Recursion over realizability structures
Information and Computation
Representing inductively defined sets by wellorderings in Martin-Löf's type theory
Theoretical Computer Science
Object-oriented software construction (2nd ed.)
Object-oriented software construction (2nd ed.)
The Vienna Development Method: The Meta-Language
The Vienna Development Method: The Meta-Language
Synthetic Domain Theory in Type Theory: Another Logic of Computable Functions
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Local Reasoning about Programs that Alter Data Structures
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Admissibility of Fixpoint Induction over Partial Types
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Simple general recursion in type theory
Nordic Journal of Computing
Ynot: dependent types for imperative programs
Proceedings of the 13th ACM SIGPLAN international conference on Functional programming
Hoare type theory, polymorphism and separation1
Journal of Functional Programming
Structuring the verification of heap-manipulating programs
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A realizability model for impredicative Hoare type theory
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Realisability semantics of parametric polymorphism, general references and recursive types
Mathematical Structures in Computer Science
Hoare-style reasoning with (algebraic) continuations
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
Probabilistic relational verification for cryptographic implementations
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Combining proofs and programs in a dependently typed language
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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Partial type theories allow reasoning about recursively-defined computations using fixed-point induction. However, fixed-point induction is only sound for admissible types and not all types are admissible in sufficiently expressive dependent type theories. Previous solutions have either introduced explicit admissibility conditions on the use of fixed points, or limited the underlying type theory. In this paper we propose a third approach, which supports Hoare-style partial correctness reasoning, without admissibility conditions, but at a tradeoff that one cannot reason equationally about effectful computations. The resulting system is still quite expressive and useful in practice, which we confirm by an implementation as an extension of Coq.