📐 FormalOrbit

📋 Logic

📊 Model

✅ Proof

🔍 Verify

📐 Formal Methods

Logic • Specification • Verification • Model Checking • Theorem Proving • Formal Semantics

Master the art of mathematical reasoning — from propositional logic and formal specification to model checking, theorem proving, and verified software.

44+

Formal Methods Concepts & Techniques

Formal Methods Basics

Specification, verification, correctness, formal reasoning.

Propositional Logic

Connectives, truth tables, equivalences, normal forms.

Predicate Logic

Quantifiers, variables, predicates, first-order.

First-Order Logic

Syntax, semantics, proofs, completeness.

Modal Logic

Necessity, possibility, Kripke semantics.

Temporal Logic

LTL, CTL, CTL*, time-based reasoning.

Higher-Order Logic

Quantification over functions, HOL.

Intuitionistic Logic

Constructive reasoning, BHK interpretation.

Formal Specification

Specification languages, invariants, pre/post-conditions.

Z Notation

Schemas, invariants, pre/post, refinement.

VDM (Vienna Development Method)

Specification, validation, refinement.

Alloy Specification

Relational logic, lightweight, model finding.

B Method

Formal refinement, proof obligations, Atelier B.

Hoare Logic

Triples, pre/post-conditions, inference rules.

Loop Invariants

Verification of loops, termination.

Separation Logic

Pointer reasoning, frame rule, heap.

Dafny Verification

Automated program verification, SMT-based.

Why3 Framework

Multi-backend verification, Frama-C.

Model Checking

State-space, reachability, model checking algorithms.

SPIN Model Checker

Promela, LTL verification, partial order reduction.

nuSMV Model Checker

CTL, LTL, symbolic model checking, BDD.

Probabilistic Model Checking

PRISM, Markov chains, probabilistic logic.

Interactive Theorem Proving

Proof assistants, tactics, proof automation.

Coq Proof Assistant

Gallina, tactics, dependent types, extraction.

Isabelle/HOL

Higher-order logic, code generation, automation.

Agda Proof Assistant

Dependently typed, constructive, programming.

Lean Theorem Prover

Dependent types, automation, mathematical proof.

SMT Solvers

Theories, Z3, CVC4, quantifier-free.

SAT Solvers

DPLL, CDCL, SAT/SMT solving.

Z3 Theorem Prover

Microsoft Z3, SMT-based verification.

Regular Languages

RE, DFA, NFA, pumping lemma.

Context-Free Grammars

CFG, PDA, Chomsky hierarchy.

Automata Theory

Finite automata, Turing machines, decidability.

Operational Semantics

Big-step, small-step, structural semantics.

Denotational Semantics

Domain theory, continuations, fixed points.

Axiomatic Semantics

Hoare axioms, verification condition generation.

Type Theory Basics

Simple types, type safety, Curry-Howard.

Dependent Types

Pi/Sigma types, proof-as-programs, Idris.

Formal Verification in Industry

Hardware, aerospace, automotive, security.

Verified Compilers

CompCert, verified compilation, correctness.

Verified OS Kernels

seL4 verification, microkernels, capabilities.

Formal Methods Tools

Tools overview, IDEs, frameworks.

Athena Tools

Proof assistants, model checkers, SMT.

📐 Formal Methods Mastery Roadmap

🔰 Foundation

Propositional/predicate logic, formal basics

📶 Core

First-order logic, Hoare logic, Z notation, VDM

🔥 Deep Dive

Model checking, SMT, type theory, theorem proving

🏆 Frontier

Dependent types, separation logic, verified systems

📐 Prove Correctness — Master Formal Methods

Interactive proofs, verification challenges, and real-world correctness guarantees.

Back to Home Verification Services