System Description: Twelf - A Meta-Logical Framework for Deductive Systems

  title={System Description: Twelf - A Meta-Logical Framework for Deductive Systems},
  author={F. Pfenning and C. Sch{\"u}rmann},
Twelf is a meta-logical framework for the specification, implementation, and meta-theory of deductive systems from the theory of programming languages and logics. It relies on the LF type theory and the judgments-as-types methodology for specification [HHP93], a constraint logic programming interpreter for implementation [Pfe91], and the meta-logic M2 for reasoning about object languages encoded in LF [SP98]. It is a significant extension and complete reimplementation of the Elf system [Pfe94… Expand
System Description : Celf – A Logical Framework for Deductive and Concurrent Systems
CLF (Concurrent LF) [CPWW02a] is a logical framework for specifying and implementing deductive and concurrent systems from areas, such as programming language theory, security protocol analysis,Expand
Celf - A Logical Framework for Deductive and Concurrent Systems (System Description)
Celf is an implementation of the CLF type theory that extends the LF type theory by linear types toSupport representation of state and a monad to support representation of concurrency. Expand
A meta-programming approach to realizing dependently typed logic programming
This work presents a simple mapping from LF specifications to a set of formulas in the higher-order hereditary Harrop (hohh) language, that relates derivations and proof-search between the two frameworks, and shows that this encoding can be improved by exploiting knowledge of the well-formedness of the original LF specification to elide much redundant type-checking information. Expand
The Twelf Proof Assistant
This work designs special purpose logical frameworks for capturing reoccurring concepts for special domains, such as, for example, variable renaming, substitution application, and resource management for programming language theory. Expand
Mechanizing metatheory in a logical framework
An up-to-date overview of the LF λ-calculus, the LF methodology for adequate representation, and the Twelf methodology for mechanizing metatheory is provided. Expand
Twelf and Delphin: Logic and Functional Programming in a Meta-logical Framework
The meta-logical framework Twelf [PS99] is being discussed here that is a logical framework that supports reasoning about encodings of object-languages and deductions prevalent in the areas of programming languages, mobile code and logics design. Expand
Two-Level Meta-reasoning in Coq
  • A. Felty
  • Computer Science, Mathematics
  • TPHOLs
  • 2002
This paper presents a methodology which allows Coq to be used as a framework for meta-reasoning and gives an approach to reasoning in Coq which very closely mimics reasoning in FOλ ΔN illustrating a close correspondence between the two frameworks. Expand
Implementing Substructural Logical Frameworks
This thesis develops the theoretical infrastructure required to implement — and gives an implementation of — a new logical framework that extends LF with the concepts of both linear resources and affine resources, and proves strong normalization, type preservation, and confluence for a context-split-oblivious reduction semantics. Expand
Imperative LF Meta-Programming
  • Aaron Stump
  • Computer Science
  • Electron. Notes Theor. Comput. Sci.
  • 2008
This paper presents work in progress on a programming language called Rogue-Sigma-Pi, in which general programs can be written for soundly manipulating objects represented in the Edinburgh Logical Framework, and demonstrates RSP through representative LF meta-programs. Expand
Programming proofs : a novel approach based on contextual types
We present an overview of Beluga, a dependently-typed programming and proof development environment. Beluga uses a two-level approach: it supports specifying formal systems within the logicalExpand


Elf: A Meta-Language for Deductive Systems (System Descrition)
An overview of how speciica-tion, implementation, and meta-theory tasks are supported in the Elf language and some case studies are described. Expand
Automated Theorem Proving in a Simple Meta-Logic for LF
A meta-logic M2 is developed which allows inductive reasoning over LF encodings, and its implementation is described in Twelf, a special-purpose automated theorem prover for properties of logics and programming languages. Expand
A framework for defining logics
The Edinburgh Logical Framework provides a means to define (or present) logics through a general treatment of syntax, rules, and proofs by means of a typed λ-calculus with dependent types, whereby each judgment is identified with the type of its proofs. Expand
Algorithms for Equality and Unification in the Presence of Notational Definitions
Notational definitions are pervasive in mathematical practice and are therefore supported in most automated theorem proving systems such as Coq [B+98], PVS [ORS92], Lego [LP92], or Isabelle [Pau94].Expand
Logic programming in the LF logical framework
3 A Meta-Logic for Unification 4 3.1 A First-Order Unification Logic with Quantifier Dependencies . . . . . . . . . . . . . 5 3.2 Transformations for First-Order Unification . . . . . . . . . . . . .Expand
Unification via Explicit Substitutions: The Case of Higher-Order Patterns
This paper investigates the case of higher-order patterns as introduced by Miller and sketches an efficient implementation of the abstract algorithm and its generalization to constraint simplification, which has yielded good experimental results at the core of a higher- order constraint logic programming language. Expand
Mode and Termination Checking for Higher-Order Logic Programs
We consider how mode (such as input and output) and termination properties of typed higher-order constraint logic programming languages may be declared and checked effectively. The systems that weExpand
Computation and Deduction
Draft notes for a course given at Carnegie Mellon University during the fall semester of 1994, with author Frank Pfenning and the National Football League. Expand
The Practice of Logical Frameworks
A framework for deening logics Pfe] Frank Pfenning. Computation and Deduction
  • 143{ 184
  • 1993