Views: a way for pattern matching to cohabit with data abstraction
POPL '87 Proceedings of the 14th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Telescopic mappings in typed lambda calculus
Information and Computation
Unification under a mixed prefix
Journal of Symbolic Computation
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Extensional Constructs in Intensional Type Theory
Extensional Constructs in Intensional Type Theory
Automating Inversion of Inductive Predicates in Coq
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Inverting Inductively Defined Relations in LEGO
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
COLOG '88 Proceedings of the International Conference on Computer Logic
Extensional Equality in Intensional Type Theory
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Journal of Functional Programming
Functional pearl: i am not a number--i am a free variable
Haskell '04 Proceedings of the 2004 ACM SIGPLAN workshop on Haskell
A coinductive monad for prop-bounded recursion
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
Polytypic properties and proofs in Coq
Proceedings of the 2009 ACM SIGPLAN workshop on Generic programming
Trace-Based Coinductive Operational Semantics for While
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Toward a verified relational database management system
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proving properties about lists using containers
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
A Tutorial Implementation of a Dependently Typed Lambda Calculus
Fundamenta Informaticae - Dependently Typed Programming
Formal polytypic programs and proofs
Journal of Functional Programming
TLDI '12 Proceedings of the 8th ACM SIGPLAN workshop on Types in language design and implementation
On the strength of proof-irrelevant type theories
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
A few constructions on constructors
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
Exploring the regular tree types
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
A datastructure for iterated powers
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
A polymorphic intermediate verification language: design and logical encoding
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Equations: a dependent pattern-matching compiler
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Strongly Typed Term Representations in Coq
Journal of Automated Reasoning
System FC with explicit kind equality
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
Leveling up dependent types: generic programming over a predicative hierarchy of universes
Proceedings of the 2013 ACM SIGPLAN workshop on Dependently-typed programming
Explicit convertibility proofs in pure type systems
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
Handcrafted inversions made operational on operational semantics
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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Elimination rules tell us how we may exploit hypotheses in the course of a proof. Many common elimination rules, such as 驴-elim and the induction principles for inductively defined datatypes and relations, are parametric in their conclusion. We typically instantiate this parameter with the goal we are trying to prove, and acquire subproblems specialising this goal to particular circumstances in which the eliminated hypothesis holds. This paper describes a generic tactic, Elim, which supports this ubiquitous idiom in interactive proof and subsumes the functionality of the more specific 'induction' and 'inversion' tactics found in systems like Coq and Lego[6, 7, 15]. Elim also supports user-derived rules which follow the same style.