Formaliset

Formaliset is a theoretical framework for expressing and reasoning about formal systems across logic, computer science, and linguistics. It provides a formal meta-language, a typed syntax, and a rule-based proof apparatus designed to coexist with existing theories while enabling cross-domain verification.

At its core, Formaliset offers a typed, lambda-like language for terms and propositions, a set of inference rules (including a sequent calculus and natural deduction variants), and a semantics defined by an interpretation function. The type system distinguishes objects, predicates, and proofs to enforce correct composition.

A typical Formaliset development defines an alphabet of atomic propositions, constructors for connectives and quantifiers, and axioms and rules such as Modus Ponens and substitution. Proofs are represented as judgments or sequents and checked by a formal verifier. The framework supports definitions, inductive types, and modular theories.

Applications span formal verification of software and hardware, specification and verification of programming languages, and linguistic modeling of syntax and semantics. Formaliset is designed to interoperate with existing proof assistants, enabling exports and imports of Formaliset proofs with systems such as Coq or Lean.

In scholarly literature, Formaliset is treated as a notional framework for comparing formal systems rather than a single implemented tool. It is valued for a unifying perspective but criticized for potential complexity and integration overhead. See also formal language, logic, type theory, sequent calculus, and proof assistant.