Mathematical Logic in Computer Science
- Computer ScienceArXiv
The article retraces major events and milestones in the mutual influences between mathematical logic and computer science since the 1950s.
Exploitation as code reuse: On the need of formalization
- Computer Science, Engineeringit Inf. Technol.
The need for modeling exploit computations and possible formal approaches to it are discussed and a comparison of current and proposed approaches to this problem is suggested.
A Combinatorial Testing Framework for Intuitionistic Propositional Theorem Provers
Proving a theorem in intuitionistic propositional logic, with implication as its single connective, is known as one of the simplest to state PSPACE-complete problem. At the same time, via the…
Lambda: the ultimate sublanguage (experience report)
- Computer ScienceProc. ACM Program. Lang.
We describe our experience teaching an advanced typed functional programming course based around the use of System Fω as a programming language.
On the concurrent computational content of intermediate logics
- Computer ScienceTheor. Comput. Sci.
Functional Pearl: Witness Me - Constructive Arguments Must Be Guided with Concrete Witness
It is demonstrated how useful the Curry–Howard correspondence point of view is as the guiding principle for developing dependently-typed programs.
Classical Proofs as Parallel Programs
- Computer ScienceGandALF
A parallel and more powerful extension of the simply typed lambda calculus corresponding to an analytic natural deduction based on the excluded middle law is defined, which features a natural higher-order communication mechanism between processes, which also supports broadcasting.
The Significance of the Curry-Howard Isomorphism
- Computer Science
The Curry-Howard isomorphism is a proof-theoretic result that establishes a connection between derivations in natural deduction and terms in typed lambda calculus, which underlies the development of type systems for programming languages.
Homotopy Type Theory: A synthetic approach to higher equalities
This is an introduction to Homotopy Type Theory and Univalent Foundations for philosophers, written as a chapter for the book "Categories for the Working Philosopher" (ed. Elaine Landry)
Perspective Computational logic: its origins and applications
- Computer Science
A refinement of LCF, called Isabelle, retains advantages ofLCF while providing flexibility in the choice of logical formalism and much stronger automation.
SHOWING 1-10 OF 102 REFERENCES
A Taste of Linear Logic
- Philosophy, Computer ScienceMFCS
This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of ‘Propositions as…
Type theory and functional programming
- EconomicsInternational computer science series
This book explores the role of Martin-Lof s constructive type theory in computer programming and how the theory can be successfully applied in practice.
A symmetric modal lambda calculus for distributed computing
- Computer ScienceProceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
This work forms a novel system of natural deduction for IS5, decomposing the introduction and elimination rules for /spl square/ and /spl diams/, thereby allowing the corresponding programs to be more direct.
Computational types from a logical perspective
- MathematicsJournal of Functional Programming
This paper shows that the computational lambda calculus also arises naturally as the term calculus corresponding to a novel intuitionistic modal propositional logic and gives natural deduction, sequent calculus and Hilbert-style presentations of this logic and proves strong normalisation and confluence results.
Session Types as Intuitionistic Linear Propositions
- Computer ScienceCONCUR
This paper introduces a type system for the π-calculus that exactly corresponds to the standard sequent calculus proof system for dual intuitionistic linear logic, and provides the first purely logical account of all features of session types.
A modal analysis of staged computation
- Computer SciencePOPL '96
The main technical result is a conservative embedding of Nielson & Nielson's two-level functional language in the language Mini-ML, thus proving that binding-time correctness is equivalent to modal correctness on this fragment.
A formulae-as-type notion of control
- Computer SciencePOPL '90
It is proved that all evaluations of typed terms in Idealized Scheme are finite, and the existence of computationally interesting “classical programs” is illustrated by the definition of conjunctively, disjunctive, and existential types using standard classical definitions.