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System Description: Twelf  A MetaLogical Framework for Deductive Systems
 Proceedings of the 16th International Conference on Automated Deduction (CADE16
, 1999
"... . Twelf is a metalogical framework for the specification, implementation, and metatheory of deductive systems from the theory of programming languages and logics. It relies on the LF type theory and the judgmentsastypes methodology for specification [HHP93], a constraint logic programming interp ..."
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Cited by 315 (49 self)
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. Twelf is a metalogical framework for the specification, implementation, and metatheory of deductive systems from the theory of programming languages and logics. It relies on the LF type theory and the judgmentsastypes methodology for specification [HHP93], a constraint logic programming interpreter for implementation [Pfe91], and the metalogic M2 for reasoning about object languages encoded in LF [SP98]. It is a significant extension and complete reimplementation of the Elf system [Pfe94]. Twelf is written in Standard ML and runs under SML of New Jersey and MLWorks on Unix and Window platforms. The current version (1.2) is distributed with a complete manual, example suites, a tutorial in the form of online lecture notes [Pfe], and an Emacs interface. Source and binary distributions are accessible via the Twelf home page http://www.cs.cmu.edu/~twelf. 1 The Twelf System The Twelf system is a tool for experimentation in the theory of programming languages and logics. It supports...
A Linear Logical Framework
, 1996
"... We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF c ..."
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Cited by 217 (44 self)
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We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of MiniML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cutelimination. 1 Introduction A logical framework is a formal system desig...
A Coverage Checking Algorithm for LF
, 2003
"... Coverage checking is the problem of deciding whether any closed term of a given type is an instance of at least one of a given set of patterns. It can be used to verify if a function defined by pattern matching covers all possible cases. This problem has a straightforward solution for the first ..."
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Cited by 40 (12 self)
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Coverage checking is the problem of deciding whether any closed term of a given type is an instance of at least one of a given set of patterns. It can be used to verify if a function defined by pattern matching covers all possible cases. This problem has a straightforward solution for the firstorder, simplytyped case, but is in general undecidable in the presence of dependent types. In this paper we present a terminating algorithm for verifying coverage of higherorder, dependently typed patterns.
Automated Theorem Proving in a Simple MetaLogic for LF
 PROCEEDINGS OF THE 15TH INTERNATIONAL CONFERENCE ON AUTOMATED DEDUCTION (CADE15
, 1998
"... Higherorder representation techniques allow elegant encodings of logics and programming languages in the logical framework LF, but unfortunately they are fundamentally incompatible with induction principles needed to reason about them. In this paper we develop a metalogic M_2 which allows i ..."
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Cited by 35 (16 self)
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Higherorder representation techniques allow elegant encodings of logics and programming languages in the logical framework LF, but unfortunately they are fundamentally incompatible with induction principles needed to reason about them. In this paper we develop a metalogic M_2 which allows inductive reasoning over LF encodings, and describe its implementation in Twelf, a specialpurpose automated theorem prover for properties of logics and programming languages. We have used Twelf to automatically prove a number of nontrivial theorems, including type preservation for MiniML and the deduction theorem for intuitionistic propositional logic.
Tabled HigherOrder Logic Programming
 In 20th International Conference on Automated Deduction
, 2003
"... Elf is a general metalanguage for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each ..."
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Cited by 26 (11 self)
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Elf is a general metalanguage for the specification and implementation of logical systems in the style of the logical framework LF. Based on a logic programming interpretation, it supports executing logical systems and reasoning with and about them, thereby reducing the effort required for each particular logical system. The traditional logic programming paradigm is extended by replacing firstorder terms with dependently typed terms and allowing implication and universal quantification in the bodies of clauses. These higherorder features allow us to model concisely and elegantly conditions on variables and the discharge of assumptions which are prevalent in many logical systems. However, many specifications are not executable under the traditional logic programming semantics and performance may be hampered by redundant computation. To address these problems, I propose a tabled higherorder logic programming interpretation for Elf. Some redundant computation is eliminated by memoizing subcomputation and reusing its result later. If we do not distinguish different proofs for a property, then search based on tabled logic programming is complete and terminates for programs with bounded recursion. In this proposal, I present a prooftheoretical characterization for tabled higherorder logic programming. It is the basis of the implemented prototype for tabled logic programming interpreter for Elf. Preliminary experiments indicate that many more logical specifications are executable under the tabled semantics. In addition, tabled computation leads to more efficient execution of programs. The goal of the thesis is to demonstrate that tabled logic programming allows us to efficiently automate reasoning with and about logical systems in the logical f...
Hybridizing a logical framework
 In International Workshop on Hybrid Logic 2006 (HyLo 2006), Electronic Notes in Computer Science
, 2006
"... The logical framework LF is a constructive type theory of dependent functions that can elegantly encode many other logical systems. Prior work has studied the benefits of extending it to the linear logical framework LLF, for the incorporation linear logic features into the type theory affords good r ..."
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Cited by 20 (1 self)
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The logical framework LF is a constructive type theory of dependent functions that can elegantly encode many other logical systems. Prior work has studied the benefits of extending it to the linear logical framework LLF, for the incorporation linear logic features into the type theory affords good representations of state change. We describe and argue for the usefulness of an extension of LF by features inspired by hybrid logic, which has several benefits. For one, it shows how linear logic features can be decomposed into primitive operations manipulating abstract resource labels. More importantly, it makes it possible to realize a metalogical framework capable of reasoning about stateful deductive systems encoded in the style familiar from prior work with LLF, taking advantage of familiar methodologies used for metatheoretic reasoning in LF.Acknowledgments From the very first computer science course I took at CMU, Frank Pfenning has been an exceptional teacher and mentor. For his patience, breadth of knowledge, and mathematical good taste I am extremely thankful. No less do I owe to the other two major contributors to my programming languages
Termination and Reduction Checking in the Logical Framework
 IN WORKSHOP OF AUTOMATION OF PROOFS BY MATHEMATICAL INDUCTION
, 2000
"... ..."
Termination and Reduction Checking for HigherOrder Logic Programs
 In First International Joint Conference on Automated Reasoning (IJCAR
"... . In this paper, we present a syntaxdirected termination and reduction checker for higherorder logic programs. The reduction checker verifies parametric higherorder subterm orderings describing input and output relations. These reduction orderings are exploited during termination checking to ..."
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Cited by 13 (3 self)
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. In this paper, we present a syntaxdirected termination and reduction checker for higherorder logic programs. The reduction checker verifies parametric higherorder subterm orderings describing input and output relations. These reduction orderings are exploited during termination checking to infer that a specified termination order holds. To reason about parametric higherorder subterm orderings, we introduce a deductive system as a logical foundation for proving termination. This allows the study of prooftheoretical properties, such as consistency, local soundness and completeness and decidability. We concentrate here on proving consistency of the presented inference system. The termination and reduction checker are implemented as part of the Twelf system and enables us to verify proofs by complete induction. 1 Introduction One of the central problems in verifying specifications and checking proofs about them is the need to prove termination. Several automated methods...
Elimination of Negation in a Logical Framework
, 2000
"... Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negationasfailure does not fit well in a logical framework, especially one endowed with ..."
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Cited by 10 (3 self)
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Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [15] cannot express directly negative information, although negation is a useful specification tool. Since negationasfailure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgements, we adapt the idea of elimination of negation introduced in [21] for Horn logic to a fragment of higherorder HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.
Delphin: Functional Programming with Deductive Systems
, 2002
"... We present the design and implementation of the strict and pure functional programming language Delphin. Its novel and distinctive features include a twolevel design that distinguishes cleanly between the tasks of representing data and programming with data. One level is the logical framework LF [5 ..."
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Cited by 6 (2 self)
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We present the design and implementation of the strict and pure functional programming language Delphin. Its novel and distinctive features include a twolevel design that distinguishes cleanly between the tasks of representing data and programming with data. One level is the logical framework LF [5], serving as Delphin's data representation language. The other level is # [15], a type theory designed to support programming using pattern matching and recursion. The main contribution of this work is therefore Delphin, in which one can program with higherorder, dependentlytyped data structures such as proofs and typing derivations in a natural and intuitive way.