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| Name | Last modified | Size | Description |
|---|---|---|---|---|
| Parent Directory | - | ||
| Accessibility.html | 2025-05-12 09:11 | 94K | |
| Adjunction.html | 2025-05-12 09:11 | 65K | |
| Agda.Builtin.Bool.html | 2025-05-12 09:11 | 3.1K | |
| Agda.Builtin.Char.html | 2025-05-12 09:11 | 4.0K | |
| Agda.Builtin.Cubical..> | 2025-05-12 09:11 | 53K | |
| Agda.Builtin.Cubical..> | 2025-05-12 09:11 | 9.7K | |
| Agda.Builtin.Cubical..> | 2025-05-12 09:11 | 53K | |
| Agda.Builtin.Cubical..> | 2025-05-12 09:11 | 3.2K | |
| Agda.Builtin.Cubical..> | 2025-05-12 09:11 | 5.1K | |
| Agda.Builtin.Equalit..> | 2025-05-12 09:11 | 2.6K | |
| Agda.Builtin.Float.html | 2025-05-12 09:11 | 32K | |
| Agda.Builtin.Int.html | 2025-05-12 09:11 | 3.4K | |
| Agda.Builtin.List.html | 2025-05-12 09:11 | 4.7K | |
| Agda.Builtin.Maybe.html | 2025-05-12 09:11 | 2.3K | |
| Agda.Builtin.Nat.html | 2025-05-12 09:11 | 23K | |
| Agda.Builtin.Reflect..> | 2025-05-12 09:11 | 164K | |
| Agda.Builtin.Sigma.html | 2025-05-12 09:11 | 3.4K | |
| Agda.Builtin.Size.html | 2025-05-12 09:11 | 4.2K | |
| Agda.Builtin.Strict...> | 2025-05-12 09:11 | 4.8K | |
| Agda.Builtin.String...> | 2025-05-12 09:11 | 10K | |
| Agda.Builtin.Unit.html | 2025-05-12 09:11 | 1.7K | |
| Agda.Builtin.Word.html | 2025-05-12 09:11 | 2.0K | |
| Agda.Primitive.Cubic..> | 2025-05-12 09:11 | 24K | |
| Agda.Primitive.html | 2025-05-12 09:11 | 5.4K | |
| Agda.css | 2025-05-12 09:11 | 1.8K | |
| Algebra.Bundles.Raw...> | 2025-05-12 09:11 | 66K | |
| Algebra.Bundles.html | 2025-05-12 09:11 | 282K | |
| Algebra.Consequences..> | 2025-05-12 09:11 | 9.5K | |
| Algebra.Consequences..> | 2025-05-12 09:11 | 48K | |
| Algebra.Consequences..> | 2025-05-12 09:11 | 179K | |
| Algebra.Construct.Li..> | 2025-05-12 09:11 | 84K | |
| Algebra.Construct.Na..> | 2025-05-12 09:11 | 17K | |
| Algebra.Construct.Na..> | 2025-05-12 09:11 | 7.5K | |
| Algebra.Construct.Na..> | 2025-05-12 09:11 | 18K | |
| Algebra.Construct.Na..> | 2025-05-12 09:11 | 13K | |
| Algebra.Construct.Na..> | 2025-05-12 09:11 | 56K | |
| Algebra.Construct.Na..> | 2025-05-12 09:11 | 109K | |
| Algebra.Core.html | 2025-05-12 09:11 | 3.3K | |
| Algebra.Definitions...> | 2025-05-12 09:11 | 19K | |
| Algebra.Definitions...> | 2025-05-12 09:11 | 11K | |
| Algebra.Definitions...> | 2025-05-12 09:11 | 21K | |
| Algebra.Definitions...> | 2025-05-12 09:11 | 118K | |
| Algebra.Lattice.Bund..> | 2025-05-12 09:11 | 7.4K | |
| Algebra.Lattice.Bund..> | 2025-05-12 09:11 | 53K | |
| Algebra.Lattice.Cons..> | 2025-05-12 09:11 | 4.8K | |
| Algebra.Lattice.Cons..> | 2025-05-12 09:11 | 19K | |
| Algebra.Lattice.Cons..> | 2025-05-12 09:11 | 6.5K | |
| Algebra.Lattice.Prop..> | 2025-05-12 09:11 | 292K | |
| Algebra.Lattice.Prop..> | 2025-05-12 09:11 | 6.2K | |
| Algebra.Lattice.Prop..> | 2025-05-12 09:11 | 43K | |
| Algebra.Lattice.Prop..> | 2025-05-12 09:11 | 11K | |
| Algebra.Lattice.Stru..> | 2025-05-12 09:11 | 40K | |
| Algebra.Morphism.Def..> | 2025-05-12 09:11 | 11K | |
| Algebra.Morphism.Str..> | 2025-05-12 09:11 | 210K | |
| Algebra.Morphism.html | 2025-05-12 09:11 | 47K | |
| Algebra.Properties.A..> | 2025-05-12 09:11 | 13K | |
| Algebra.Properties.C..> | 2025-05-12 09:11 | 112K | |
| Algebra.Properties.G..> | 2025-05-12 09:11 | 70K | |
| Algebra.Properties.L..> | 2025-05-12 09:11 | 21K | |
| Algebra.Properties.M..> | 2025-05-12 09:11 | 32K | |
| Algebra.Properties.Q..> | 2025-05-12 09:11 | 17K | |
| Algebra.Properties.R..> | 2025-05-12 09:11 | 6.4K | |
| Algebra.Properties.R..> | 2025-05-12 09:11 | 44K | |
| Algebra.Properties.S..> | 2025-05-12 09:11 | 8.2K | |
| Algebra.Properties.S..> | 2025-05-12 09:11 | 39K | |
| Algebra.Solver.Ring...> | 2025-05-12 09:11 | 45K | |
| Algebra.Solver.Ring...> | 2025-05-12 09:11 | 96K | |
| Algebra.Solver.Ring...> | 2025-05-12 09:11 | 4.6K | |
| Algebra.Solver.Ring...> | 2025-05-12 09:11 | 288K | |
| Algebra.Structures.B..> | 2025-05-12 09:11 | 65K | |
| Algebra.Structures.html | 2025-05-12 09:11 | 233K | |
| Algebra.html | 2025-05-12 09:11 | 1.9K | |
| Axiom.Extensionality..> | 2025-05-12 09:11 | 21K | |
| Axiom.UniquenessOfId..> | 2025-05-12 09:11 | 21K | |
| Bijection.html | 2025-05-12 09:11 | 226K | |
| Bool.html | 2025-05-12 09:11 | 74K | |
| Category.html | 2025-05-12 09:11 | 799K | |
| Colimit.Sequential.V..> | 2025-05-12 09:11 | 179K | |
| Conat.html | 2025-05-12 09:11 | 432K | |
| Data.Bool.Base.html | 2025-05-12 09:11 | 13K | |
| Data.Bool.ListAction..> | 2025-05-12 09:11 | 7.3K | |
| Data.Bool.Properties..> | 2025-05-12 09:11 | 207K | |
| Data.Empty.Polymorph..> | 2025-05-12 09:11 | 4.5K | |
| Data.Empty.html | 2025-05-12 09:11 | 5.0K | |
| Data.Fin.Base.html | 2025-05-12 09:11 | 114K | |
| Data.Fin.Patterns.html | 2025-05-12 09:11 | 4.7K | |
| Data.Fin.Properties...> | 2025-05-12 09:11 | 547K | |
| Data.Irrelevant.html | 2025-05-12 09:11 | 12K | |
| Data.List.Base.html | 2025-05-12 09:11 | 223K | |
| Data.List.Effectful...> | 2025-05-12 09:11 | 147K | |
| Data.List.Extrema.Co..> | 2025-05-12 09:11 | 62K | |
| Data.List.Extrema.html | 2025-05-12 09:11 | 132K | |
| Data.List.Membership..> | 2025-05-12 09:11 | 44K | |
| Data.List.Membership..> | 2025-05-12 09:11 | 239K | |
| Data.List.Membership..> | 2025-05-12 09:11 | 9.3K | |
| Data.List.Membership..> | 2025-05-12 09:11 | 261K | |
| Data.List.Membership..> | 2025-05-12 09:11 | 20K | |
| Data.List.Properties..> | 2025-05-12 09:11 | 867K | |
| Data.List.Relation.B..> | 2025-05-12 09:11 | 6.9K | |
| Data.List.Relation.B..> | 2025-05-12 09:11 | 51K | |
| Data.List.Relation.B..> | 2025-05-12 09:11 | 31K | |
| Data.List.Relation.B..> | 2025-05-12 09:11 | 37K | |
| Data.List.Relation.B..> | 2025-05-12 09:11 | 132K | |
| Data.List.Relation.B..> | 2025-05-12 09:11 | 2.8K | |
| Data.List.Relation.B..> | 2025-05-12 09:11 | 11K | |
| Data.List.Relation.U..> | 2025-05-12 09:11 | 49K | |
| Data.List.Relation.U..> | 2025-05-12 09:11 | 388K | |
| Data.List.Relation.U..> | 2025-05-12 09:11 | 112K | |
| Data.List.Relation.U..> | 2025-05-12 09:11 | 6.3K | |
| Data.List.Relation.U..> | 2025-05-12 09:11 | 36K | |
| Data.List.Relation.U..> | 2025-05-12 09:11 | 459K | |
| Data.List.Relation.U..> | 2025-05-12 09:11 | 38K | |
| Data.List.Relation.U..> | 2025-05-12 09:11 | 3.8K | |
| Data.Maybe.Base.html | 2025-05-12 09:11 | 37K | |
| Data.Maybe.Relation...> | 2025-05-12 09:11 | 56K | |
| Data.Maybe.Relation...> | 2025-05-12 09:11 | 33K | |
| Data.Nat.Base.html | 2025-05-12 09:11 | 103K | |
| Data.Nat.DivMod.Core..> | 2025-05-12 09:11 | 224K | |
| Data.Nat.DivMod.html | 2025-05-12 09:11 | 356K | |
| Data.Nat.Divisibilit..> | 2025-05-12 09:11 | 16K | |
| Data.Nat.Divisibilit..> | 2025-05-12 09:11 | 170K | |
| Data.Nat.Generalised..> | 2025-05-12 09:11 | 68K | |
| Data.Nat.Induction.html | 2025-05-12 09:11 | 25K | |
| Data.Nat.Properties...> | 2025-05-12 09:11 | 938K | |
| Data.Nat.Solver.html | 2025-05-12 09:11 | 2.4K | |
| Data.Parity.Base.html | 2025-05-12 09:11 | 19K | |
| Data.Product.Algebra..> | 2025-05-12 09:11 | 55K | |
| Data.Product.Base.html | 2025-05-12 09:11 | 87K | |
| Data.Product.Functio..> | 2025-05-12 09:11 | 163K | |
| Data.Product.Functio..> | 2025-05-12 09:11 | 49K | |
| Data.Product.Functio..> | 2025-05-12 09:11 | 59K | |
| Data.Product.Propert..> | 2025-05-12 09:11 | 57K | |
| Data.Product.Relatio..> | 2025-05-12 09:11 | 97K | |
| Data.Product.Relatio..> | 2025-05-12 09:11 | 5.4K | |
| Data.Sign.Base.html | 2025-05-12 09:11 | 8.9K | |
| Data.Sum.Algebra.html | 2025-05-12 09:11 | 33K | |
| Data.Sum.Base.html | 2025-05-12 09:11 | 26K | |
| Data.Sum.Function.Pr..> | 2025-05-12 09:11 | 46K | |
| Data.Sum.Function.Se..> | 2025-05-12 09:11 | 73K | |
| Data.Sum.Properties...> | 2025-05-12 09:11 | 60K | |
| Data.Sum.Relation.Bi..> | 2025-05-12 09:11 | 106K | |
| Data.Sum.html | 2025-05-12 09:11 | 12K | |
| Data.These.Base.html | 2025-05-12 09:11 | 37K | |
| Data.Unit.Base.html | 2025-05-12 09:11 | 1.9K | |
| Data.Unit.Polymorphi..> | 2025-05-12 09:11 | 3.6K | |
| Data.Unit.Polymorphi..> | 2025-05-12 09:11 | 27K | |
| Data.Unit.Polymorphi..> | 2025-05-12 09:11 | 1.9K | |
| Data.Vec.Base.html | 2025-05-12 09:11 | 150K | |
| Data.Vec.Bounded.Bas..> | 2025-05-12 09:11 | 68K | |
| Data.Vec.Functional...> | 2025-05-12 09:11 | 67K | |
| Data.Vec.N-ary.html | 2025-05-12 09:11 | 92K | |
| Data.Vec.html | 2025-05-12 09:11 | 12K | |
| Dec.html | 2025-05-12 09:11 | 12K | |
| Delay-monad.Alternat..> | 2025-05-12 09:11 | 181K | |
| Delay-monad.Alternat..> | 2025-05-12 09:11 | 121K | |
| Delay-monad.Alternat..> | 2025-05-12 09:11 | 33K | |
| Delay-monad.Alternat..> | 2025-05-12 09:11 | 102K | |
| Delay-monad.Alternat..> | 2025-05-12 09:11 | 108K | |
| Delay-monad.Alternat..> | 2025-05-12 09:11 | 27K | |
| Delay-monad.Alternat..> | 2025-05-12 09:11 | 11K | |
| Delay-monad.Always.html | 2025-05-12 09:11 | 14K | |
| Delay-monad.Bisimila..> | 2025-05-12 09:11 | 57K | |
| Delay-monad.Bisimila..> | 2025-05-12 09:11 | 9.0K | |
| Delay-monad.Bisimila..> | 2025-05-12 09:11 | 195K | |
| Delay-monad.Bisimila..> | 2025-05-12 09:11 | 246K | |
| Delay-monad.Monad.html | 2025-05-12 09:11 | 61K | |
| Delay-monad.Partial-..> | 2025-05-12 09:11 | 158K | |
| Delay-monad.Terminat..> | 2025-05-12 09:11 | 42K | |
| Delay-monad.html | 2025-05-12 09:11 | 16K | |
| Double-negation.html | 2025-05-12 09:11 | 96K | |
| Effect.Applicative.html | 2025-05-12 09:11 | 36K | |
| Effect.Choice.html | 2025-05-12 09:11 | 4.4K | |
| Effect.Empty.html | 2025-05-12 09:11 | 3.8K | |
| Effect.Functor.html | 2025-05-12 09:11 | 13K | |
| Effect.Monad.html | 2025-05-12 09:11 | 35K | |
| Embedding.Erased.html | 2025-05-12 09:11 | 67K | |
| Embedding.html | 2025-05-12 09:11 | 93K | |
| Equality.Decidable-U..> | 2025-05-12 09:11 | 76K | |
| Equality.Decision-pr..> | 2025-05-12 09:11 | 97K | |
| Equality.Groupoid.html | 2025-05-12 09:11 | 100K | |
| Equality.Instances-r..> | 2025-05-12 09:11 | 120K | |
| Equality.Path.Isomor..> | 2025-05-12 09:11 | 5.5K | |
| Equality.Path.Isomor..> | 2025-05-12 09:11 | 259K | |
| Equality.Path.Unival..> | 2025-05-12 09:11 | 66K | |
| Equality.Path.html | 2025-05-12 09:11 | 347K | |
| Equality.Proposition..> | 2025-05-12 09:11 | 10K | |
| Equality.Proposition..> | 2025-05-12 09:11 | 19K | |
| Equality.Tactic.html | 2025-05-12 09:11 | 129K | |
| Equality.html | 2025-05-12 09:11 | 1.0M | |
| Equivalence-relation..> | 2025-05-12 09:11 | 82K | |
| Equivalence.Contract..> | 2025-05-12 09:11 | 128K | |
| Equivalence.Erased.B..> | 2025-05-12 09:11 | 97K | |
| Equivalence.Erased.C..> | 2025-05-12 09:11 | 71K | |
| Equivalence.Erased.C..> | 2025-05-12 09:11 | 155K | |
| Equivalence.Erased.C..> | 2025-05-12 09:11 | 3.4K | |
| Equivalence.Erased.html | 2025-05-12 09:11 | 880K | |
| Equivalence.Half-adj..> | 2025-05-12 09:11 | 133K | |
| Equivalence.List.html | 2025-05-12 09:11 | 355K | |
| Equivalence.Path-spl..> | 2025-05-12 09:11 | 413K | |
| Equivalence.html | 2025-05-12 09:11 | 502K | |
| Erased.Basics.html | 2025-05-12 09:11 | 14K | |
| Erased.Box-cong-axio..> | 2025-05-12 09:11 | 7.0K | |
| Erased.Cubical.html | 2025-05-12 09:11 | 49K | |
| Erased.Level-1.html | 2025-05-12 09:11 | 1.2M | |
| Erased.Level-2.html | 2025-05-12 09:11 | 334K | |
| Erased.Stability.html | 2025-05-12 09:11 | 1.1M | |
| Erased.html | 2025-05-12 09:11 | 6.2K | |
| Excluded-middle.html | 2025-05-12 09:11 | 6.6K | |
| Extensionality.html | 2025-05-12 09:11 | 189K | |
| Fin.html | 2025-05-12 09:11 | 183K | |
| For-iterated-equalit..> | 2025-05-12 09:11 | 337K | |
| Function-universe.html | 2025-05-12 09:11 | 2.6M | |
| Function.Base.html | 2025-05-12 09:11 | 76K | |
| Function.Bundles.html | 2025-05-12 09:11 | 128K | |
| Function.Consequence..> | 2025-05-12 09:11 | 12K | |
| Function.Consequence..> | 2025-05-12 09:11 | 23K | |
| Function.Consequence..> | 2025-05-12 09:11 | 35K | |
| Function.Construct.C..> | 2025-05-12 09:11 | 119K | |
| Function.Construct.I..> | 2025-05-12 09:11 | 46K | |
| Function.Construct.S..> | 2025-05-12 09:11 | 72K | |
| Function.Core.html | 2025-05-12 09:11 | 5.0K | |
| Function.Definitions..> | 2025-05-12 09:11 | 21K | |
| Function.Dependent.B..> | 2025-05-12 09:11 | 9.3K | |
| Function.Indexed.Rel..> | 2025-05-12 09:11 | 8.2K | |
| Function.Metric.Bund..> | 2025-05-12 09:11 | 37K | |
| Function.Metric.Core..> | 2025-05-12 09:11 | 2.8K | |
| Function.Metric.Defi..> | 2025-05-12 09:11 | 35K | |
| Function.Metric.Nat...> | 2025-05-12 09:11 | 29K | |
| Function.Metric.Nat...> | 2025-05-12 09:11 | 2.8K | |
| Function.Metric.Nat...> | 2025-05-12 09:11 | 18K | |
| Function.Metric.Nat...> | 2025-05-12 09:11 | 19K | |
| Function.Metric.Nat...> | 2025-05-12 09:11 | 1.8K | |
| Function.Metric.Stru..> | 2025-05-12 09:11 | 22K | |
| Function.Properties...> | 2025-05-12 09:11 | 21K | |
| Function.Properties...> | 2025-05-12 09:11 | 46K | |
| Function.Properties...> | 2025-05-12 09:11 | 53K | |
| Function.Properties...> | 2025-05-12 09:11 | 19K | |
| Function.Properties...> | 2025-05-12 09:11 | 23K | |
| Function.Related.Pro..> | 2025-05-12 09:11 | 120K | |
| Function.Related.Typ..> | 2025-05-12 09:11 | 165K | |
| Function.Structures...> | 2025-05-12 09:11 | 47K | |
| Functor.html | 2025-05-12 09:11 | 332K | |
| Groupoid.html | 2025-05-12 09:11 | 189K | |
| H-level.Closure.html | 2025-05-12 09:11 | 406K | |
| H-level.Truncation.C..> | 2025-05-12 09:11 | 584K | |
| H-level.Truncation.P..> | 2025-05-12 09:11 | 417K | |
| H-level.Truncation.P..> | 2025-05-12 09:11 | 277K | |
| H-level.Truncation.P..> | 2025-05-12 09:11 | 157K | |
| H-level.Truncation.P..> | 2025-05-12 09:11 | 246K | |
| H-level.Truncation.P..> | 2025-05-12 09:11 | 558K | |
| H-level.html | 2025-05-12 09:11 | 53K | |
| Induction.WellFounde..> | 2025-05-12 09:11 | 96K | |
| Induction.html | 2025-05-12 09:11 | 14K | |
| Injection.html | 2025-05-12 09:11 | 18K | |
| Integer.Basics.html | 2025-05-12 09:11 | 40K | |
| Interval.html | 2025-05-12 09:11 | 34K | |
| Lambda.Compiler.html | 2025-05-12 09:11 | 13K | |
| Lambda.Delay-monad.C..> | 2025-05-12 09:11 | 94K | |
| Lambda.Delay-monad.I..> | 2025-05-12 09:11 | 22K | |
| Lambda.Delay-monad.T..> | 2025-05-12 09:11 | 29K | |
| Lambda.Delay-monad.V..> | 2025-05-12 09:11 | 6.2K | |
| Lambda.Partiality-mo..> | 2025-05-12 09:11 | 105K | |
| Lambda.Partiality-mo..> | 2025-05-12 09:11 | 106K | |
| Lambda.Partiality-mo..> | 2025-05-12 09:11 | 47K | |
| Lambda.Partiality-mo..> | 2025-05-12 09:11 | 14K | |
| Lambda.Simplified.Co..> | 2025-05-12 09:11 | 12K | |
| Lambda.Simplified.De..> | 2025-05-12 09:11 | 67K | |
| Lambda.Simplified.De..> | 2025-05-12 09:11 | 12K | |
| Lambda.Simplified.De..> | 2025-05-12 09:11 | 5.4K | |
| Lambda.Simplified.Pa..> | 2025-05-12 09:11 | 100K | |
| Lambda.Simplified.Pa..> | 2025-05-12 09:11 | 120K | |
| Lambda.Simplified.Pa..> | 2025-05-12 09:11 | 6.8K | |
| Lambda.Simplified.Sy..> | 2025-05-12 09:11 | 12K | |
| Lambda.Simplified.Vi..> | 2025-05-12 09:11 | 26K | |
| Lambda.Syntax.html | 2025-05-12 09:11 | 46K | |
| Lambda.Virtual-machi..> | 2025-05-12 09:11 | 26K | |
| Level.html | 2025-05-12 09:11 | 5.6K | |
| Lifting.Partiality-m..> | 2025-05-12 09:11 | 54K | |
| Lifting.html | 2025-05-12 09:11 | 104K | |
| List.html | 2025-05-12 09:11 | 265K | |
| Logical-equivalence...> | 2025-05-12 09:11 | 50K | |
| Maybe.html | 2025-05-12 09:11 | 52K | |
| Modality.Basics.html | 2025-05-12 09:11 | 2.1M | |
| Modality.Box-cong.html | 2025-05-12 09:11 | 59K | |
| Modality.Commutes-wi..> | 2025-05-12 09:11 | 189K | |
| Modality.Empty-modal..> | 2025-05-12 09:11 | 150K | |
| Modality.Has-choice...> | 2025-05-12 09:11 | 861K | |
| Modality.Identity.html | 2025-05-12 09:11 | 17K | |
| Modality.Left-exact...> | 2025-05-12 09:11 | 238K | |
| Modality.Very-modal...> | 2025-05-12 09:11 | 251K | |
| Monad.Raw.html | 2025-05-12 09:11 | 18K | |
| Monad.html | 2025-05-12 09:11 | 115K | |
| Nat.Solver.html | 2025-05-12 09:11 | 59K | |
| Nat.html | 2025-05-12 09:11 | 476K | |
| Omega-cpo.html | 2025-05-12 09:11 | 43K | |
| Partiality-algebra.C..> | 2025-05-12 09:11 | 212K | |
| Partiality-algebra.E..> | 2025-05-12 09:11 | 244K | |
| Partiality-algebra.F..> | 2025-05-12 09:11 | 112K | |
| Partiality-algebra.M..> | 2025-05-12 09:11 | 54K | |
| Partiality-algebra.O..> | 2025-05-12 09:11 | 48K | |
| Partiality-algebra.P..> | 2025-05-12 09:11 | 42K | |
| Partiality-algebra.P..> | 2025-05-12 09:11 | 114K | |
| Partiality-algebra.S..> | 2025-05-12 09:11 | 48K | |
| Partiality-algebra.html | 2025-05-12 09:11 | 105K | |
| Partiality-monad.Coi..> | 2025-05-12 09:11 | 15K | |
| Partiality-monad.Coi..> | 2025-05-12 09:11 | 50K | |
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------------------------------------------------------------------------
-- Code related to the paper "Partiality, Revisited: The Partiality
-- Monad as a Quotient Inductive-Inductive Type"
--
-- Thorsten Altenkirch, Nils Anders Danielsson and Nicolai Kraus
------------------------------------------------------------------------
-- Note that this is a version of the code that does not quite match
-- the description in the paper. Some key changes (there might be
-- others):
--
-- * The partiality monad is not postulated, but defined as a QIIT
-- (Agda's cubical features are used). The types and eliminators are
-- marked as "abstract", so the eliminators do not compute.
--
-- * Rewrite rules are no longer used. Instead the propositional
-- truncation and set quotient operators are defined as
-- (non-abstract) QITs.
--
-- * The set quotient operator that is used can be applied to
-- arbitrary binary relations, not only propositional ones.
{-# OPTIONS --cubical --sized-types #-}
module README where
-- Note that our definition of the partiality monad and some of the
-- results are heavily inspired by the section on Cauchy reals in the
-- HoTT book (first edition).
-- The partiality algebra code uses ideas and concepts from "Inductive
-- types in homotopy type theory" by Awodey, Gambino and Sojakova,
-- "Inductive Types in Homotopy Type Theory" by Sojakova, "Quotient
-- inductive-inductive types" by Altenkirch, Capriotti, Dijkstra and
-- Nordvall Forsberg, and Gabe Dijkstra's PhD thesis.
------------------------------------------------------------------------
-- Pointers to results from the paper
-- In order to more easily find code corresponding to results from the
-- paper, see the following module. Note that some of the code
-- referenced below is not discussed at all in the paper.
import README.Pointers-to-results-from-the-paper
------------------------------------------------------------------------
-- Partiality algebras
-- Partiality algebras.
import Partiality-algebra
-- Some partiality algebra properties.
import Partiality-algebra.Properties
-- Partiality algebra categories.
import Partiality-algebra.Category
-- Eliminators and initiality.
import Partiality-algebra.Eliminators
-- Monotone functions.
import Partiality-algebra.Monotone
-- ω-continuous functions.
import Partiality-algebra.Omega-continuous
-- Strict ω-continuous functions.
import Partiality-algebra.Strict-omega-continuous
-- Fixpoint combinators.
import Partiality-algebra.Fixpoints
-- Pi with partiality algebra families as codomains.
import Partiality-algebra.Pi
------------------------------------------------------------------------
-- The partiality monad
-- A quotient inductive-inductive definition of the partiality monad.
import Partiality-monad.Inductive
-- Specialised eliminators.
import Partiality-monad.Inductive.Eliminators
-- A function that runs computations.
import Partiality-monad.Inductive.Approximate
-- An alternative characterisation of the information ordering, along
-- with related results.
import Partiality-monad.Inductive.Alternative-order
-- Monotone functions.
import Partiality-monad.Inductive.Monotone
-- ω-continuous functions.
import Partiality-monad.Inductive.Omega-continuous
-- The partiality monad's monad instance.
import Partiality-monad.Inductive.Monad
-- The partiality monad's monad instance, defined via an adjunction.
import Partiality-monad.Inductive.Monad.Adjunction
-- Strict ω-continuous functions.
import Partiality-monad.Inductive.Strict-omega-continuous
-- Fixpoint combinators.
import Partiality-monad.Inductive.Fixpoints
------------------------------------------------------------------------
-- Some examples
-- A function that, given a stream, tries to find an element
-- satisfying a predicate.
import Search
-- Examples involving simple λ-calculi.
import README.Lambda
------------------------------------------------------------------------
-- An alternative definition of the delay monad
-- The delay monad, defined using increasing sequences of potential
-- values.
import Delay-monad.Alternative
-- Various properties.
import Delay-monad.Alternative.Properties
-- Theorems relating the coinductive definition of the delay
-- monad to the alternative one and to another type.
import Delay-monad.Alternative.Equivalence
-- Termination predicates.
import Delay-monad.Alternative.Termination
-- Information orderings.
import Delay-monad.Alternative.Partial-order
-- Weak bisimilarity.
import Delay-monad.Alternative.Weak-bisimilarity
-- Two eliminators for Delay-monad.Alternative.Delay (A / R).
import Delay-monad.Alternative.Eliminators
------------------------------------------------------------------------
-- The delay monad quotiented by weak bisimilarity
-- The delay monad quotiented by weak bisimilarity.
import Partiality-monad.Coinductive
-- A partial order.
import Partiality-monad.Coinductive.Partial-order
-- An alternative definition of the partiality monad: a variant of the
-- delay monad quotiented by a notion of weak bisimilarity.
import Partiality-monad.Coinductive.Alternative
------------------------------------------------------------------------
-- A proof of equivalence
-- The partiality monads in Partiality-monad.Inductive and
-- Partiality-monad.Coinductive are pointwise equivalent, for sets,
-- assuming extensionality and countable choice.
import Partiality-monad.Equivalence
------------------------------------------------------------------------
-- ω-cpos
-- Pointed and non-pointed ω-cpos.
import Omega-cpo
-- The code in the following three modules is based on a suggestion
-- from Paolo Capriotti.
-- A quotient inductive-inductive definition of the lifting
-- construction on ω-cpos.
import Lifting
-- An alternative but equivalent definition of the partiality monad
-- (but only for sets), based on the lifting construction in Lifting.
import Lifting.Partiality-monad