The categorical abstract machine
Science of Computer Programming
Information and Computation - Semantics of Data Types
An abstract machine for Lambda-terms normalization
LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
Inductively defined types in the calculus of constructions
Proceedings of the fifth international conference on Mathematical foundations of programming semantics
Compiling with continuations
A framework for defining logics
Journal of the ACM (JACM)
Partial evaluation and automatic program generation
Partial evaluation and automatic program generation
Type-directed partial evaluation
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A notation for lambda terms. A generalization of environment
Theoretical Computer Science
Functional runtime systems within the lambda-sigma calculus
Journal of Functional Programming
An Introduction to Dependent Type Theory
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
A symmetric approach to compilation and decompilation
The essence of computation
A functional correspondence between evaluators and abstract machines
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Explicit substitutions in the reduction of lambda terms
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Choices in Representation and Reduction Strategies for Lambda Terms in Intensional Contexts
Journal of Automated Reasoning
A verified staged interpreter is a verified compiler
Proceedings of the 5th international conference on Generative programming and component engineering
Proof-carrying code from certified abstract interpretation and fixpoint compression
Theoretical Computer Science - Applied semantics
Implementing the cylindrical algebraic decomposition within the Coq system
Mathematical Structures in Computer Science
Strongly reducing variants of the Krivine abstract machine
Higher-Order and Symbolic Computation
Proof Synthesis and Reflection for Linear Arithmetic
Journal of Automated Reasoning
Towards Constructive Homological Algebra in Type Theory
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Checking Dependent Types Using Compiled Code
Implementation and Application of Functional Languages
Central European Functional Programming School
A Compiled Implementation of Normalization by Evaluation
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
New Developments in Environment Machines
Electronic Notes in Theoretical Computer Science (ENTCS)
Science of Computer Programming
A Modular Type-Checking Algorithm for Type Theory with Singleton Types and Proof Irrelevance
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
MOBIUS: mobility, ubiquity, security objectives and progress report
TGC'06 Proceedings of the 2nd international conference on Trustworthy global computing
Deriving compilers and virtual machines for a multi-level language
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
Fast reflexive arithmetic tactics the linear case and beyond
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Constructive mathematics and functional programming
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
Typed applicative structures and normalization by evaluation for system Fω
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
A computer-verified monadic functional implementation of the integral
Theoretical Computer Science
Certified result checking for polyhedral analysis of bytecode programs
TGC'10 Proceedings of the 5th international conference on Trustworthly global computing
Proof certificates for algebra and their application to automatic geometry theorem proving
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
Computer certified efficient exact reals in Coq
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
A computational approach to pocklington certificates in type theory
FLOPS'06 Proceedings of the 8th international conference on Functional and Logic Programming
Verifying and reflecting quantifier elimination for presburger arithmetic
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
PADL'10 Proceedings of the 12th international conference on Practical Aspects of Declarative Languages
Formal global optimisation with taylor models
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving formally the implementation of an efficient gcd algorithm for polynomials
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
On the strength of proof-irrelevant type theories
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving equalities in a commutative ring done right in coq
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Reflecting proofs in first-order logic with equality
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
On the role of type decorations in the calculus of inductive constructions
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Towards normalization by evaluation for the βη-calculus of constructions
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
Extending coq with imperative features and its application to SAT verification
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Modular SMT proofs for fast reflexive checking inside coq
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Full reduction at full throttle
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Towards a certified computation of homology groups for digital images
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
PEPM '13 Proceedings of the ACM SIGPLAN 2013 workshop on Partial evaluation and program manipulation
New equations for neutral terms: a sound and complete decision procedure, formalized
Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming
Deriving the full-reducing Krivine machine from the small-step operational semantics of normal order
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
Computing persistent homology within Coq/SSReflect
ACM Transactions on Computational Logic (TOCL)
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Motivated by applications to proof assistants based on dependent types, we develop and prove correct a strong reducer and ß-equivalence checker for the λ-calculus with products, sums, and guarded fixpoints. Our approach is based on compilation to the bytecode of an abstract machine performing weak reductions on non-closed terms, derived with minimal modifications from the ZAM machine used in the Objective Caml bytecode interpreter, and complemented by a recursive "read back" procedure. An implementation in the Coq proof assistant demonstrates important speed-ups compared with the original interpreter-based implementation of strong reduction in Coq.