Abstract
This entry contains the accompanying formalisation of the paper
"Transport via Partial Galois Connections and Equivalences" (APLAS 2023).
It contains a theoretical framework to transport programs via equivalences,
subsuming the theory of Isabelle's Lifting package.
It also contains a prototype to automate transports using this framework in Isabelle/HOL,
but this prototype is not yet ready for production.
Finally, it contains a library on top of Isabelle/HOL's axioms,
including various relativised concepts on orders, functions, binary relations,
and Galois connections and equivalences.
License
Topics
- Computer science/Programming languages/Lambda calculi
- Computer science/Programming languages/Type systems
- Computer science/Semantics and reasoning
- Mathematics/Order
Related publications
- Kappelmann, K. (2023). Transport via Partial Galois Connections and Equivalences. ArXiv. https://doi.org/10.48550/ARXIV.2303.05244
Session Transport
- Adhoc_Overloading
- HOL_Basics_Base
- HOL_Syntax_Bundles_Lattices
- Predicates_Lattice
- Bounded_Quantifiers
- Binary_Relation_Functions
- Binary_Relations_Order_Base
- Functions_Base
- Function_Relators
- Predicate_Functions
- Predicates_Order
- Functions_Monotone
- Reverse_Implies
- Binary_Relations_Injective
- Binary_Relations_Agree
- Dependent_Binary_Relations
- Binary_Relations_Extend
- Binary_Relations_Right_Unique
- Binary_Relations_Function_Evaluation
- Binary_Relations_Left_Total
- Binary_Relations_Function_Base
- Binary_Relations_Clean_Functions
- Binary_Relations_Symmetric
- Binary_Relations_Reflexive
- Binary_Relations_Transitive
- Preorders
- Partial_Equivalence_Relations
- Equivalence_Relations
- Binary_Relations_Antisymmetric
- Partial_Orders
- Restricted_Equality
- Binary_Relations_Function_Composition
- Binary_Relations_Function_Extend
- Binary_Relations_Function_Lambda
- Binary_Relations_Functions
- Binary_Relations_Order
- Binary_Relations_Irreflexive
- Binary_Relations_Asymmetric
- Binary_Relations_Surjective
- Binary_Relations_Bi_Total
- Binary_Relations_Bi_Unique
- Functions_Injective
- Binary_Relations_Connected
- Binary_Relations_Wellfounded
- Binary_Relation_Properties
- Bounded_Definite_Description
- Binary_Relations_Least
- Binary_Relations_Transitive_Closure
- Functions_Restrict
- Wellfounded_Transitive_Recursion
- Wellfounded_Recursion
- Binary_Relations_Lattice
- Binary_Relations_Reflexive_Closure
- LBinary_Relations
- Functions_Inverse
- Functions_Bijection
- Functions_Surjective
- Function_Properties
- LFunctions
- Order_Functions_Base
- Order_Functors_Base
- Galois_Base
- Galois_Relator_Base
- Order_Equivalences
- Half_Galois_Property
- Galois_Property
- Galois_Connections
- Galois_Equivalences
- Galois_Relator
- Transport_Base
- Transport_Compositions_Agree_Base
- Transport_Compositions_Agree_Monotone
- Transport_Compositions_Agree_Galois_Property
- Transport_Compositions_Agree_Galois_Connection
- Transport_Compositions_Agree_Galois_Equivalence
- Galois_Equivalent
- Galois
- Linear_Orders
- Closure_Operators
- Order_Functions
- Transport_Bijections
- Order_Isomorphisms
- Order_Functors
- Strict_Partial_Orders
- Strict_Linear_Orders
- Wellorders
- Orders
- Predicates
- HOL_Basics
- HOL_Mem_Of
- HOL_Alignment_Binary_Relations
- HOL_Syntax_Bundles_Functions
- HOL_Alignment_Functions
- HOL_Syntax_Bundles_Orders
- HOL_Alignment_Orders
- HOL_Alignment_Predicates
- HOL_Alignments
- HOL_Algebra_Alignment_Orders
- HOL_Algebra_Alignment_Galois
- HOL_Algebra_Alignments
- HOL_Syntax_Bundles_Base
- HOL_Syntax_Bundles_Groups
- HOL_Syntax_Bundles
- Transport_Compositions_Agree_Galois_Relator
- Transport_Compositions_Agree_Order_Equivalence
- Transport_Compositions_Agree
- Transport_Compositions_Generic_Base
- Transport_Compositions_Generic_Galois_Property
- Transport_Compositions_Generic_Monotone
- Transport_Compositions_Generic_Galois_Connection
- Transport_Compositions_Generic_Galois_Equivalence
- Transport_Compositions_Generic_Galois_Relator
- Transport_Compositions_Generic_Order_Base
- Transport_Compositions_Generic_Order_Equivalence
- Transport_Compositions_Generic
- Transport_Compositions
- Reflexive_Relator
- Monotone_Function_Relator
- Transport_Functions_Base
- Transport_Functions_Monotone
- Transport_Functions_Galois_Property
- Transport_Functions_Galois_Connection
- Transport_Functions_Order_Base
- Transport_Functions_Galois_Equivalence
- Transport_Functions_Relation_Simplifications
- Transport_Functions_Galois_Relator
- Transport_Functions_Order_Equivalence
- Transport_Functions
- Transport_Identity
- Transport_Black_Box
- Transport_Equality
- Transport_Universal_Quantifier
- Transport_Existential_Quantifier
- Transport_Galois_Relator_Properties
- Transport_White_Box
- Transport
- Transport_Rel_If
- Transport_Prototype
- Transport_Syntax
- Transport_Dep_Fun_Rel_Examples
- Transport_Lists_Sets_Examples
- Transport_Partial_Quotient_Types
- Transport_Typedef_Base
- Transport_Typedef
- Transport_Natural_Functors_Base
- Transport_Natural_Functors_Galois
- Transport_Natural_Functors_Galois_Relator
- Transport_Natural_Functors_Order_Base
- Transport_Natural_Functors_Order_Equivalence
- Transport_Natural_Functors
- Transport_Via_Partial_Galois_Connections_Equivalences_Paper