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Adds CubicalTransport/Bridge.lean with the CubicalEmbed α typeclass
and the principal forward / backward bridges between Lean's discrete
Eq world and the embedded cubical Path world.
CubicalEmbed α:
· ctype : CType — where embedded values live
· toCTerm : α → CTerm
· fromCTerm : CTerm → Option α
· roundtrip : ∀ a, fromCTerm (toCTerm a) = some a
· toCTerm_typed : ∀ a, HasType [] (toCTerm a) ctype
Default instances (REL2.0):
· CubicalEmbed Bool via boolSchema (true/false ctors)
· CubicalEmbed Nat via natSchema (zero/succ tower; uses
natLit + fromCTermNat helper)
· CubicalEmbed (List α) parametric over [CubicalEmbed α], via
listSchema (nil/cons + listToCTerm /
listFromCTerm helpers)
Each instance ships a verified roundtrip proof and a typing witness
proof; all reduce by structural induction.
Forward bridge (always available):
· Eq.toPath : (a = b) → CTerm — produces a constant `.plam`.
· Eq.toPath_endpoints — equational witness.
Backward bridge (REL2.0 canonical case):
· CubicalEmbed.toCTerm_injective — direct corollary of roundtrip.
· Path.toEq_canonical — for syntactically-equal toCTerm endpoints.
· Full backward bridge over arbitrary well-typed paths is REL2.1
(depends on full Glue NbE).
Prop-level coincidence: trivial via proof irrelevance.
Tests: 81/81 (35 smoke + 46 property; +5 new Bridge round-trip arms
covering Bool, Nat, List Bool, and Eq.toPath readback).
Doc: KERNEL_BOUNDARY.md §2.6 updated from "planned" to "landed in
REL2 Phase 2 as CubicalTransport/Bridge.lean". Re-export from
CubicalTransport.lean.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
24 lines
767 B
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24 lines
767 B
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import CubicalTransport.Interval
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import CubicalTransport.Face
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import CubicalTransport.Syntax
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import CubicalTransport.Subst
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import CubicalTransport.DimLine
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import CubicalTransport.Typing
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import CubicalTransport.Equiv
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import CubicalTransport.Glue
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import CubicalTransport.Value
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import CubicalTransport.Transport
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import CubicalTransport.Line
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import CubicalTransport.Eval
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import CubicalTransport.EvalTest
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import CubicalTransport.Readback
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import CubicalTransport.FFI
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import CubicalTransport.FFITest
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import CubicalTransport.ValueTyping
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import CubicalTransport.TransportLaws
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import CubicalTransport.System
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import CubicalTransport.CompLaws
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import CubicalTransport.Soundness
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import CubicalTransport.Inductive
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import CubicalTransport.Bridge
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import CubicalTransport.PropertyTest
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