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The Power of Pi
, 2008
"... This paper exhibits the power of programming with dependent types by dint of embedding three domainspecific languages: Cryptol, a language for cryptographic protocols; a small data description language; and relational algebra. Each example demonstrates particular design patterns inherent to depende ..."
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Cited by 17 (0 self)
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This paper exhibits the power of programming with dependent types by dint of embedding three domainspecific languages: Cryptol, a language for cryptographic protocols; a small data description language; and relational algebra. Each example demonstrates particular design patterns inherent to dependentlytyped programming. Documenting these techniques paves the way for further research in domainspecific embedded type systems.
A Dependently Typed Framework for Static Analysis of Program Execution Costs
 In Revised selected papers from IFL 2005: 17th international workshop on implementation and application of functional languages
, 2005
"... Abstract. This paper considers the use of dependent types to capture information about dynamic resource usage in a static type system. Dependent types allow us to give (explicit) proofs of properties with a program; we present a dependently typed core language ��, and define a framework within this ..."
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Cited by 13 (9 self)
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Abstract. This paper considers the use of dependent types to capture information about dynamic resource usage in a static type system. Dependent types allow us to give (explicit) proofs of properties with a program; we present a dependently typed core language ��, and define a framework within this language for representing size metrics and their properties. We give several examples of size bounded programs within this framework and show that we can construct proofs of their size bounds within ��. We further show how the framework handles recursive higher order functions and sum types, and contrast our system with previous work based on sized types. 1
Constructing strictly positive families
 In The Australasian Theory Symposium (CATS2007
, 2007
"... We present an inductive definition of a universe containing codes for strictly positive families (SPFs) such as vectors or simply typed lambda terms. This construction extends the usual definition of inductive strictly positive types as given in previous joint work with McBride. We relate this to In ..."
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Cited by 9 (3 self)
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We present an inductive definition of a universe containing codes for strictly positive families (SPFs) such as vectors or simply typed lambda terms. This construction extends the usual definition of inductive strictly positive types as given in previous joint work with McBride. We relate this to Indexed Containers, which were recently proposed in joint work with Ghani, Hancock and McBride. We demonstrate by example how dependent types can be encoded in this universe and give examples for generic programs.
Beating the Productivity Checker Using Embedded Languages
"... Abstract. Some total languages, like Agda and Coq, allow the use of guarded corecursion to construct infinite values and proofs. Guarded corecursion is a form of recursion in which arbitrary recursive calls are allowed, as long as they are guarded by a coinductive constructor. Guardedness ensures th ..."
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Cited by 6 (3 self)
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Abstract. Some total languages, like Agda and Coq, allow the use of guarded corecursion to construct infinite values and proofs. Guarded corecursion is a form of recursion in which arbitrary recursive calls are allowed, as long as they are guarded by a coinductive constructor. Guardedness ensures that programs are productive, i.e. that every finite prefix of an infinite value can be computed in finite time. However, many productive programs are not guarded, and it can be nontrivial to put them in guarded form. This paper gives a method for turning a productive program into a guarded program. The method amounts to defining a problemspecific language as a data type, writing the program in the problemspecific language, and writing a guarded interpreter for this language. 1
Mixing Induction and Coinduction
, 2009
"... Purely inductive definitions give rise to treeshaped values where all branches have finite depth, and purely coinductive definitions give rise to values where all branches are potentially infinite. If this is too restrictive, then an alternative is to use mixed induction and coinduction. This techn ..."
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Purely inductive definitions give rise to treeshaped values where all branches have finite depth, and purely coinductive definitions give rise to values where all branches are potentially infinite. If this is too restrictive, then an alternative is to use mixed induction and coinduction. This technique appears to be fairly unknown. The aim of this paper is to make the technique more widely known, and to present several new applications of it, including a parser combinator library which guarantees termination of parsing, and a method for combining coinductively defined inference systems with rules like transitivity. The developments presented in the paper have been formalised and checked in Agda, a dependently typed programming language and proof assistant.
Phase distinctions in the compilation of Epigram
, 2005
"... Abstract. It is commonly believed that in dependently typed programming languages, the blurring of the distinction between types and values means that no type erasure is possible at runtime. In this paper, however, we propose an alternative phase distinction. Rather than distinguishing types and va ..."
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Abstract. It is commonly believed that in dependently typed programming languages, the blurring of the distinction between types and values means that no type erasure is possible at runtime. In this paper, however, we propose an alternative phase distinction. Rather than distinguishing types and values in the compilation of EPIGRAM, we distinguish compiletime and runtime evaluation, and show by a series of program transformations that values which are not required at runtime can be erased. 1
A Generic Formal Metatheory Framework for FirstOrder Representations
"... This paper presents GMETA: a generic framework for firstorder representations of variable binding that provides once and for all many of the socalled infrastructure lemmas and definitions required in mechanizations of formal metatheory. The framework employs datatypegeneric programming and modula ..."
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This paper presents GMETA: a generic framework for firstorder representations of variable binding that provides once and for all many of the socalled infrastructure lemmas and definitions required in mechanizations of formal metatheory. The framework employs datatypegeneric programming and modular programming techniques to provide a universe representing a family of datatypes. This universe is generic in two different ways: it is languagegeneric in the sense that several object languages can be represented within the universe; and it is representationgeneric, meaning that it is parameterizable over the particular choice of firstorder representations for binders (for example, locally nameless or de Bruijn). Using this universe, several libraries providing generic infrastructure lemmas and definitions are implemented. These libraries are used in case studies based on the POPLmark challenge, showing that dealing with challenging binding constructs, like the ones found in System F<:, is possible with GMETA. All of GMETA’s generic infrastructure is implemented in the Coq theorem prover, ensuring the soundness of that infrastructure. Furthermore, due to GMETA’s modular design, the libraries can be easily used, extended and customized by end users. 1.
GMeta: A Generic Formal Metatheory Framework for FirstOrder Representations ⋆
"... Abstract. This paper presents GMeta: a generic framework for firstorder representations of variable binding that provides once and for all many of the socalled infrastructure lemmas and definitions required in mechanizations of formal metatheory. The key idea is to employ datatypegeneric programmin ..."
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Abstract. This paper presents GMeta: a generic framework for firstorder representations of variable binding that provides once and for all many of the socalled infrastructure lemmas and definitions required in mechanizations of formal metatheory. The key idea is to employ datatypegeneric programming (DGP) and modular programming techniques to deal with the infrastructure overhead. Using a generic universe for representing a large family of object languages we define datatypegeneric libraries of infrastructure for firstorder representations such as locally nameless or de Bruijn indices. Modules are used to provide templates: a convenient interface between the datatypegeneric libraries and the endusers of GMeta. We conducted case studies based on the POPLmark challenge, and showed that dealing with challenging binding constructs, like the ones found in System F<:, is possible with GMeta. All of GMeta’s generic infrastructure is implemented in the Coq theorem prover. Furthermore, due to GMeta’s modular design, the libraries can be easily used, extended, and customized by users.
Abstract Generic Programming for Dependent Types
"... We begin by revisiting the idea of using a universe of types to write generic programs in a dependently typed setting by constructing a universe for Strictly Positive Types (SPTs). Here we extend this construction to cover dependent types, i.e. Strictly Positive Families (SPFs), thereby fixing a gap ..."
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We begin by revisiting the idea of using a universe of types to write generic programs in a dependently typed setting by constructing a universe for Strictly Positive Types (SPTs). Here we extend this construction to cover dependent types, i.e. Strictly Positive Families (SPFs), thereby fixing a gap left open in previous work. Using the approach presented here we are able to represent all of Epigram’s datatypes within Epigram including the universe of datatypes itself.