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82 lines
3.1 KiB
Text
82 lines
3.1 KiB
Text
namespace Semantics
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/--
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The single primitive of the Cambrian collapse.
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A Metric measures the cost of lawful assemblage between two objects.
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All scalar fields use Q16.16 fixed-point (UInt32) for hardware-native
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execution: 0x00010000 = 1.0, 0xFFFFFFFF ≈ infinity/illegal.
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-/
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structure Metric where
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cost : UInt32 -- Q16.16 scalar cost of the bind
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tensor : String -- "identity", "riemannian", "thermodynamic", "informational", "physical"
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torsion : UInt32 -- Q16.16 informatic torsion (0 = Euclidean)
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reference : String -- human-readable reference tag
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history_len : Nat -- how many previous binds informed this metric
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def Metric.euclidean : Metric := {
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cost := 0x00000000,
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tensor := "identity",
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torsion := 0x00000000,
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reference := "euclidean_baseline",
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history_len := 0
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}
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/--
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Witness: the trace that a bind occurred lawfully.
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-/
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structure Witness where
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left_invariant : String
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right_invariant : String
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conserved : Bool
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trace_hash : String
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def Witness.lawful (left right : String) : Witness := {
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left_invariant := left,
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right_invariant := right,
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conserved := true,
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trace_hash := s!"lawful:{left}={right}"
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}
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/--
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The universal bind primitive.
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bind(A, B, g) = (cost, witness)
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Lawful iff the invariants of A and B match.
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-/
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structure Bind (A B : Type) where
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left : A
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right : B
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metric : Metric
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cost : UInt32 -- Q16.16
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witness : Witness
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lawful : Bool -- simplified to Bool for clean compilation
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def bind {A B : Type}
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(left : A) (right : B)
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(metric : Metric)
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(cost_fn : A → B → Metric → UInt32)
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(invA : A → String) (invB : B → String)
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: Bind A B :=
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let c := cost_fn left right metric
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let w := Witness.lawful (invA left) (invB right)
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let is_lawful := invA left = invB right
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{ left := left, right := right, metric := metric, cost := c, witness := w, lawful := is_lawful }
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def informationalBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → UInt32) (invA : A → String) (invB : B → String) : Bind A B :=
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bind left right { metric with tensor := "informational" } cost_fn invA invB
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def geometricBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → UInt32) (invA : A → String) (invB : B → String) : Bind A B :=
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bind left right { metric with tensor := "geometric" } cost_fn invA invB
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def thermodynamicBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → UInt32) (invA : A → String) (invB : B → String) : Bind A B :=
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bind left right { metric with tensor := "thermodynamic" } cost_fn invA invB
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def physicalBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → UInt32) (invA : A → String) (invB : B → String) : Bind A B :=
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bind left right { metric with tensor := "physical" } cost_fn invA invB
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def controlBind {A B : Type} (left : A) (right : B) (metric : Metric) (cost_fn : A → B → Metric → UInt32) (invA : A → String) (invB : B → String) : Bind A B :=
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bind left right { metric with tensor := "control" } cost_fn invA invB
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end Semantics
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