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Not urgent, but please fix the title of the PR at some point to start with the required |
chenson2018
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chenson2018
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This looks much better! The theory now all lines up, there are some additional small style/technical issues I have pointed out below. Please also see the failures in CI now that it has made it to the linting step.
| def lift (trans : State → Label → State → Prop) : | ||
| State → (Option Label) → State → Prop := |
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This signature fits on one line now.
| def LTS.Morphism.comp {lts₁ lts₂ lts₃ : LTSCat} : | ||
| LTS.Morphism lts₁ lts₂ → LTS.Morphism lts₂ lts₃ → LTS.Morphism lts₁ lts₃ := | ||
| fun ⟨f, μ, p⟩ ⟨g, ν, q⟩ => | ||
| let r := by | ||
| intro s s' l h | ||
| have hp := p s s' l h | ||
| change ((μ l).bind ν).elim (g (f s) = g (f s')) _ | ||
| cases hμ : μ l with | ||
| | none => | ||
| rw [hμ] at hp | ||
| exact congrArg g hp | ||
| | some m => | ||
| rw [hμ] at hp | ||
| exact q (f s) (f s') m hp | ||
| ⟨g ∘ f, μ >=> ν, r⟩ |
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I think it is more idiomatic/clear to use where to split this up. I would write:
| def LTS.Morphism.comp {lts₁ lts₂ lts₃ : LTSCat} : | |
| LTS.Morphism lts₁ lts₂ → LTS.Morphism lts₂ lts₃ → LTS.Morphism lts₁ lts₃ := | |
| fun ⟨f, μ, p⟩ ⟨g, ν, q⟩ => | |
| let r := by | |
| intro s s' l h | |
| have hp := p s s' l h | |
| change ((μ l).bind ν).elim (g (f s) = g (f s')) _ | |
| cases hμ : μ l with | |
| | none => | |
| rw [hμ] at hp | |
| exact congrArg g hp | |
| | some m => | |
| rw [hμ] at hp | |
| exact q (f s) (f s') m hp | |
| ⟨g ∘ f, μ >=> ν, r⟩ | |
| def LTS.Morphism.comp {lts₁ lts₂ lts₃} (f : LTS.Morphism lts₁ lts₂) (g : LTS.Morphism lts₂ lts₃) : | |
| LTS.Morphism lts₁ lts₃ where | |
| stateMap := g.stateMap ∘ f.stateMap | |
| labelMap := f.labelMap >=> g.labelMap | |
| labelMap_tr s s' l h := by | |
| obtain ⟨f, μ, p⟩ := f | |
| obtain ⟨g, ν, q⟩ := g | |
| change ((μ l).bind ν).elim (g (f s) = g (f s')) _ | |
| cases hμ : μ l with grind [lift] |
| Hom lts₁ lts₂ := LTS.Morphism lts₁ lts₂ | ||
| id lts := LTS.Morphism.id lts | ||
| comp {lts₁} {lts₂} {lts₃} f g := @LTS.Morphism.comp lts₁ lts₂ lts₃ f g |
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Easier to read if you eta reduce
| Hom lts₁ lts₂ := LTS.Morphism lts₁ lts₂ | |
| id lts := LTS.Morphism.id lts | |
| comp {lts₁} {lts₂} {lts₃} f g := @LTS.Morphism.comp lts₁ lts₂ lts₃ f g | |
| Hom := LTS.Morphism | |
| id := LTS.Morphism.id | |
| comp := LTS.Morphism.comp |
| id_comp := by | ||
| intro _ _ f | ||
| cases f | ||
| simp only [LTS.Morphism.comp, LTS.Morphism.id, Function.comp_id] | ||
| congr 1 |
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This direction can be inferred
| id_comp := by | |
| intro _ _ f | |
| cases f | |
| simp only [LTS.Morphism.comp, LTS.Morphism.id, Function.comp_id] | |
| congr 1 |
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| public import Mathlib.CategoryTheory.Category.Basic | ||
| public import Cslib.Foundations.Semantics.LTS.Basic | ||
| open Cslib |
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All modules should be in at least the Cslib namepsace, so this should move down below the @[expose] public section and become namespace Cslib. (As it is now below you are making LTS.Morphism etc. in a fresh namespace at the top level)
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This PR resolves #387.