Commit 1c44128e by ComFreek

### add notions of relative equivalence

parent a59603c9
 ... ... @@ -6,5 +6,5 @@ theory Concretization = include ?Propositions ❙ // Concretization semantics provide a subset of substitutions from Γ to empty context ❙ concrete_substitutions: {V, Γ: Ctx V, F: Exp Γ} (⊦ Γ |- F ∶ cprop) ⟶ GSubst Γ ⟶ prop ❙ concrete_substitutions: {V, Γ: Ctx V, F: Exp Γ} (⊦ Γ |- F ∶ cprop) ⟶ GSubst Γ ⟶ prop ❘ # ConcrRow 4 5 ❙ ❚
 ... ... @@ -53,3 +53,48 @@ theory SubstitutionTranslations = ⟶ ⊦ K/((TransCtx Γ) |- (TransExp (e[γ])) ≣ (TransExp e)[(TransSubst γ)] ❙ ❚ theory CompositionalTranslations = include ?SubstitutionTranslations ❙ structure L : ?DeductionEq = ❚ structure K : ?DeductionEq = ❚ is_compositional: {V, Γ: L/Ctx V, Δ: L/Ctx V, γ: Subst Γ Δ, e: Exp Γ} ⊦ K/IsThm ((TransExp (e⟬γ⟭)) ≡ (TransExp e)⟬(TransSubst γ)⟭) ❙ ❚ // Notions of equivalence ❚ theory DeductionEquivalence = structure L : ?FormalSystem = ❚ // can I force Sem1|?FormalSystem = L? same for Sem2? ❙ structure Sem1 : ?Deduction = ❚ structure Sem2 : ?Deduction = ❚ equivalent : {V, Γ: L/Ctx V, e: L/Exp Γ, E: L/Exp Γ} ⊦ (Γ Sem1/|- e ∶ E) ⇔ (Γ Sem2/|- e ∶ E) ❙ ❚ theory ComputationEquivalence = structure L : ?FormalSystem = ❚ // can I force Sem1|?FormalSystem = L? same for Sem2? ❙ structure Sem1 : ?Computation = ❚ structure Sem2 : ?Computation = ❚ equivalent : {V, Γ: L/Ctx V, e: L/Exp Γ, f: L/Exp Γ} ⊦ (e Sem1/⇝ f) ⇔ (e Sem2/⇝ f) ❙ ❚ theory ConcretizationEquivalence = structure L : ?FormalSystem = ❚ // can I force Sem1|?FormalSystem = L? same for Sem2? ❙ structure Sem1 : ?Concretization = ❚ structure Sem2 : ?Concretization = ❚ // actually Sem2/ConcrRow should not get p, but `q: ⊦ (Γ Sem2/|- F ∶ cprop)`, but that should be equivalent to p if the previous two structures are accordingly unified wrt. L ❙ equivalent : {V, Γ: L/Ctx V, F: L/Exp Γ, p: ⊦ (Γ Sem1/|- F ∶ cprop), γ: GSubst Γ} ⊦ (Sem1/ConcrRow p γ) ⇔ (Sem2/ConcrRow p γ) ❙ ❚ \ No newline at end of file
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