├── .envrc ├── .github └── workflows │ └── ci-ubuntu.yml ├── .gitignore ├── Everything.agda ├── LICENSE ├── Makefile ├── README.md ├── agda-fragment.agda-lib ├── shell.nix └── src └── Fragment ├── Algebra ├── Algebra.agda ├── Free.agda ├── Free │ ├── Atoms.agda │ ├── Base.agda │ ├── Evaluation.agda │ ├── Monad.agda │ ├── Properties.agda │ └── Syntax.agda ├── Homomorphism.agda ├── Homomorphism │ ├── Base.agda │ ├── Definitions.agda │ ├── Equivalence.agda │ ├── Properties.agda │ └── Setoid.agda ├── Properties.agda ├── Quotient.agda └── Signature.agda ├── Equational ├── Coproduct.agda ├── FreeExtension.agda ├── FreeExtension │ ├── Base.agda │ ├── Properties.agda │ └── Synthetic.agda ├── Model.agda ├── Model │ ├── Base.agda │ ├── Properties.agda │ ├── Satisfaction.agda │ └── Synthetic.agda ├── Structures.agda ├── Theory.agda └── Theory │ ├── Base.agda │ ├── Bundles.agda │ ├── Combinators.agda │ └── Laws.agda ├── Examples ├── CSemigroup │ ├── Arith │ │ ├── Atomic.agda │ │ ├── Base.agda │ │ ├── Functions.agda │ │ └── Reasoning.agda │ └── Types.agda └── Semigroup │ ├── Arith │ ├── Atomic.agda │ ├── Base.agda │ ├── Functions.agda │ └── Reasoning.agda │ └── Types.agda ├── Extensions ├── CSemigroup.agda ├── CSemigroup │ ├── Base.agda │ ├── Monomial.agda │ └── Nat.agda └── Semigroup.agda ├── Prelude.agda ├── Setoid ├── Morphism.agda └── Morphism │ ├── Base.agda │ ├── Properties.agda │ └── Setoid.agda └── Tactic ├── Fragment.agda └── Utils.agda /.envrc: -------------------------------------------------------------------------------- 1 | use_nix 2 | -------------------------------------------------------------------------------- /.github/workflows/ci-ubuntu.yml: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/.github/workflows/ci-ubuntu.yml -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/.gitignore -------------------------------------------------------------------------------- /Everything.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/Everything.agda -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/LICENSE -------------------------------------------------------------------------------- /Makefile: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/Makefile -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/README.md -------------------------------------------------------------------------------- /agda-fragment.agda-lib: -------------------------------------------------------------------------------- 1 | name: agda-fragment 2 | depend: standard-library 3 | include: src/ 4 | -------------------------------------------------------------------------------- /shell.nix: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/shell.nix -------------------------------------------------------------------------------- /src/Fragment/Algebra/Algebra.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Algebra.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Free.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Free.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Free/Atoms.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Free/Atoms.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Free/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Free/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Free/Evaluation.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Free/Evaluation.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Free/Monad.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Free/Monad.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Free/Properties.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Free/Properties.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Free/Syntax.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Free/Syntax.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Homomorphism.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Homomorphism.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Homomorphism/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Homomorphism/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Homomorphism/Definitions.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Homomorphism/Definitions.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Homomorphism/Equivalence.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Homomorphism/Equivalence.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Homomorphism/Properties.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Homomorphism/Properties.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Homomorphism/Setoid.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Homomorphism/Setoid.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Properties.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Properties.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Quotient.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Quotient.agda -------------------------------------------------------------------------------- /src/Fragment/Algebra/Signature.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Algebra/Signature.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Coproduct.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Coproduct.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/FreeExtension.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/FreeExtension.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/FreeExtension/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/FreeExtension/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/FreeExtension/Properties.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/FreeExtension/Properties.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/FreeExtension/Synthetic.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/FreeExtension/Synthetic.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Model.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Model.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Model/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Model/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Model/Properties.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Model/Properties.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Model/Satisfaction.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Model/Satisfaction.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Model/Synthetic.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Model/Synthetic.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Structures.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Structures.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Theory.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Theory.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Theory/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Theory/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Theory/Bundles.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Theory/Bundles.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Theory/Combinators.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Theory/Combinators.agda -------------------------------------------------------------------------------- /src/Fragment/Equational/Theory/Laws.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Equational/Theory/Laws.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/CSemigroup/Arith/Atomic.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/CSemigroup/Arith/Atomic.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/CSemigroup/Arith/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/CSemigroup/Arith/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/CSemigroup/Arith/Functions.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/CSemigroup/Arith/Functions.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/CSemigroup/Arith/Reasoning.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/CSemigroup/Arith/Reasoning.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/CSemigroup/Types.agda: -------------------------------------------------------------------------------- 1 | {-# OPTIONS --without-K --safe #-} 2 | 3 | module Fragment.Examples.CSemigroup.Types where 4 | -------------------------------------------------------------------------------- /src/Fragment/Examples/Semigroup/Arith/Atomic.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/Semigroup/Arith/Atomic.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/Semigroup/Arith/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/Semigroup/Arith/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/Semigroup/Arith/Functions.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/Semigroup/Arith/Functions.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/Semigroup/Arith/Reasoning.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/Semigroup/Arith/Reasoning.agda -------------------------------------------------------------------------------- /src/Fragment/Examples/Semigroup/Types.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Examples/Semigroup/Types.agda -------------------------------------------------------------------------------- /src/Fragment/Extensions/CSemigroup.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Extensions/CSemigroup.agda -------------------------------------------------------------------------------- /src/Fragment/Extensions/CSemigroup/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Extensions/CSemigroup/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Extensions/CSemigroup/Monomial.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Extensions/CSemigroup/Monomial.agda -------------------------------------------------------------------------------- /src/Fragment/Extensions/CSemigroup/Nat.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Extensions/CSemigroup/Nat.agda -------------------------------------------------------------------------------- /src/Fragment/Extensions/Semigroup.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Extensions/Semigroup.agda -------------------------------------------------------------------------------- /src/Fragment/Prelude.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Prelude.agda -------------------------------------------------------------------------------- /src/Fragment/Setoid/Morphism.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Setoid/Morphism.agda -------------------------------------------------------------------------------- /src/Fragment/Setoid/Morphism/Base.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Setoid/Morphism/Base.agda -------------------------------------------------------------------------------- /src/Fragment/Setoid/Morphism/Properties.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Setoid/Morphism/Properties.agda -------------------------------------------------------------------------------- /src/Fragment/Setoid/Morphism/Setoid.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Setoid/Morphism/Setoid.agda -------------------------------------------------------------------------------- /src/Fragment/Tactic/Fragment.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Tactic/Fragment.agda -------------------------------------------------------------------------------- /src/Fragment/Tactic/Utils.agda: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/frex-project/agda-fragment/HEAD/src/Fragment/Tactic/Utils.agda --------------------------------------------------------------------------------