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Denotational Proof Languages: Expressive Tools for Writing and Verifying Proofs

Denotational Proof Languages (DPLs) provide powerful frameworks for constructing and checking proofs across various logics, featuring innovative syntax and semantics grounded in assumption bases. They ensure readability, writability, and efficient proof verification while guaranteeing soundness. DPLs are applicable to classical logics, intuitionist logics, modal and temporal logics, as well as program logics like Hoare-Floyd. Athena, a DPL for classical first-order logic, incorporates natural deduction and a higher-order functional programming language, enabling advanced features such as induction, recursion, and pattern matching.

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Denotational Proof Languages: Expressive Tools for Writing and Verifying Proofs

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  1. Denotational Proof Languages (DPLs) • DPLs are languages for writing proofs and proof tactics in arbitrary logics • Novel syntax and semantics (based on the abstraction on assumption bases) ensure: • Readability and writability • Efficient proof checking • Guaranteed soundness • Powerful mechanisms for expressing complex proof tactics and tacticals

  2. Wide applicability • DPLs have been designed and implemented for: • Classical logics (both first- and higher-order) • Intuitionist logics • Modal and temporal logics • Program logics (Hoare-Floyd logics) • Type systems

  3. Athena • A DPL for classical first-order logic • Uses natural deduction • Incorporates a higher-order functional programming language with algebraic data types • Supports induction, recursion, pattern matching • Other logics (e.g. modal logic) can be rapidly prototyped by implementing them on top of Athena

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