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88 lines
2.3 KiB
Text
88 lines
2.3 KiB
Text
/-
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Semantics/SLUG3.lean - Authoritative SLUG-3 Ternary Gate & Opcode Mapping
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This module formalizes the 27 OISC opcodes derived from the SLUG-3 ternary
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classification as specified in the N-Folded MMR Gossip EBML Schema.
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Key mapping:
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- Ternary: { -1, 0, 1 }
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- Formula: k = 9*(y+1) + 3*(u+1) + (v+1)
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- Range: [0, 26]
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Lean is the source of truth.
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-/
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import Semantics.DynamicCanal
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namespace Semantics.SLUG3
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open DynamicCanal
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/-- Binary-compatible 16-bit integer for operands -/
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def OpVal := Fix16
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/-- SLUG-3 ternary states: -1 (Low), 0 (Mid), 1 (High) -/
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inductive Ternary where
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| low -- -1
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| mid -- 0
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| high -- 1
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deriving DecidableEq, Repr, Inhabited
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namespace Ternary
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def toInt : Ternary → Int
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| low => -1
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| mid => 0
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| high => 1
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/-- Mapping to 0..2 for key calculation -/
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def toIdx : Ternary → Nat
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| low => 0
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| mid => 1
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| high => 2
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end Ternary
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/-- SLUG-3 Decision State (Y, U, V) -/
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structure SLUG3State where
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y : Ternary
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u : Ternary
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v : Ternary
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deriving DecidableEq, Repr, Inhabited
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namespace SLUG3State
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/-- Authoritative key calculation: k = 9*(y+1) + 3*(u+1) + (v+1) -/
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def key (s : SLUG3State) : Nat :=
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9 * s.y.toIdx + 3 * s.u.toIdx + s.v.toIdx
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end SLUG3State
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/-- OISC Opcode Set (27 Instructions) -/
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inductive OISCOp where
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| nop | add | sub | mul | div
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| min | max | abs | neg | shl
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| shr | and | or | xor | eq
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| lt | gt | load | store | jmp
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| jz | jnz | call | ret | dup
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| drop | halt
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deriving DecidableEq, Repr, Inhabited
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/-- Authoritative Decode Table (as per EBML Schema Section 3.1) -/
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def decodeOp (k : Nat) : OISCOp :=
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match k with
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| 0 => .nop | 1 => .add | 2 => .sub | 3 => .mul
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| 4 => .div | 5 => .min | 6 => .max | 7 => .abs
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| 8 => .neg | 9 => .shl | 10 => .shr | 11 => .and
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| 12 => .or | 13 => .xor | 14 => .eq | 15 => .lt
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| 16 => .gt | 17 => .load | 18 => .store | 19 => .jmp
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| 20 => .jz | 21 => .jnz | 22 => .call | 23 => .ret
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| 24 => .dup | 25 => .drop | 26 => .halt | _ => .nop
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/-- Entropy cost per operation in units of ln(2)
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C_slug3 = log2(27) ≈ 4.755 bits
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-/
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def landauerCostBits : Fix16 :=
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Fix16.mk 0x0004C160 -- log2(27) ≈ 4.755 bits in Q16.16 (placeholder)
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end Semantics.SLUG3
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