6592cd058d
git-subtree-dir: octive-lean git-subtree-mainline:fd3d42ae33git-subtree-split:4b6fcec565
106 lines
3.3 KiB
Text
106 lines
3.3 KiB
Text
import OctiveLean.Core.Semantics
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namespace OctiveLean.Core
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/-! # Determinism of TOC big-step.
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`BigStep env e v₁ env₁ → BigStep env e v₂ env₂ → v₁ = v₂ ∧ env₁ = env₂`
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Proof structure mirrors TGC's `Determinism` line-for-line on the shared
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ten constructors. Octave-specific cases (`assign`, `whileT`) follow the
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same three patterns: terminal, structural-functional, contradiction-collapse.
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The `whileFR`/`whileTR` cross-case is closed exactly like `ifTR`/`ifFR`:
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the IH on the condition produces `vBool true = vBool false`, dispatched
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by `Bool.noConfusion`. -/
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theorem BigStep.deterministic
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{env : Env} {e : Term} {v₁ v₂ : Value} {env₁ env₂ : Env}
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(D₁ : BigStep env e v₁ env₁) (D₂ : BigStep env e v₂ env₂) :
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v₁ = v₂ ∧ env₁ = env₂ := by
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induction D₁ generalizing v₂ env₂ with
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| unitR => cases D₂; exact ⟨rfl, rfl⟩
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| intLitR n => cases D₂; exact ⟨rfl, rfl⟩
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| boolLitR b => cases D₂; exact ⟨rfl, rfl⟩
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| varR hLook =>
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cases D₂ with
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| varR hLook' =>
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have heq := hLook.symm.trans hLook'
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exact ⟨Option.some.inj heq, rfl⟩
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| lamR x body => cases D₂; exact ⟨rfl, rfl⟩
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| appR _ _ _ ih1 ih2 ihb =>
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cases D₂ with
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| appR D1' D2' Db' =>
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have ⟨hClos, hE1⟩ := ih1 D1'
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injection hClos with hx hbody henv
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subst hx; subst hbody; subst henv; subst hE1
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have ⟨hArg, hE2⟩ := ih2 D2'
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subst hArg; subst hE2
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have ⟨hv, _⟩ := ihb Db'
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exact ⟨hv, rfl⟩
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| letInR _ _ ih1 ih2 =>
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cases D₂ with
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| letInR D1' D2' =>
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have ⟨hv1, hE1⟩ := ih1 D1'
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subst hv1; subst hE1
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have ⟨hv2, _⟩ := ih2 D2'
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exact ⟨hv2, rfl⟩
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| ifTR _ _ ihc iht =>
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cases D₂ with
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| ifTR Dc' Dt' =>
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have ⟨_, hE1⟩ := ihc Dc'; subst hE1
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exact iht Dt'
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| ifFR Dc' _ =>
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have ⟨hb, _⟩ := ihc Dc'
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injection hb with hb_eq
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exact Bool.noConfusion hb_eq
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| ifFR _ _ ihc ihf =>
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cases D₂ with
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| ifTR Dc' _ =>
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have ⟨hb, _⟩ := ihc Dc'
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injection hb with hb_eq
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exact Bool.noConfusion hb_eq
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| ifFR Dc' Df' =>
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have ⟨_, hE1⟩ := ihc Dc'; subst hE1
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exact ihf Df'
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| binopR _ _ Hop ih1 ih2 =>
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cases D₂ with
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| binopR D1' D2' Hop' =>
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have ⟨hv1, hE1⟩ := ih1 D1'
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subst hv1; subst hE1
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have ⟨hv2, hE2⟩ := ih2 D2'
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subst hv2; subst hE2
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have heq := Hop.symm.trans Hop'
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exact ⟨Option.some.inj heq, rfl⟩
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| seqR _ _ ih1 ih2 =>
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cases D₂ with
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| seqR D1' D2' =>
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have ⟨_, hE1⟩ := ih1 D1'; subst hE1
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exact ih2 D2'
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| assignR _ ih =>
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cases D₂ with
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| assignR D' =>
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have ⟨hv, hE⟩ := ih D'
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subst hv; subst hE
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exact ⟨rfl, rfl⟩
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| whileFR _ ihc =>
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cases D₂ with
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| whileFR Dc' =>
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have ⟨_, hE⟩ := ihc Dc'; subst hE
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exact ⟨rfl, rfl⟩
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| whileTR Dc' _ _ =>
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have ⟨hb, _⟩ := ihc Dc'
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injection hb with hb_eq
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exact Bool.noConfusion hb_eq
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| whileTR _ _ _ ihc ihb ihw =>
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cases D₂ with
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| whileFR Dc' =>
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have ⟨hb, _⟩ := ihc Dc'
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injection hb with hb_eq
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exact Bool.noConfusion hb_eq
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| whileTR Dc' Db' Dw' =>
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have ⟨_, hE1⟩ := ihc Dc'; subst hE1
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have ⟨_, hE2⟩ := ihb Db'; subst hE2
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exact ihw Dw'
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end OctiveLean.Core
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