Related papers: Elegant elaboration with function invocation
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…
System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…
We present a calculus, called the scheme-calculus, that permits to express natural deduction proofs in various theories. Unlike $\lambda$-calculus, the syntax of this calculus sticks closely to the syntax of proofs, in particular, no names…
Due to long generations, large language model (LLM) math reasoning demands significant computational resources and time. While many existing efficient inference methods have been developed with excellent performance preservation on language…
This paper presents a logical approach to the translation of functional calculi into concurrent process calculi. The starting point is a type system for the {\pi}-calculus closely related to linear logic. Decompositions of intuitionistic…
This short note presents a new formal language, lambda dependency-based compositional semantics (lambda DCS) for representing logical forms in semantic parsing. By eliminating variables and making existential quantification implicit, lambda…
Weak-head normalization is inconsistent with functional extensionality in the call-by-name $\lambda$-calculus. We explore this problem from a new angle via the conflict between extensionality and effects. Leveraging ideas from work on the…
A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…
Dedukti is a Logical Framework based on the $\lambda$$\Pi$-Calculus Modulo Theory. We show that many theories can be expressed in Dedukti: constructive and classical predicate logic, Simple type theory, programming languages, Pure type…
We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
We give a new type inference algorithm for typing lambda-terms in Elementary Affine Logic (EAL), which is motivated by applications to complexity and optimal reduction. Following previous references on this topic, the variant of EAL type…
The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension…
This work presents an analytical framework for the design and analysis of LLM-based algorithms, i.e., algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of…
We present a novel linear $\lambda$-calculus for Classical Multiplicative Exponential Linear Logic (\MELL) along the lines of the propositions-as-types paradigm. Starting from the standard term assignment for Intuitionistic Multiplicative…
We classify programming languages according to evaluation order: each language fixes one evaluation order as the default, making it transparent to program in that evaluation order, and troublesome to program in the other. This paper…
Large Language Models (LLMs) have achieved remarkable performance across a wide variety of natural language tasks; however, their large size makes their inference slow and computationally expensive. Focusing on this problem, we propose to…
We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of…
In this paper, we describe an IDE called CAPS (Calculational Assistant for Programming from Specifications) for the interactive, calculational derivation of imperative programs. In building CAPS, our aim has been to make the IDE accessible…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…