67 lines
2.1 KiB
Markdown
67 lines
2.1 KiB
Markdown
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# Design Decisions
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## Geometric Logic Foundation
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- **Axioms as Sequents:** `forall vars. premises |- conclusion`
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- **Positive Conclusions:** Existentials and disjunctions allowed, but never negation
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- **Geometric Morphisms:** Preserved by design for category-theoretic semantics
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---
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## Identity System
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- **Luid** ("Local Universe ID"): Globally unique across all structures
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- **Slid** ("Structure-Local ID"): Index within a single structure
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- Bidirectional mapping enables persistent identity despite structure changes
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---
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## Storage
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- **Append-Only:** Elements only tombstoned, never deleted
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- **Patch-based Versioning:** Each commit is a delta from parent
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- **GeologMeta:** Single homoiconic theory instance storing all data
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---
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## Type System
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- **Postfix Application:** `x f` not `f(x)` — categorical style
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- **Derived Sorts:** Products of base sorts for record domains
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- **Product Domains:** Functions can take record arguments: `[x: M, y: M] -> M`
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- **Relations → Prop:** Relations are functions to `Prop`
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---
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## Chase Algorithm
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- **Fixpoint Iteration:** Derives consequences until closure
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- **Congruence Closure:** Merges elements when axioms conclude `x = y`
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- **Tensor Algebra:** Efficient axiom checking via sparse tensors
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- **Termination:** Unit laws no longer cause infinite loops
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---
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## Solver Architecture
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- **Explicit Search Tree:** Not implicit in call stack
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- **Refinement Preorder:** Structures can grow (carriers, functions, relations)
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- **Obligations vs Unsat:** Axiom obligation = need to witness conclusion (not failure)
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- **Tactics-based:** AutoTactic composes CheckTactic, ForwardChainingTactic, PropagateEquationsTactic
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---
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## Query Compilation
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- **QueryOp Intermediate:** SQL-like operators (Scan, Filter, Join, Project)
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- **Optimization Passes:** Filter fusion, projection pushdown
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- **Store-aware:** Compiled directly to GeologMeta queries with indexing
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---
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## Tensor Algebra
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- **Sparse Representation:** Roaring Bitmaps for efficient membership
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- **Lazy Expression Trees:** Tensor products fused with contractions
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- **Boolean Semiring:** AND for product, OR for sum
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