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A Polymorphic Environment Calculus and its Type-Inference Algorithm
Higher-Order and Symbolic Computation
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Higher-Order and Symbolic Computation
Primitive Recursion for Higher-Order Abstract Syntax
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
A New Approach to Abstract Syntax Involving Binders
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Automating the meta theory of deductive systems
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FreshML: programming with binders made simple
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Boxes go bananas: Encoding higher-order abstract syntax with parametric polymorphism*
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Parametric higher-order abstract syntax for mechanized semantics
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On the Expressivity of Minimal Generic Quantification
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On the Role of Names in Reasoning about λ-tree Syntax Specifications
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System Description: Delphin -- A Functional Programming Language for Deductive Systems
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Case Analysis of Higher-Order Data
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The calculus of nominal inductive constructions: an intensional approach to encoding name-bindings
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Programming inductive proofs: a new approach based on contextual types
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Programming inductive proofs: a new approach based on contextual types
Verification, induction termination analysis
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2-Dimensional Directed Type Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
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Beluga: programming with dependent types, contextual data, and contexts
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Beluga: a framework for programming and reasoning with deductive systems (system description)
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Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
First-class substitutions in contextual type theory
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
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Higher-order abstract syntax (HOAS) is a simple, powerful technique for implementing object languages, since it directly supports common and tricky routines dealing with variables, such as capture-avoiding substitution and renaming. This is achieved by representing binders in the object-language via binders in the meta-language. However, enriching functional programming languages with direct support for HOAS has been a major challenge, because recursion over HOAS encodings requires one to traverse lambda-abstractions and necessitates programming with open objects. We present a novel type-theoretic foundation based on contextual modal types which allows us to recursively analyze open terms via higher-order pattern matching. By design, variables occurring in open terms can never escape their scope. Using several examples, we demonstrate that our framework provides a name-safe foundation to operations typically found in nominal systems. In contrast to nominal systems however, we also support capture-avoiding substitution operations and even provide first-class substitutions to the programmer. The main contribution of this paper is a syntax-directed bi-directional type system where we distinguish between the data language and the computation language together with the progress and preservation proof for our language.