相关论文: LFPL: Revisited and Mechanized

We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…

We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…

In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…

We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…

Practical checkers based on refinement types use the combination of implicit semantic sub-typing and parametric polymorphism to simplify the specification and automate the verification of sophisticated properties of programs. However, a…

We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our…

LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…

While statement autoformalization has advanced rapidly, full-theorem autoformalization remains largely unexplored. Existing iterative refinement methods in statement autoformalization typically improve isolated aspects of formalization,…

Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…

Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce an affine bounded linear typing discipline on a general notion of resource which can…

Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…

This paper is a structured introduction to Light Affine Logic, and to its intuitionistic fragment. Light Affine Logic has a polynomially costing cut elimination (P-Time correctness), and encodes all P-Time Turing machines (P-Time…

In the past decade, many techniques have been developed to prove linearizability, the gold standard of correctness for concurrent data structures. Intuitively, linearizability requires that every operation on a concurrent data structure…

The class of Basic Feasible Functionals BFF is the second-order counterpart of the class of first-order functions computable in polynomial time. We present several implicit characterizations of BFF based on a typed programming language of…

Logical Frameworks such as Automath [de Bruijn, 1968] or LF [Harper et al., 1993] were originally conceived as metalanguages for the specification of foundationally uncommitted deductive systems, yielding generic proof checkers. Their high…

This paper presents language techniques for applying memoization selectively. The techniques provide programmer control over equality, space usage, and identification of precise dependences so that memoization can be applied according to…

In a previous work Baillot and Terui introduced Dual light affine logic (DLAL) as a variant of Light linear logic suitable for guaranteeing complexity properties on lambda calculus terms: all typable terms can be evaluated in polynomial…

Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…

Large Language Models (LLMs) are increasingly integrated into the software engineering ecosystem. Their test-time compute (TTC) reasoning capabilities show significant potential for understanding program logic and semantics beyond mere…