core CPU: Cache-Aware Parallelism
// Data processing with mixed patterns
let analyzeTimeSeries (data: TimePoint[]) =
data
|> Array.windowed 100
|> Array.Parallel.map (fun window ->
let stats = computeStatistics window
let anomalies = detectAnomalies window stats
(stats, anomalies))
|> consolidateResults
// Coeffect analysis:
// - Sliding window → temporal coeffect
// - Pure computation within windows
// - Window size fits in L2 cache
//
// Compilation strategy:
// - Use CPU SIMD for statistics
// - Parallelize across cores with cache-aware chunking
// - No GPU transfer overhead worth it
GPU: Massive Data Parallelism
// Image processing pipeline
let processImages (images: Image[]) =
images
|> Array.map (fun img ->
img
|> applyConvolution kernel1
|> applyConvolution kernel2
|> normalizeHistogram)
// Coeffect analysis:
// - Pure computation
// - Regular 2D access pattern
// - High arithmetic intensity
//
// Compilation strategy:
// - Interaction nets mapping to GPU warps
// - Texture memory for convolution kernels
// - Fused kernel execution
Custom Accelerators: Adaptive Execution
Modern accelerators with novel architectures will be able to accept different workload patterns. Coeffects enable this novel adaptation to maximize their potential:
// ML inference with dynamic characteristics
let runInference (model: Model) (input: Tensor) =
let layers = model.Layers
let rec forward (input: Tensor) (layers: Layer list) =
match layers with
| [] -> input
| Linear weights :: rest ->
// Coeffect: Matrix multiplication pattern
let output = input |> matmul weights |> activate
forward output rest
| Attention heads :: rest ->
// Coeffect: All-to-all communication pattern
let output = multiHeadAttention input heads
forward output rest
| Convolution kernel :: rest ->
// Coeffect: Local spatial pattern
let output = convolveSpatial input kernel
forward output rest
forward input layers
// Coeffect analysis per layer type:
// - Linear → Pure matrix ops → Configure as systolic array
// - Attention → All-to-all → Configure as crossbar
// - Convolution → Spatial → Configure as 2D mesh
//
// Maverick reconfigures between layers!
The Coeffect Advantage: Clean Code, Optimal Execution
The beauty of coeffect-driven compilation is that developers write clean, intent-focused code while the compiler handles the messy details of determining strategies for parallel execution:
Business Logic Only] end subgraph "Coeffect Analysis" CODE --> INFER[Infer Context
Requirements] INFER --> PURE{Pure
Computation?} INFER --> RESOURCE{Resource
Access?} INFER --> TEMPORAL{Temporal
Dependencies?} end subgraph "Compilation Strategy" PURE -->|Yes| INET[Interaction Nets
Maximum Parallelism] RESOURCE -->|Yes| DCONT[Delimited Continuations
Controlled Execution] TEMPORAL -->|Yes| STREAM[Streaming Architecture
Pipeline Parallelism] INET --> GPU[GPU/TPU
Thousands of Threads] DCONT --> CPU[CPU
Smart Scheduling] STREAM --> CUSTOM[Custom Accelerator
Adaptive Pipeline] end style CODE fill:#e8f4fd style INET fill:#d4edda style DCONT fill:#fff3e0
Beyond AI: Parallelism Everywhere
While AI workloads grab headlines, coeffect-driven compilation benefits any parallel computation:
Financial Modeling
let monteCarloSimulation (initialState: MarketState) (scenarios: int) =
[|1..scenarios|]
|> Array.Parallel.map (fun i ->
let rng = Random(i)
simulateScenario initialState rng)
|> Array.map calculateValue
|> computeRiskMetrics
// Pure computation with independent scenarios
// → Interaction nets on GPU for massive parallelism
Real-Time Signal Processing
let processAudioStream (stream: AudioSample seq) =
stream
|> Seq.windowed 1024
|> Seq.map (fun window ->
let spectrum = FastFourierTransform window
let features = extractFeatures spectrum
classifySound features)
// Temporal coeffects with real-time constraints
// → CPU SIMD with predictable latency
Bioinformatics
let alignSequences (reference: DNA) (samples: DNA[]) =
samples
|> Array.Parallel.map (fun sample ->
findBestAlignment reference sample)
|> filterHighQualityAlignments
// Memory-intensive pure computation
// → NUMA-aware CPU parallelism
The Telemetry Bonus
A powerful bonus in coeffect analysis is automatic observability. Since the compiler already tracks context requirements, adding telemetry becomes trivial:
// Your code remains clean
let processOrder order =
validateOrder order
|> Result.bind calculatePricing
|> Result.bind checkInventory
|> Result.bind createShipment
// Compiler knows:
// - validateOrder is pure → Time CPU cycles
// - calculatePricing accesses pricing service → Track service latency
// - checkInventory queries database → Monitor query performance
// - createShipment calls external API → Record API metrics
//
// Telemetry inserted at natural boundaries with zero overhead
This isn’t instrumentation bolted on after the fact - it’s derived from the same analysis that drives optimization. Fidelity’s Program Semantic Graph the static resolution of interaction nets and delimited continuations mean that all code paths are known and fully traceable. There are no opaque allocations or “object downcasts” of convenience that obscure data and control flow. Establishing determinism and tracking it through the compute graph is the secret superpower of this approach.
Engineering in this system not only saves money at runtime, but it also saves on the “fixed costs” of day-over-day development cycles. REducing the time from inspiration to deployment for use by business is this framework’s most potent advantage. And the immediate transparency that these designs enjoy also makes production monitoring and maintenance less of an ongoing business cost. This approach is efficient in the lab and at the data center.
Separate Analysis, Accurate Workloads
Fidelity’s architecture keeps coeffect analysis separate from your code structure:
// Your AST stays clean
type PSGNode = {
Id: NodeId
Kind: PSGNodeKind
Symbol: FSharpSymbol option
SourceRange: range
}
// Coeffects live in external analysis maps
type CoeffectAnalysis = {
ComputationPatterns: Map<NodeId, ComputationPattern>
MemoryAccessPatterns: Map<NodeId, AccessPattern>
ResourceRequirements: Map<NodeId, Set<Resource>>
TemporalDependencies: Map<NodeId, HistoryDepth>
}
// Compilation uses both for intelligent decisions
let selectBackend (node: PSGNode) (coeffects: CoeffectAnalysis) =
match Map.tryFind node.Id coeffects.ComputationPatterns with
| Some PureDataParallel -> InteractionNetBackend
| Some ResourceDependent -> DelimitedContinuationBackend
| Some StreamingComputation -> PipelineParallelBackend
| _ -> DefaultSequentialBackend
Academic Rigor Yields Real World Performance
Coeffects aren’t just theoretical elegance - they deliver measurable performance wins:
- 10-100x speedups by choosing the right parallel execution model
- Near-linear scaling on multi-core systems through intelligent work distribution
- Optimal hardware utilization by matching computation patterns to processor strengths
- Zero abstraction penalty with optimal decisions are made at compile time
The key innovation is recognizing that the choice between interaction nets and delimited continuations isn’t arbitrary - it’s determined by what your code needs to accomplish for a given server architecture. By making this choice automatically based on coeffect analysis, Fidelity will target the right workload for a given chipset every time.
As we enter an era of increasingly heterogeneous hardware - CPUs, GPUs, TPUs, DPUs, and exotic accelerators - this context-aware compilation becomes essential. Your code expresses intent, this approach to intelligent analysis discovers requirements, and the compiler generates optimal execution strategies. That’s the power of coeffects: turning academic insight into real-world performance.
Advanced Implementation: Hybrid BitNet with Compressed KV Cache
To illustrate the transformative power of coeffect-guided compilation, consider a cutting-edge hybrid architecture that combines BitNet’s ternary operations with DeepSeek-style compressed key-value caching. This exemplifies how coeffects enable optimal workload distribution across heterogeneous hardware.
The Architectural Innovation
Traditional approaches run entire models on GPUs, missing a fundamental insight: different layers have vastly different computational characteristics. By combining coeffect analysis with BAREWire’s zero-copy technology, Fidelity can automatically split workloads optimally:
// Coeffect analysis discovers the natural CPU/GPU boundary
type HybridDeepSeekBitNet = {
// CPU-optimized layers (ternary operations)
BitNetAttention: {
Operations: Add/Subtract only
MemoryPattern: Sequential streaming
Coeffect: Pure, LowArithmeticIntensity
→ Target: CPU with AVX-512
}
// GPU-optimized components (parallel decompression)
CompressedKVCache: {
Operations: Parallel decompression
MemoryPattern: Random access
Coeffect: HighParallelism, MemoryIntensive
→ Target: GPU with warp-level primitives
}
}
Zero-Copy Memory Architecture
The key enabler is BAREWire’s unified memory abstraction, eliminating the traditional CPU-GPU transfer bottleneck:
module HybridInference =
// Shared memory pool - no copies needed!
let kvCache = BAREWire.createUnified<byte> {
Size = 16<GB>
Layout = CompressedKVLayout
AccessPattern = CPUWrite_GPURead
}
// CPU processes BitNet layers efficiently
let processBitNetLayer (input: Tensor) (weights: TernaryWeights) =
// Just adds and subtracts - perfect for CPU!
let output = CPU.ternaryMatmul input weights
// Write directly to shared KV cache
// GPU can read without any memory transfer
kvCache.WriteCompressedScores output.AttentionScores
output
// GPU handles parallel KV decompression
let retrieveContext (query: Query) =
GPU.kernel {
// Read directly from CPU-written memory
let! compressed = kvCache.ReadCompressedBlock query.Range
// Decompress in parallel across GPU warps
let! decompressed = parallelDecompress compressed
return reshapeToContext decompressed
}
Quaternary Encoding for Sparse Attention
The hybrid architecture benefits from sophisticated encoding that represents both ternary values and sparsity:
type QuaternaryValue =
| Neg // -1
| Zero // 0
| Pos // +1
| NoValue // Sparse/undefined
// Efficient packing enables CPU SIMD operations
type CompressedAttentionBlock = {
Mask: uint64 // Bit mask for value presence
PackedValues: byte[] // 4 quaternary values per byte
Metadata: BlockStats // For adaptive processing
}
// CPU can efficiently process sparse patterns
let processSparseTernary (block: CompressedAttentionBlock) =
if block.Mask = 0UL then
Vector.zero // Skip entirely
else
// SIMD process only present values
CPU.simdTernaryOps block.PackedValues block.Mask
Performance Implications
This hybrid approach achieves remarkable efficiency by letting each processor do what it excels at:
Component | Traditional (GPU-only) | Hybrid (CPU+GPU) | Improvement |
---|---|---|---|
BitNet Layers | Underutilizes GPU cores | 512 ops/cycle on CPU | 8x throughput |
KV Compression | Sequential on GPU | Parallel decompression | 4x faster |
Memory Transfers | Constant CPU↔GPU copies | Zero-copy via BAREWire | ∞ improvement |
Power Efficiency | 300W GPU always active | 50W CPU + GPU when needed | 3-6x better |
Dynamic Adaptation Through Coeffects
The coeffect system enables runtime adaptation based on workload characteristics:
// Coeffects monitor and adapt the CPU/GPU split dynamically
let adaptiveHybridInference (model: HybridModel) (stream: TokenStream) =
coeffectAsync {
// Initial split based on static analysis
let! initial = processTokens stream
// Runtime telemetry through coeffects
observe "cpu_ternary_throughput" adjustCPULoad
observe "gpu_decompression_latency" adjustGPULoad
observe "memory_bandwidth_usage" optimizeLayout
// Coeffects guide dynamic rebalancing
match workloadPattern with
| LongContext →
// Shift more KV processing to GPU
CompileStrategy.IncreaseGPUDecompression
| RapidTokenGeneration →
// Maximize CPU ternary throughput
CompileStrategy.OptimizeCPUPipeline
| Interactive →
// Balance for low latency
CompileStrategy.MinimizeHandoffs
}
The Future of Heterogeneous AI
This hybrid BitNet + compressed KV architecture represents a glimpse into the future of AI systems:
- Models designed for heterogeneous execution - Not monolithic GPU workloads
- Compression as a first-class concern - Enabling efficient memory usage
- Zero-copy memory architectures - Eliminating transfer bottlenecks
- Automatic workload distribution - Coeffects guide optimal placement
The Fidelity framework, with its coeffect analysis and BAREWire technology, makes this future achievable. By understanding what each component needs from its environment, the compiler will be able to automatically generate code that puts the right computation on the right processor - achieving performance that would be impossible with traditional approaches.
This is the power of context-aware compilation: not just choosing between interaction nets and delimited continuations, but orchestrating entire heterogeneous systems where CPUs handle ternary operations, GPUs accelerate parallel decompression, and zero-copy memory enables them to work in perfect harmony. The academic rigor of coeffects doesn’t just yield performance - it enables entirely new architectures that were previously unimaginable.