Abductive Repl

---
name: abductive-repl
description: "Hypothesis-Test Loops via REPL for Exploratory Abductive Inference with Gay.jl colors"
---

# abductive-repl

> Hypothesis-Test Loops via REPL for Exploratory Abductive Inference

**Version**: 1.1.0 (music-topos enhanced)
**Trit**: 0 (Ergodic - coordinates inference)
**Bundle**: repl

## Overview

Abductive-REPL enables exploratory abductive reasoning through an interactive REPL. Given observed outcomes, it generates hypotheses, tests them, and refines understanding through iterative loops.

## Core Concept

```
Observation → Generate Hypotheses → Test → Refine → Repeat

Abduction: Given effect E and rule "A implies E",
           hypothesize A as possible cause.
```

## Enhanced Integration: Interpreters

### Julia (Gay.jl) - Primary

```julia
# Start abductive REPL with Gay.jl
julia --project=Gay.jl -e 'using Gay; Gay.repl()'

# In REPL:
gay> !abduce 216 125 157
# Searches invader space for color match
```

### Hy (HyJAX) - Secondary

```hy
;; thread_relational_hyjax.hy integration
(import lib.thread_relational_hyjax :as tra)

(defn abduce-from-color [r g b]
  "Abduce invader ID from observed RGB"
  (let [target [r g b]
        analyzer (tra.ThreadRelationalAnalyzer)]
    ;; Search hypothesis space
    (lfor id (range 1 10000)
          :if (color-match? id target 0.05)
          {:hypothesis id :confidence (- 1.0 (color-distance id target))})))
```

### Babashka (bb) - Scripting

```clojure
;; abductive_repl.bb
(require '[babashka.process :refer [shell]])

(defn abduce [observed-color]
  (let [result (shell {:out :string} 
                      "julia" "--project=Gay.jl" "-e"
                      (format "using Gay; Gay.abduce(RGB(%s))" 
                              (clojure.string/join "," observed-color)))]
    (parse-hypotheses (:out result))))
```

## REPL Commands Enhanced

| Command | Description | Interpreter |
|---------|-------------|-------------|
| `!teleport <id>` | Jump to invader's world state | Julia |
| `!abduce r g b` | Infer invader from observed RGB | Julia/Hy |
| `!test [n]` | Run n abductive roundtrip tests | Julia |
| `!hy-analyze` | Run HyJAX relational analysis | Hy |
| `!bb-export` | Export hypotheses via Babashka | Babashka |

## Properties (Testable Predicates)

```ruby
# world_broadcast.rb integration
module AbductiveProperties
  def self.spi_determinism(id, seed)
    # Same input always produces same output
    c1 = WorldBroadcast::CondensedAnima.liquid_norm([id], r: 0.5)
    c2 = WorldBroadcast::CondensedAnima.liquid_norm([id], r: 0.5)
    c1 == c2
  end
  
  def self.abductive_roundtrip(id, seed)
    # Forward → Abduce → Verify
    forward = CondensedAnima.analytic_stack([id])
    cellular = CondensedAnima.to_cellular_sheaf(forward)
    cellular[:vertices].include?(id)
  end
end
```

## GF(3) Triad Integration

| Trit | Skill | Role |
|------|-------|------|
| -1 | slime-lisp | Validates REPL expressions |
| 0 | **abductive-repl** | Coordinates inference |
| +1 | cider-clojure | Generates evaluations |

**Conservation**: (-1) + (0) + (+1) = 0 ✓

## Justfile Recipes

```makefile
# Start abductive REPL
abduce-repl:
    julia --project=Gay.jl -e 'using Gay; Gay.repl()'

# Run via Hy
abduce-hy:
    uv run hy -c '(import lib.thread_relational_hyjax) (print "HyJAX ready")'

# Babashka roundtrip test
abduce-bb-test n="100":
    bb -e '(println "Abductive tests:" {{n}})'
```

## Related Skills

- `world-hopping` - Possible world navigation
- `unworld` - Derivation chains
- `gay-mcp` - Color generation
- `condensed-analytic-stacks` - 6-functor sheaf bridge