# Design Decisions

## Geometric Logic Foundation

- **Axioms as Sequents:** `forall vars. premises |- conclusion`
- **Positive Conclusions:** Existentials and disjunctions allowed, but never negation
- **Geometric Morphisms:** Preserved by design for category-theoretic semantics

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## Identity System

- **Luid** ("Local Universe ID"): Globally unique across all structures
- **Slid** ("Structure-Local ID"): Index within a single structure
- Bidirectional mapping enables persistent identity despite structure changes

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## Storage

- **Append-Only:** Elements only tombstoned, never deleted
- **Patch-based Versioning:** Each commit is a delta from parent
- **GeologMeta:** Single homoiconic theory instance storing all data

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## Type System

- **Postfix Application:** `x f` not `f(x)` — categorical style
- **Derived Sorts:** Products of base sorts for record domains
- **Product Domains:** Functions can take record arguments: `[x: M, y: M] -> M`
- **Relations → Prop:** Relations are functions to `Prop`

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## Chase Algorithm

- **Fixpoint Iteration:** Derives consequences until closure
- **Congruence Closure:** Merges elements when axioms conclude `x = y`
- **Tensor Algebra:** Efficient axiom checking via sparse tensors
- **Termination:** Unit laws no longer cause infinite loops

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## Solver Architecture

- **Explicit Search Tree:** Not implicit in call stack
- **Refinement Preorder:** Structures can grow (carriers, functions, relations)
- **Obligations vs Unsat:** Axiom obligation = need to witness conclusion (not failure)
- **Tactics-based:** AutoTactic composes CheckTactic, ForwardChainingTactic, PropagateEquationsTactic

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## Query Compilation

- **QueryOp Intermediate:** SQL-like operators (Scan, Filter, Join, Project)
- **Optimization Passes:** Filter fusion, projection pushdown
- **Store-aware:** Compiled directly to GeologMeta queries with indexing

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## Tensor Algebra

- **Sparse Representation:** Roaring Bitmaps for efficient membership
- **Lazy Expression Trees:** Tensor products fused with contractions
- **Boolean Semiring:** AND for product, OR for sum