Results 11  20
of
40
Scrap your Nameplate  Functional Pearl
"... Recent research has shown how boilerplate code, or repetitive code for traversing datatypes, can be eliminated using generic programming techniques already available within some implementations of Haskell. One particularly intractable kind of boilerplate is nameplate, or code having to do with names ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
Recent research has shown how boilerplate code, or repetitive code for traversing datatypes, can be eliminated using generic programming techniques already available within some implementations of Haskell. One particularly intractable kind of boilerplate is nameplate, or code having to do with names, namebinding, and fresh name generation. One reason for the difficulty is that operations on data structures involving names, as usually implemented, are not regular instances of standard map, fold , or zip operations. However, in nominal abstract syntax, an alternative treatment of names and binding based on swapping, operations such as #equivalence, captureavoiding substitution, and free variable set functions are much betterbehaved.
A Dependent Type Theory with Names and Binding
 In Proceedings of the 2004 Computer Science Logic Conference, number 3210 in Lecture notes in Computer Science
, 2004
"... We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on FraenkelMostowski (FM) set theory how to address this through firstclass names: in this paper we present a dependent type theory for prog ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on FraenkelMostowski (FM) set theory how to address this through firstclass names: in this paper we present a dependent type theory for programming and reasoning with such names. Our development is based on a categorical axiomatisation of names, with freshness as its central notion. An associated adjunction captures constructions known from FM theory: the freshness quantifier N , namebinding, and unique choice of fresh names. The Schanuel topos  the category underlying FM set theory  is an instance of this axiomatisation.
Numbering matters: Firstorder canonical forms for secondorder recursive types
 In Proceedings of the 2004 ACM SIGPLAN International Conference on Functional Programming (ICFP’04
, 2004
"... We study a type system equipped with universal types and equirecursive types, which we refer to as Fµ. We show that type equality may be decided in time O(n log n), an improvement over the previous known bound of O(n 2). In fact, we show that two more general problems, namely entailment of type equa ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
We study a type system equipped with universal types and equirecursive types, which we refer to as Fµ. We show that type equality may be decided in time O(n log n), an improvement over the previous known bound of O(n 2). In fact, we show that two more general problems, namely entailment of type equations and type unification, may be decided in time O(n log n), a new result. To achieve this bound, we associate, with every Fµ type, a firstorder canonical form, which may be computed in time O(n log n). By exploiting this notion, we reduce all three problems to equality and unification of firstorder recursive terms, for which efficient algorithms are known. 1
A Framework for Specifying, Prototyping, and Reasoning about Computational Systems
, 2009
"... In this thesis we are interested in a framework for specifying, prototyping, and reasoning about systems that describe computations over formal objects such as formulas, proofs, and programs. The computations of interest include those like evaluation and typing in a programming language, provability ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
In this thesis we are interested in a framework for specifying, prototyping, and reasoning about systems that describe computations over formal objects such as formulas, proofs, and programs. The computations of interest include those like evaluation and typing in a programming language, provability in a logic, and behavior in a concurrency system. The development of these computational systems is often an iterative
Simple nominal type theory
"... Abstract. Nominal logic is an extension of firstorder logic with features useful for reasoning about abstract syntax with bound names. For computational applications such as programming and formal reasoning, it is desirable to develop constructive type theories for nominal logic which extend standa ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
Abstract. Nominal logic is an extension of firstorder logic with features useful for reasoning about abstract syntax with bound names. For computational applications such as programming and formal reasoning, it is desirable to develop constructive type theories for nominal logic which extend standard type theories for propositional, first or higherorder logic. This has proven difficult, largely because of complex interactions between nominal logic’s nameabstraction operation and ordinary functional abstraction. This difficulty already arises in the case of propositional logic and simple type theory. In this paper we show how this difficulty can be overcome, and present a simple nominal type theory which enjoys properties such as type soundness and strong normalization, and which can be soundly interpreted using existing nominal set models of nominal logic. We also sketch how recursion combinators for languages with binding structure can be provided. This is an important first step towards understanding the constructive content of nominal logic and incorporating it into existing logics and type theories. 1
A.: Nominal algebra
, 2006
"... Abstract. Nominal terms are a termlanguage used to accurately and expressively represent systems with binding. We present Nominal Algebra (NA), a theory of algebraic equality on nominal terms. Builtin support for binding in the presence of metavariables allows NA to closely mirror informal mathem ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Abstract. Nominal terms are a termlanguage used to accurately and expressively represent systems with binding. We present Nominal Algebra (NA), a theory of algebraic equality on nominal terms. Builtin support for binding in the presence of metavariables allows NA to closely mirror informal mathematical usage and notation, where expressions such as λa.t or ∀a.φ are common, in which metavariables t and φ explicitly occur in the scope of a variable a. We describe the syntax and semantics of NA, and provide a sound and complete proof system for it. We also give some examples of axioms; other work has considered sets of axioms of particular interest in some detail. 1.
Alphastructural recursion and induction (extended abstract
 Theorem Proving in Higher Order Logics, 18th International Conference, TPHOLs 2005, Oxford UK, August 2005, Proceedings, volume 3603 of Lecture Notes in Computer Science
, 2005
"... Abstract. There is growing evidence for the usefulness of name permutations when dealing with syntax involving names and namebinding. In particular they facilitate an attractively simple formalisation of common, but often technically incorrect uses of structural recursion and induction for abstract ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Abstract. There is growing evidence for the usefulness of name permutations when dealing with syntax involving names and namebinding. In particular they facilitate an attractively simple formalisation of common, but often technically incorrect uses of structural recursion and induction for abstract syntax trees modulo αequivalence. At the heart of this formalisation is the notion of finitely supported mathematical objects. This paper explains the idea in as concrete a way as possible and gives a new derivation within higherorder logic of principles of αstructural recursion and induction for αequivalence classes from the ordinary versions of these principles for abstract syntax trees. 1
A metalanguage for structural operational semantics
 In Symposium on Trends in Functional Programming
, 2007
"... We present MLSOS, a functional metalanguage for encoding definitions of structural operational semantics. The key features of this language are inbuilt support for representing objectlanguage binding structures and performing proofsearch. MLSOS uses the nominal approach to dealing with binders and ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
We present MLSOS, a functional metalanguage for encoding definitions of structural operational semantics. The key features of this language are inbuilt support for representing objectlanguage binding structures and performing proofsearch. MLSOS uses the nominal approach to dealing with binders and a FreshMLstyle generative treatment of atoms. This allows us to prototype systems in a natural way, starting from a semiformal specification. We outline the main design choices behind the language and illustrate its use. 1
Nominal System T
, 2010
"... This paper introduces a new recursion principle for inductive data modulo ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
This paper introduces a new recursion principle for inductive data modulo
Structural Recursion with Locally Scoped Names
"... This paper introduces a new recursion principle for inductively defined data modulo αequivalence of bound names that makes use of Oderskystyle local names when recursing over bound names. It is formulated in simply typed λcalculus extended with names that can be restricted to a lexical scope, tes ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
This paper introduces a new recursion principle for inductively defined data modulo αequivalence of bound names that makes use of Oderskystyle local names when recursing over bound names. It is formulated in simply typed λcalculus extended with names that can be restricted to a lexical scope, tested for equality, explicitly swapped and abstracted. The new recursion principle is motivated by the nominal sets notion of “αstructural recursion”, whose use of names and associated freshness sideconditions in recursive definitions formalizes common practice with binders. The new calculus has a simple interpretation in nominal sets equipped with name restriction operations. It is shown to adequately represent αstructural recursion while avoiding the need to verify freshness sideconditions in definitions and computations. The paper is a revised and expanded version of (Pitts, 2010). 1