'formal' 검색 결과

Generate formal specifications (definitions, predicates, invariants, pre/post-conditions) in Isabelle/HOL or Coq from informal requirements, source code, pseudocode, or mathematical descriptions. Use when users need to: (1) Formalize algorithms or data structures, (2) Create function specifications with contracts, (3) Generate predicates and properties for verification, (4) Translate informal requirements into formal logic, (5) Specify invariants for loops or data structures, or (6) Create formal definitions for mathematical concepts. Supports both Isabelle/HOL and Coq equally.

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Formally verify programs by writing Lean 4 proofs. Trigger this skill whenever the user wants to formally verify code, generate Lean 4 proofs, prove properties about algorithms or smart contracts, verify invariants, convert program logic into formal specifications, or anything involving Lean 4 and formal verification. Also trigger when the user mentions "qedgen", "lean proof", "formal proof", "verify my code", "prove correctness", "formal verification", or wants mathematical guarantees about their implementation.

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Expert-level formal methods covering formal specification, model checking, theorem proving, type theory, program verification, and formal languages.

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Develop mathematical proofs in Lean, a system that checks formal proofs, continue unfinished projects, or audit existing results. Check that the theorem matches the original claim, examine its assumptions, and prepare sources and commands for reproduction.

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• Turn a mathematical statement into a checked Lean proof
• Continue an unfinished Lean proof project
• Audit whether a theorem proves the original claim

Turn mathematical claims into definitions, lemmas, and proofs for Lean 4 and Mathlib. Check proofs with Lean’s trusted core, separately review whether the formal statement matches the original claim, and record verification evidence.

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• Verifying an important lemma with Lean 4
• Breaking a theorem into definitions and supporting lemmas
• Checking proofs for sorry, admit, and unauthorized axioms

Cultural adaptation for translated content. Run AFTER blog-translate completes. Adjusts brand examples, CTAs, legal references, and formality for the target market (German, French, Japanese, Spanish, etc.). Deep cultural adaptation of translated blog posts. Goes beyond translation to swap brand examples, adapt CTAs, substitute legal references, localize statistic sources where possible, and adjust formality (Sie/du, tu/vous, formal/informal). Built-in profiles for DACH, Francophone, Hispanic, and Japanese markets, plus a custom-locale template. Makes content feel locally authored, not translated. Use when user says "localize blog", "blog localize", "cultural adaptation", "adapt for Germany", "adapt for France", "lokalisieren", "localiser", "adaptar".

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Cultural adaptation for translated content. Run AFTER blog-translate completes. Adjusts brand examples, CTAs, legal references, and formality for the target market (German, French, Japanese, Spanish, etc.). Deep cultural adaptation of translated blog posts. Goes beyond translation to swap brand examples, adapt CTAs, substitute legal references, localize statistic sources where possible, and adjust formality (Sie/du, tu/vous, formal/informal). Built-in profiles for DACH, Francophone, Hispanic, and Japanese markets, plus a custom-locale template. Makes content feel locally authored, not translated. Use when user says "localize blog", "blog localize", "cultural adaptation", "adapt for Germany", "adapt for France", "lokalisieren", "localiser", "adaptar".

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Mathematical foundations, logical structures, and formal verification guidance. Trigger when: - Designing protocol contracts, formal specifications, verifying state spaces, or using proof assistants. - Tasks involve: TLA+, Alloy, Lean, Coq, model checkers, invariants, temporal logic. - Prompt contains keywords: formal verification, alloy, tla+, lean, coq, invariant, state machine, model checker, liveness, safety.

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Produces a narrow-interval quality signal for a WinDAGs skill that a third party can verify without inspecting model weights or method internals. The mechanism is attribution-kNN over a tamper-evident outcome log (task→skills→accept/reject store), combined with a conformal-prediction calibration certificate that provides a formal coverage guarantee. Thompson/Beta sampling is explicitly rejected as a category error: it produces a selection signal for stationary i.i.d. rewards, not an attestation signal for context-dependent LLM output quality. The resulting bundle — outcome-log Merkle root + conformal threshold + optional TEE guardrail signature — constitutes a "narrow-interval trust" credential: verifiable, bounded, and internals-opaque.

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Approach engineering problems by checking assumptions, defining performance constraints, and choosing suitable tools before implementation. The skill guides algorithm analysis, complete code, performance optimization, and correctness checks through tests, assertions, or formal verification, meaning mathematical checks of correctness.

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• Checking algorithm complexity and design assumptions
• Choosing languages for numerical or distributed systems
• Implementing concurrent code with explicit error handling

Turn a Mermaid sequence diagram of a cryptographic protocol into a ProVerif model, a file for formal security checks. It includes queries for secrecy, authentication, replay resistance, and forward secrecy where applicable.

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• Converting a cryptographic protocol diagram into a .pv file
• Preparing session key secrecy checks
• Modeling authentication and replay resistance

This skill covers formal identification arguments and proofs in structural and reduced-form econometrics. Use when the user needs to prove or formalize that a parameter is identified — including writing identification propositions, stating regularity conditions, deriving rank conditions, or showing observational equivalence fails. Triggers on "identification proof", "identification argument", "identify the parameter", "show identification", "identification condition", "exclusion restriction proof", "rank condition", "order condition", "identification strategy formal", "nonparametric identification", "parametric identification", "local identification", "global identification", "observational equivalence", "identification at infinity", "completeness condition", "regularity conditions", "Rothenberg", "proof of identification", "identification result", "identified parameter", "point identified", "set identified", "partial identification".

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Classical end-to-end empirical analysis workflow in the modern tidyverse + econometrics R ecosystem — dplyr + tidyr + haven + fixest + sandwich + lmtest + clubSandwich + AER + ivreg + did + bacondecomp + HonestDiD + eventstudyr + rdrobust + rddensity + Synth + gsynth + synthdid + MatchIt + WeightIt + cobalt + ebal + grf + DoubleML + mediation + marginaleffects + modelsummary + kableExtra + gt + ggplot2 + ggpubr + cowplot + binsreg. **Defaults to economics empirical-paper style** (AER / QJE / AEJ) — every run produces a publication-ready output set with a multi-column regression table (M1→M6 progressive controls/FE) as the centerpiece, plus Table 1 (descriptives), mechanism / heterogeneity / robustness tables, and event-study + coefficient + trend figures. Covers the full 8-step R pipeline an applied economist runs on every paper — (1) data import & cleaning (read_dta/read_csv, naniar, janitor, validate-merges), (2) variable construction (mutate/across/winsorize/group_by + lag/lead with dplyr), (3) descriptive statistics & Table 1 (gtsummary, modelsummary::datasummary, tableone), (4) classical diagnostic tests (shapiro/jarque.bera.test/bptest/dwtest/bgtest/vif/adf.test/kpss.test/Hausman), (5) baseline modeling (fixest::feols, ivreg, did::att_gt, eventstudyr, sun_ab, did_imputation, synthdid, rdrobust, MatchIt, WeightIt, grf::causal_forest, DoubleML, mediation), (6) robustness battery (modelsummary stack, clubSandwich CRSE, fwildclusterboot, ri2, robomit Oster, bacondecomp, HonestDiD), (7) further analysis (interactions + marginaleffects, mediation::mediate, gsem via lavaan, dose-response splines, grf CATE), (8) publication-ready tables & figures (modelsummary, kableExtra, gt, stargazer, texreg, flextable to LaTeX/Word/HTML; ggplot2 + ggpubr + cowplot + binsreg + iplot for figures). **Also covers two parallel domain modes that share the same 8-step scaffolding** — **Mode A — Epidemiology / public health** (target-trial emulation, IPTW + g-formula + TMLE doubly-robust triplet via `WeightIt` / `gfoRmula` / `tmle` / `ltmle`, Mendelian randomization via `MendelianRandomization` / `TwoSampleMR` / `MRPRESSO`, KM / Cox / AFT / RMST survival via `survival` / `survminer` / `flexsurv`, E-value sensitivity via `EValue`, principal stratification — STROBE / TRIPOD reporting), and **Mode B — ML causal inference** (DML via `DoubleML`, S/T/X/R/DR meta-learners via `causalweight` / `grf`, causal forest via `grf::causal_forest`, BART/BCF via `bartCause` / `bcf`, matrix completion via `MCPanel`, CATE distribution + policy tree via `policytree`, off-policy evaluation, conformal causal via `conformalInference` / `cfcausal`, fairness audit via `fairmodels`, DAG learning via `pcalg` / `bnlearn` / LLM-assisted). Use when the user asks for a complete R empirical analysis, wants a tidyverse-style reproducible R script / Quarto workflow, prefers fixest over reghdfe, needs the R counterpart to StatsPAI / 00.1 / 00.2, or names a specific R step in isolation ("feols with cluster", "MatchIt nearest neighbor", "bacondecomp in R", "gtsummary table 1", "modelsummary to Word"). Mode A triggers on "target trial emulation R", "tmle ltmle", "MendelianRandomization", "TwoSampleMR", "MRPRESSO", "survival cox AFT", "STROBE R", "EValue R", "公共健康 R", "流行病学 R". Mode B triggers on "DoubleML R", "grf causal forest", "policytree", "bartCause bcf", "conformal causal R", "fairmodels", "pcalg NOTEARS", "因果机器学习 R".

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Plan, draft, audit, globally revise, format, and verify a formal mathematical-modeling paper after the Standard evidence gate passes. Use for the sole S7/S8 formal manuscript path, not for legacy micro-unit scaffolds.

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Generate formal specifications including preconditions, postconditions, invariants, and contracts from code or requirements. Use this skill when documenting APIs, creating formal verification annotations, defining function contracts, specifying class invariants, writing design-by-contract code, or preparing code for formal verification. Supports multiple specification languages including JML, ACSL, Dafny, Eiffel contracts, and documentation annotations.

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Translate natural-language requirements or structured specification documents into formal temporal logic properties (LTL, CTL, safety/liveness properties). Use when users need to formalize requirements for model checking, formal verification, or property specification. Handles embedded/real-time systems, hardware verification, concurrent systems, and reactive systems. Resolves ambiguities, asks clarifying questions when needed, and outputs machine-checkable formulas with explanations. Supports multiple output formats (SPIN, NuSMV, Uppaal, TLA+, Maude).

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Automatically infer formal correctness properties from Verilog/SystemVerilog RTL code and generate SystemVerilog Assertions (SVA). Identifies control-flow invariants (mutual exclusion, valid-ready handshakes, pipeline ordering, safety properties), liveness expectations, and temporal properties. Use when working with RTL designs that need formal property generation, when adding assertions to existing RTL, or when users ask to infer properties, generate assertions, or create formal specifications from hardware designs.

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Create ACSL (ANSI/ISO C Specification Language) formal annotations for C/C++ programs. Use this skill when working with formal verification, adding function contracts (requires/ensures), loop invariants, assertions, memory safety annotations, or any ACSL specifications. Supports Frama-C verification and generates comprehensive formal specifications for C/C++ code.

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Think and work like an expert Formal Methods Researcher. Use when a task calls for Formal Methods Researcher judgment. Reasons from operational semantics and temporal logics through SPIN/TLA+/PRISM, Coq/Lean/Isabelle, Z3/CVC5, refinement and separation logic, vacuity and false-positive diagnosis, and Dafny/F* versus property-based testing boundaries.

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Expert guide for mathematical formal verification, SMT solver constraints (Z3, Dafny, TLA+), invariant theorem proving for FinTech billing state machines, RBAC/ABAC authorization, and zero-violation architecture / Panduan ahli verifikasi formal matematis, SMT solver (Z3, Dafny, TLA+), pembuktian invarian state machine billing FinTech, otorisasi RBAC/ABAC, dan arsitektur zero-violation.

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The logic of sentential connectives -- and, or, not, if-then, if-and-only-if -- as a formal system. Covers syntax (well-formed formulas), semantics (truth tables), satisfiability, validity, logical equivalence, normal forms (CNF, DNF), natural-deduction rules, and common translation pitfalls. Use when formalizing arguments with propositional structure, checking validity mechanically, or teaching the foundations of formal reasoning.

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Catalog of informal fallacies with definitions, canonical examples, and detection heuristics. Covers relevance fallacies (ad hominem, straw man, red herring, appeal to authority, appeal to emotion), presumption fallacies (false dichotomy, complex question, begging the question), ambiguity fallacies (equivocation, amphiboly, accent), causal fallacies (post hoc, slippery slope, correlation-causation), and statistical fallacies (hasty generalization, cherry-picking). Use when evaluating arguments for rhetorical or informal reasoning errors.

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Verify and write proofs using the Acorn theorem prover for mathematical and cryptographic formalization. Use when working with Acorn proof files (.ac), verifying theorems, formalizing mathematical or cryptographic protocols, or writing proofs in the Acorn language. Triggers on: (1) Creating or editing .ac files, (2) Running acorn verify commands, (3) Formalizing math or crypto proofs, (4) Questions about Acorn syntax or standard library.

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Expert-level mathematical logic knowledge. Use when working with propositional logic, first-order logic, proof theory, model theory, computability theory, Godel incompleteness theorems, set theory, type theory, or formal verification. Also use when the user mentions 'formal proof', 'Godel', 'incompleteness', 'Turing machine', 'decidability', 'Zermelo-Fraenkel', 'axiom of choice', 'model theory', 'completeness theorem', 'computability', 'formal language', or 'type theory'.

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