Lax Lean Archive

Invariance and characterization of evaluation

Lax420092.EvaluationInvariance · concepts/Lax420092/EvaluationInvariance.lean · lax-420092

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    Natural Language Statement

    Lemma

    Whether the query of an instance holds in its database is invariant under isomorphism of instances, and an instance is a yes-instance of CQEval exactly when its query holds in its database.

    Concept map
    11 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    This concept declares 2 statements. Each proof establishes one of them relative to its assumptions.

    1 cqEval_iff proven

    2 queryHolds_iso proven

    Lean source view on GitHub

    1import Lax904597.Problems
    2import Lax904597.Interpretations
    3import Lax904597.Classes
    4import Lax799700.Problems
    5import Lax420092.QueryDatabases
    6import Lax420092.Evaluation
    7import Lax420092.QueryPairs
    8import Lax420092.PackagedInstances
    9
    10/-!
    11---
    12title: Invariance and characterization of evaluation
    13type: lemma
    14---
    15Whether the query of an instance holds in its database is invariant under
    16isomorphism of instances, and an instance is a yes-instance of CQEval exactly
    17when its query holds in its database.
    18-/
    19
    20namespace Lax420092.EvaluationInvariance
    21
    22open FirstOrder FirstOrder.Language
    23open Lax904597.Problems Lax904597.Interpretations Lax904597.Classes Lax799700.Problems
    24open Lax420092.QueryDatabases Lax420092.Evaluation Lax420092.QueryPairs Lax420092.PackagedInstances
    25
    26/-- The property `QueryHolds` is isomorphism-invariant. -/
    27axiom queryHolds_iso : ∀ {A B : Type} [queryDb.Structure A] [queryDb.Structure B],
    28 (A ≃[queryDb] B) → (QueryHolds A ↔ QueryHolds B)
    29
    30/-- The yes-instances of CQEval are exactly the instances whose query holds. -/
    31axiom cqEval_iff : ∀ (A : Type) [queryDb.Structure A], CQEval A ↔ QueryHolds A
    32
    33end Lax420092.EvaluationInvariance
    34
    Show ProofShow Proof
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