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131
Logic Programming in the LF Logical Framework
, 1991
"... this paper we describe Elf, a metalanguage intended for environments dealing with deductive systems represented in LF. While this paper is intended to include a full description of the Elf core language, we only state, but do not prove here the most important theorems regarding the basic building b ..."
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this paper we describe Elf, a metalanguage intended for environments dealing with deductive systems represented in LF. While this paper is intended to include a full description of the Elf core language, we only state, but do not prove here the most important theorems regarding the basic building blocks of Elf. These proofs are left to a future paper. A preliminary account of Elf can be found in [26]. The range of applications of Elf includes theorem proving and proof transformation in various logics, definition and execution of structured operational and natural semantics for programming languages, type checking and type inference, etc. The basic idea behind Elf is to unify logic definition (in the style of LF) with logic programming (in the style of Prolog, see [22, 24]). It achieves this unification by giving types an operational interpretation, much the same way that Prolog gives certain formulas (Hornclauses) an operational interpretation. An alternative approach to logic programming in LF has been developed independently by Pym [28]. Here are some of the salient characteristics of our unified approach to logic definition and metaprogramming. First of all, the Elf search process automatically constructs terms that can represent objectlogic proofs, and thus a program need not construct them explicitly. This is in contrast to logic programming languages where executing a logic program corresponds to theorem proving in a metalogic, but a metaproof is never constructed or used and it is solely the programmer's responsibility to construct objectlogic proofs where they are needed. Secondly, the partial correctness of many metaprograms with respect to a given logic can be expressed and proved by Elf itself (see the example in Section 5). This creates the possibilit...
Higherorder logic programming
 HANDBOOK OF LOGIC IN AI AND LOGIC PROGRAMMING, VOLUME 5: LOGIC PROGRAMMING. OXFORD (1998
"... ..."
Higherorder Unification via Explicit Substitutions (Extended Abstract)
 Proceedings of LICS'95
, 1995
"... Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda ..."
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Cited by 103 (13 self)
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Higherorder unification is equational unification for &beta;&eta;conversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda;&sigma;calculus of explicit substitutions.
Putting Type Annotations to Work
, 1996
"... We study an extension of the HindleyMilner system with explicit type scheme annotations and type declarations. The system can express polymorphic function arguments, userdefined data types with abstract components, and structure types with polymorphic fields. More generally, all programs of the po ..."
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Cited by 101 (1 self)
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We study an extension of the HindleyMilner system with explicit type scheme annotations and type declarations. The system can express polymorphic function arguments, userdefined data types with abstract components, and structure types with polymorphic fields. More generally, all programs of the polymorphic lambda calculus can be encoded by a translation between typing derivations. We show that type reconstruction in this system can be reduced to the decidable problem of firstorder unification under a mixed prefix.
Practical type inference for arbitraryrank types
 Journal of Functional Programming
, 2005
"... Note: This document accompanies the paper “Practical type inference for arbitraryrank types ” [6]. Prior reading of the main paper is required. 1 Contents ..."
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Cited by 98 (22 self)
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Note: This document accompanies the paper “Practical type inference for arbitraryrank types ” [6]. Prior reading of the main paper is required. 1 Contents
Elf: A Language for Logic Definition and Verified Metaprogramming
 In Fourth Annual Symposium on Logic in Computer Science
, 1989
"... We describe Elf, a metalanguage for proof manipulation environments that are independent of any particular logical system. Elf is intended for metaprograms such as theorem provers, proof transformers, or type inference programs for programming languages with complex type systems. Elf unifies logic ..."
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Cited by 78 (8 self)
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We describe Elf, a metalanguage for proof manipulation environments that are independent of any particular logical system. Elf is intended for metaprograms such as theorem provers, proof transformers, or type inference programs for programming languages with complex type systems. Elf unifies logic definition (in the style of LF, the Edinburgh Logical Framework) with logic programming (in the style of Prolog). It achieves this unification by giving types an operational interpretation, much the same way that Prolog gives certain formulas (Hornclauses) an operational interpretation. Novel features of Elf include: (1) the Elf search process automatically constructs terms that can represent objectlogic proofs, and thus a program need not construct them explicitly, (2) the partial correctness of metaprograms with respect to a given logic can be expressed and proved in Elf itself, and (3) Elf exploits Elliott's unification algorithm for a calculus with dependent types. This research was...
Types for Modules
, 1998
"... The programming language Standard ML is an amalgam of two, largely orthogonal, languages. The Core language expresses details of algorithms and data structures. The Modules language expresses the modular architecture of a software system. Both languages are statically typed, with their static and dy ..."
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Cited by 73 (11 self)
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The programming language Standard ML is an amalgam of two, largely orthogonal, languages. The Core language expresses details of algorithms and data structures. The Modules language expresses the modular architecture of a software system. Both languages are statically typed, with their static and dynamic semantics specified by a formal definition.
Dependently Typed Functional Programs and their Proofs
, 1999
"... Research in dependent type theories [ML71a] has, in the past, concentrated on its use in the presentation of theorems and theoremproving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties of programs ..."
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Cited by 73 (13 self)
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Research in dependent type theories [ML71a] has, in the past, concentrated on its use in the presentation of theorems and theoremproving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties of programs may readily be specified and established. In particular, it develops technology for programming with dependent inductive families of datatypes and proving those programs correct. It demonstrates the considerable advantage to be gained by indexing data structures with pertinent characteristic information whose soundness is ensured by typechecking, rather than human effort. Type theory traditionally presents safe and terminating computation on inductive datatypes by means of elimination rules which serve as induction principles and, via their associated reduction behaviour, recursion operators [Dyb91]. In the programming language arena, these appear somewhat cumbersome and give rise to unappealing code, complicated by the inevitable interaction between case analysis on dependent types and equational reasoning on their indices which must appear explicitly in the terms. Thierry Coquand’s proposal [Coq92] to equip type theory directly with the kind of
A Proof Theory for Generic Judgments
, 2003
"... this paper, we do this by adding the #quantifier: its role will be to declare variables to be new and of local scope. The syntax of the formula # x.B is like that for the universal and existential quantifiers. Following Church's Simple Theory of Types [Church 1940], formulas are given the ..."
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Cited by 65 (16 self)
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this paper, we do this by adding the #quantifier: its role will be to declare variables to be new and of local scope. The syntax of the formula # x.B is like that for the universal and existential quantifiers. Following Church's Simple Theory of Types [Church 1940], formulas are given the type o, and for all types # not containing o, # is a constant of type (# o) o. The expression # #x.B is ACM Transactions on Computational Logic, Vol. V, No. N, October 2003. 4 usually abbreviated as simply # x.B or as if the type information is either simple to infer or not important