# miniKanren-on-SX: relational programming on the CEK/VM

miniKanren is not a language to parse — it is an **embedded DSL** implemented as a library
of SX functions. No tokenizer, no transpiler. The entire system is a set of `define` forms
in `lib/minikanren/`. Programs are SX expressions using the miniKanren API.

The unique angle: SX's delimited continuation machinery (`perform`/`cek-resume`, call/cc)
maps almost perfectly to the search monad miniKanren needs. Backtracking is cooperative
suspension, not a separate trail machine. This is the cleanest possible host for miniKanren.

End-state goal: **full core miniKanren** (`run`, `fresh`, `==`, `conde`, `condu`, `onceo`,
`project`, `matche`) + **core.logic-style relations** (`appendo`, `membero`, `listo`,
`numbero`, etc.) + **arithmetic constraints** (`fd` domain, `CLP(FD)` subset).

## Ground rules

- **Scope:** only touch `lib/minikanren/**` and `plans/minikanren-on-sx.md`. Do **not**
  edit `spec/`, `hosts/`, `shared/`, or other `lib/<lang>/`.
- **Shared-file issues** go under "Blockers" below with a minimal repro; do not fix here.
- **SX files:** use `sx-tree` MCP tools only.
- **Architecture:** pure library — no source parser. Programs are written in SX using the API.
- **Reference:** *The Reasoned Schemer* (Friedman/Byrd/Kiselyov) + Byrd's dissertation.
- **Commits:** one feature per commit. Keep `## Progress log` updated and tick boxes.

## Architecture sketch

```
SX program using miniKanren API
    │
    ├── lib/minikanren/unify.sx      — terms, variables, walk, unification, occurs check
    ├── lib/minikanren/substitution.sx — substitution as association list / hash table
    ├── lib/minikanren/stream.sx     — lazy streams of substitutions (via delay/force)
    ├── lib/minikanren/goals.sx      — == / fresh / conde / condu / onceo / project / matche
    ├── lib/minikanren/run.sx        — run* / run n — drive the search, extract answers
    ├── lib/minikanren/relations.sx  — standard relations: appendo, membero, listo, etc.
    └── lib/minikanren/clpfd.sx      — arithmetic constraints (CLP(FD) subset)
```

Key semantic mappings:
- **Logic variable** → SX vector of length 1 (mutable box); `make-var` creates fresh one;
  `walk` follows the substitution chain
- **Substitution** → SX association list (or hash table for performance) mapping var → term
- **Stream of substitutions** → lazy list using `delay`/`force` (Phase 9 of primitives)
- **Goal** → SX function `substitution → stream-of-substitutions`
- **`==`** → unifies two terms, extending substitution or failing (empty stream)
- **`fresh`** → introduces new logic variables; `(fresh (x y) goal)` → goal with x, y bound
- **`conde`** → interleave streams from multiple goal clauses (depth-first with interleaving)
- **`run n`** → drive the stream, collect first n substitutions, reify answers

## Roadmap

### Phase 1 — variables + unification
- [ ] `make-var` → fresh logic variable (unique mutable box)
- [ ] `var?` `v` → bool — is this a logic variable?
- [ ] `walk` `term` `subst` → follow substitution chain to ground term or unbound var
- [ ] `walk*` `term` `subst` → deep walk (recurse into lists/dicts)
- [ ] `unify` `u` `v` `subst` → extended substitution or `#f` (failure)
      Handles: var/var, var/term, term/var, list unification, number/string/symbol equality.
      No occurs check by default; `unify-check` with occurs check as opt-in.
- [ ] Empty substitution `empty-s` = `(list)` (empty assoc list)
- [ ] Tests in `lib/minikanren/tests/unify.sx`: ground terms, vars, lists, failure, occurs

### Phase 2 — streams + goals
- [ ] Stream type: `mzero` (empty stream = `nil`), `unit s` (singleton = `(list s)`),
      `mplus` (interleave two streams), `bind` (apply goal to stream)
- [ ] Lazy streams via `delay`/`force` — mature pairs for depth-first, immature for lazy
- [ ] `==` goal: `(fn (s) (let ((s2 (unify u v s))) (if s2 (unit s2) mzero)))`
- [ ] `succeed` / `fail` — trivial goals
- [ ] `fresh` — `(fn (f) (fn (s) ((f (make-var)) s)))` — introduces one var; `fresh*` for many
- [ ] `conde` — interleaving disjunction of goal lists
- [ ] `condu` — committed choice (soft-cut): only explores first successful clause
- [ ] `onceo` — succeeds at most once
- [ ] Tests: basic goal composition, backtracking, interleaving

### Phase 3 — run + reification
- [ ] `run*` `goal` → list of all answers (reified)
- [ ] `run n` `goal` → list of first n answers
- [ ] `reify` `term` `subst` → replace unbound vars with `_0`, `_1`, ... names
- [ ] `reify-s` → builds reification substitution for naming unbound vars consistently
- [ ] `fresh` with multiple variables: `(fresh (x y z) goal)` sugar
- [ ] Query variable conventions: `q` as canonical query variable
- [ ] Tests: classic miniKanren programs — `(run* q (== q 1))` → `(1)`,
      `(run* q (conde ((== q 1)) ((== q 2))))` → `(1 2)`,
      Peano arithmetic, `appendo` preview

### Phase 4 — standard relations
- [ ] `appendo` `l` `s` `ls` — list append, runs forwards and backwards
- [ ] `membero` `x` `l` — x is a member of l
- [ ] `listo` `l` — l is a proper list
- [ ] `nullo` `l` — l is empty
- [ ] `pairo` `p` — p is a pair (cons cell)
- [ ] `caro` `p` `a` — car of pair
- [ ] `cdro` `p` `d` — cdr of pair
- [ ] `conso` `a` `d` `p` — cons
- [ ] `firsto` / `resto` — aliases for caro/cdro
- [ ] `reverseo` `l` `r` — reverse of list
- [ ] `flatteno` `l` `f` — flatten nested lists
- [ ] `permuteo` `l` `p` — permutation of list
- [ ] `lengtho` `l` `n` — length as a relation (Peano or integer)
- [ ] Tests: run each relation forwards and backwards; generate from partial inputs

### Phase 5 — `project` + `matche` + negation
- [ ] `project` `(x ...) body` — access reified values of logic vars inside a goal;
      escapes to ground values for arithmetic or string ops
- [ ] `matche` — pattern matching over logic terms (extension from core.logic)
      `(matche l ((head . tail) goal) (() goal))`
- [ ] `conda` — soft-cut disjunction (like Prolog `->`)
- [ ] `condu` — committed choice (already in phase 2; refine semantics here)
- [ ] `nafc` — negation as finite failure with constraint
- [ ] Tests: Zebra puzzle, N-queens, Sudoku via `project`, family relations via `matche`

### Phase 6 — arithmetic constraints CLP(FD)
- [ ] Finite domain variables: `fd-var` with domain `[lo..hi]`
- [ ] `in` `x` `domain` — constrain x to domain
- [ ] `fd-eq` `x` `y` — x = y (constraint propagation)
- [ ] `fd-neq` `x` `y` — x ≠ y
- [ ] `fd-lt` `fd-lte` `fd-gt` `fd-gte` — ordering constraints
- [ ] `fd-plus` `x` `y` `z` — x + y = z (constraint)
- [ ] `fd-times` `x` `y` `z` — x * y = z
- [ ] Arc consistency propagation — when domain narrows, propagate to constrained vars
- [ ] Labelling: `fd-run` drives search by splitting domains when propagation stalls
- [ ] Tests: send-more-money, N-queens with CLP(FD), map coloring, cryptarithmetic

### Phase 7 — tabling (memoization of relations)
- [ ] `tabled` annotation: memoize calls to a relation using a hash table
- [ ] Prevents infinite loops in recursive relations like `patho` on cyclic graphs
- [ ] Producer/consumer scheduling for tabled relations (variant of SLG resolution)
- [ ] Tests: cyclic graph reachability, mutual recursion, Fibonacci via tabling

## Blockers

_(none yet)_

## Progress log

_Newest first._

_(awaiting phase 1)_