go-pflow

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 Go to latest Published: Feb 22, 2026 License: MIT

README

go-pflow

A Go library for Petri net modeling, ODE simulation, process mining, and zero-knowledge proofs.

go-pflow is not an AI/ML library. It implements structural, dynamical computation based on Petri nets and differential equations. See Why Petri Nets? for the motivation.

For comprehensive documentation, see the book.

Installation

go get github.com/pflow-xyz/go-pflow

Quick Start

// Build a Petri net and simulate with ODE solver
net, rates := petri.Build().
    Place("S", 999).Place("I", 1).Place("R", 0).
    Transition("infect").Transition("recover").
    Arc("S", "infect", 1).Arc("I", "infect", 1).Arc("infect", "I", 2).
    Arc("I", "recover", 1).Arc("recover", "R", 1).
    WithCustomRates(map[string]float64{"infect": 0.3, "recover": 0.1})

prob := solver.NewProblem(net, net.SetState(nil), [2]float64{0, 100}, rates)
sol := solver.Solve(prob, solver.Tsit5(), solver.DefaultOptions())
fmt.Println("Final state:", sol.GetFinalState())

See The go-pflow Library for the full API guide.

Packages

Package Purpose Book Chapter
petri Core types, fluent Builder API Ch 1: Why Petri Nets?
solver ODE solvers (Tsit5, RK45, implicit) Ch 3: Discrete to Continuous
stateutil State map utilities Ch 18: go-pflow Library
hypothesis Move evaluation for game AI Ch 6: Game Mechanics
sensitivity Parameter sensitivity analysis Ch 18: go-pflow Library
cache Simulation memoization Ch 18: go-pflow Library
reachability Deadlock/liveness analysis Ch 2: Mathematics of Flow
workflow Task dependencies, SLA tracking Ch 10: Complex State Machines
statemachine Hierarchical state machines Ch 18: go-pflow Library
actor Message-passing actor model Ch 18: go-pflow Library
eventlog Event log parsing Ch 11: Process Mining
mining Process discovery, rate learning Ch 11: Process Mining
monitoring Real-time prediction, SLA alerts Ch 11: Process Mining
learn Neural ODE-ish parameter fitting Ch 18: go-pflow Library
tokenmodel Token model schemas, DSL Ch 4: Token Language
codegen/solidity Solidity smart contract generation Ch 17: Code Generation
prover Groth16 ZK proofs with gnark Ch 12: Zero-Knowledge Proofs
visualization SVG rendering Ch 18: go-pflow Library
plotter Time series SVG plots Ch 18: go-pflow Library

Examples

Each example maps to a book chapter demonstrating the modeling pattern:

Example Domain Book Chapter Run
basic Token flow fundamentals Ch 1 cd examples/basic && go run main.go
coffeeshop Resource modeling Ch 5 cd examples/coffeeshop/cmd && go run main.go
tictactoe Game AI, move evaluation Ch 6 cd examples/tictactoe && go run ./cmd
sudoku Constraint satisfaction Ch 7 cd examples/sudoku/cmd && go run *.go
knapsack Combinatorial optimization Ch 8 cd examples/knapsack/cmd && go run *.go
poker Complex state machines Ch 10 cd examples/poker && go run ./cmd
monitoring_demo Process mining, SLA prediction Ch 11 cd examples/monitoring_demo && go run main.go
erc Token standards, Solidity codegen Ch 4 go run ./examples/erc
connect4 Pattern recognition Ch 6 cd examples/connect4 && go run ./cmd
nim Optimal strategy Ch 6 cd examples/nim && go run ./cmd
chess N-Queens, Knight's Tour Ch 7 cd examples/chess/cmd && go run *.go
neural Parameter learning Ch 3 cd examples/neural && go run main.go
visualization_demo SVG generation Ch 16 make run-visualization

See examples/README.md for more details.

The Book

book.pflow.xyz covers everything from foundations to advanced topics:

Part I: Foundations — Why Petri Nets, Mathematics of Flow, Discrete to Continuous, Token Language

Part II: Applications — Resource Modeling, Game Mechanics, Constraint Satisfaction, Optimization, Enzyme Kinetics, Complex State Machines

Part III: Advanced — Process Mining, Zero-Knowledge Proofs, Topology-Driven Verification, Declarative Infrastructure

Part IV: Building — Visual Editor, Code Generation, go-pflow Library, Dual Implementation

Testing

go test ./...

CLI

The pflow CLI provides simulation, analysis, and plotting from the command line. See cmd/pflow/README.md.

Compatibility

  • Go 1.23+
  • JSON format compatible with pflow.xyz

License

MIT License - see LICENSE for details.

Directories

Path Synopsis
Package actor provides an Actor model built on Petri nets with message passing.
 Package actor provides an Actor model built on Petri nets with message passing.
Package cache provides memoization for ODE simulations.
 Package cache provides memoization for ODE simulations.
cmd
pflow command
codegen
solidity
Package solidity generates Solidity smart contracts from token model schemas.
 Package solidity generates Solidity smart contracts from token model schemas.
Package engine provides a state machine harness for continuous Petri net simulation.
 Package engine provides a state machine harness for continuous Petri net simulation.
Package eventlog provides parsing and analysis of process event logs.
 Package eventlog provides parsing and analysis of process event logs.
Package eventsource provides event sourcing infrastructure for CQRS applications.
 Package eventsource provides event sourcing infrastructure for CQRS applications.
examples
basic command
chess/cmd command
coffeeshop
Package coffeeshop demonstrates a fully automated coffee shop using go-pflow.
 Package coffeeshop demonstrates a fully automated coffee shop using go-pflow.
coffeeshop/cmd command
Coffee Shop Automation Demo
 Coffee Shop Automation Demo
coffeeshop/cmd/sim command
Coffee Shop Simulator CLI
 Coffee Shop Simulator CLI
connect4/cmd command
dataset_comparison/cmd/covid_seir command
dataset_comparison/cmd/measles_sir command
dataset_comparison/cmd/measles_sir_fixed command
dataset_comparison/cmd/synthetic_sir command
erc command
Package main demonstrates defining ERC token standards as Petri net schemas and generating Solidity contracts from them.
 Package main demonstrates defining ERC token standards as Petri net schemas and generating Solidity contracts from them.
eventlog_demo command
f91w
Package f91w provides a Petri net simulation of the Casio F-91W digital watch.
 Package f91w provides a Petri net simulation of the Casio F-91W digital watch.
f91w/cmd command
Casio F-91W Watch Simulator Based on the XState machine from https://github.com/dundalek/casio-f91w-fsm
 Casio F-91W Watch Simulator Based on the XState machine from https://github.com/dundalek/casio-f91w-fsm
incident_simulator command
knapsack/cmd command
mining_demo command
monitoring_demo command
neural/cmd/demo command
neural/cmd/main command
neural/cmd/reverse command
nim/cmd command
poker
poker/cmd command
stoplight command
sudoku/cmd command
tictactoe/cmd command
tictactoe/metamodel
Package metamodel demonstrates the struct tag DSL for Tic-tac-toe.
 Package metamodel demonstrates the struct tag DSL for Tic-tac-toe.
trafficlight command
visualization_demo command
Visualization demo - generates example SVG files for workflows and state machines
 Visualization demo - generates example SVG files for workflows and state machines
Package graphql provides a GraphQL server for Petri net models.
 Package graphql provides a GraphQL server for Petri net models.
example command
Example GraphQL server for Petri net models.
 Example GraphQL server for Petri net models.
Package hypothesis provides utilities for evaluating hypothetical states via ODE simulation.
 Package hypothesis provides utilities for evaluating hypothetical states via ODE simulation.
Package learn implements learnable rate functions for Neural ODE-style parameter estimation in Petri net models.
 Package learn implements learnable rate functions for Neural ODE-style parameter estimation in Petri net models.
Package metamodel provides compatibility utilities for migrating from the legacy Model type to the modern generic PetriNet types.
 Package metamodel provides compatibility utilities for migrating from the legacy Model type to the modern generic PetriNet types.
Package mining provides process mining algorithms including discovery and conformance checking.
 Package mining provides process mining algorithms including discovery and conformance checking.
Package monitoring provides real-time predictive process monitoring.
 Package monitoring provides real-time predictive process monitoring.
Package parser handles JSON import/export for Petri nets.
 Package parser handles JSON import/export for Petri nets.
Package petri implements core Petri net data structures.
 Package petri implements core Petri net data structures.
Package plotter provides SVG visualization for ODE solutions.
 Package plotter provides SVG visualization for ODE solutions.
Package reachability provides state space analysis for Petri nets.
 Package reachability provides state space analysis for Petri nets.
Package results defines the structured output format for simulations
 Package results defines the structured output format for simulations
Package sensitivity provides tools for analyzing how Petri net behavior changes with different parameters.
 Package sensitivity provides tools for analyzing how Petri net behavior changes with different parameters.
Package solver implements ODE (Ordinary Differential Equation) solvers for Petri net simulation using mass-action kinetics.
 Package solver implements ODE (Ordinary Differential Equation) solvers for Petri net simulation using mass-action kinetics.
Package statemachine provides a high-level API for modeling hierarchical state machines (statecharts) using Petri nets as the underlying formalism.
 Package statemachine provides a high-level API for modeling hierarchical state machines (statecharts) using Petri nets as the underlying formalism.
Package stateutil provides utility functions for manipulating Petri net state maps.
 Package stateutil provides utility functions for manipulating Petri net state maps.
Package templates provides common Petri net patterns
 Package templates provides common Petri net patterns
Package tokenmodel defines abstract building blocks for formal models.
 Package tokenmodel defines abstract building blocks for formal models.
dsl
Package dsl implements an S-expression DSL for defining token model schemas.
 Package dsl implements an S-expression DSL for defining token model schemas.
guard
Package guard implements a secure guard expression evaluator for Petri net transitions.
 Package guard implements a secure guard expression evaluator for Petri net transitions.
petri
Package petri provides structural analysis for Petri net invariant proofs.
 Package petri provides structural analysis for Petri net invariant proofs.
Package validation provides structural analysis and validation for Petri nets
 Package validation provides structural analysis and validation for Petri nets
Package visualization provides utilities for visualizing Petri nets as SVG.
 Package visualization provides utilities for visualizing Petri nets as SVG.
Package workflow provides a comprehensive workflow management framework built on Petri nets with support for task dependencies, resource management, SLA tracking, and real-time monitoring.
 Package workflow provides a comprehensive workflow management framework built on Petri nets with support for task dependencies, resource management, SLA tracking, and real-time monitoring.
Package zkcompile transforms Petri net models into ZK circuit constraints.
 Package zkcompile transforms Petri net models into ZK circuit constraints.
petrigen
Package petrigen generates gnark ZK circuits from Petri net models.
 Package petrigen generates gnark ZK circuits from Petri net models.

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