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diff --git a/docs/n-way-binding.org b/docs/n-way-binding.org new file mode 100644 index 0000000..39c9d65 --- /dev/null +++ b/docs/n-way-binding.org @@ -0,0 +1,206 @@ +#+TITLE: N-Way Binding in DCL Constraints +#+DATE: 2026-03-11 + +* Overview + +The DCL constraint language supports quantified membership checks via ~Exists~ and ~Forall~. +This document illustrates the hotel/building/room/suite example to motivate n-ary quantification +and show how 3-wise (and deeper) relational composition is expressed. + +* DML — Schema + +#+begin_src lisp +(CreateRelation + (name "Building") + (schema + ((building_id "integer") + (building_name "string") + (floors "integer")))) + +(CreateRelation + (name "Room") + (schema + ((room_id "integer") + (building_id "integer") + (floor "integer") + (room_number "string")))) + +(CreateRelation + (name "Suite") + (schema + ((suite_id "integer") + (room_id "integer") + (suite_name "string") + (capacity "integer")))) +#+end_src + +* DML — Data + +Tower B has only 2 floors, which is what causes the ~suite_in_tall_building~ constraint +to fire when suites referencing its rooms are inserted. + +#+begin_src lisp +(InsertTuple + (relation "Building") + (attributes + ((building_id (Int 1)) + (building_name (Str "Tower A")) + (floors (Int 10))))) + +(InsertTuple + (relation "Building") + (attributes + ((building_id (Int 2)) + (building_name (Str "Tower B")) + (floors (Int 2))))) ;; ≤ 3 — suites in rooms here will be rejected + +(InsertTuples + (relation "Room") + (tuples + (((room_id (Int 101)) (building_id (Int 1)) (floor (Int 1)) (room_number (Str "1A"))) + ((room_id (Int 102)) (building_id (Int 1)) (floor (Int 2)) (room_number (Str "2A"))) + ((room_id (Int 201)) (building_id (Int 2)) (floor (Int 1)) (room_number (Str "1B")))))) + +;; Suites 1001 and 1002 reference room 101 (Tower A, 10 floors) — accepted. +;; Suite 1002 references room 102 (Tower A, 10 floors) — accepted. +;; Suite 1003 references room 201 (Tower B, 2 floors) — rejected by suite_in_tall_building. +(InsertTuples + (relation "Suite") + (tuples + (((suite_id (Int 1001)) (room_id (Int 101)) (suite_name (Str "Presidential")) (capacity (Int 4))) + ((suite_id (Int 1002)) (room_id (Int 101)) (suite_name (Str "Standard")) (capacity (Int 2))) + ((suite_id (Int 1003)) (room_id (Int 102)) (suite_name (Str "Deluxe")) (capacity (Int 3)))))) +#+end_src + +* DCL — Constraints + +Binary FK constraints compose to enforce referential integrity along the chain +~Suite → Room → Building~. Each link is declared independently. + +#+begin_src lisp +;; FK: every Room must belong to an existing Building +(RegisterConstraint + (constraint_name "fk_room_building") + (relation_name "Room") + (body (MemberOf + (target "Building") + (binding ((building_id (Var "building_id"))))))) + +;; FK: every Suite must belong to an existing Room +(RegisterConstraint + (constraint_name "fk_suite_room") + (relation_name "Suite") + (body (MemberOf + (target "Room") + (binding ((room_id (Var "room_id"))))))) +#+end_src + +* DRL — Queries + +The 3-wise join is expressed by composing binary joins. No special n-ary syntax is needed +in DRL — the relational model handles this naturally through join composition. + +#+begin_src lisp +;; All suites with their room and building — full 3-way join +(Join + (room_id) + (Base "Suite") + (Join + (building_id) + (Base "Room") + (Base "Building"))) + +;; Suites in Building 1 only +(Select + (Const ((building_id (Int 1)))) + (Join + (room_id) + (Base "Suite") + (Join + (building_id) + (Base "Room") + (Base "Building")))) + +;; Just suite names and the building they ultimately belong to +(Project + (suite_name building_name) + (Join + (room_id) + (Base "Suite") + (Join + (building_id) + (Base "Room") + (Base "Building")))) +#+end_src + +* Motivation for N-Ary ~Exists~ + +The binary FK constraints above can be decomposed into independent ~MemberOf~ checks. +However, some constraints require joining through intermediate variables before a +membership check can be made. These cannot be decomposed. + +Example: /a suite is only valid if its room belongs to a building with more than 3 floors/. +The chain ~suite.room_id → room.building_id → building.floors~ requires two intermediate +variables — it is inherently a 3-wise constraint. + +Each ~Exists~ record field must be wrapped by name when written in s-expression form, as +required by ~[@@deriving sexp]~. The ~body~ field of the inner ~Exists~ must be written +explicitly as ~(body ...)~, not passed positionally. + +#+begin_src lisp +(RegisterConstraint + (constraint_name "suite_in_tall_building") + (relation_name "Suite") + (body + (Exists (variable "r") (quantifier "Room") + (body + (Exists (variable "b") (quantifier "Building") + (body + (And + ((MemberOf (target "Room") + (binding ((room_id (Var "room_id"))))) + (MemberOf (target "Building") + (binding ((building_id (Var "r.building_id"))))) + (MemberOf (target "greater_than_natural") + (binding ((left (Var "b.floors")) (right (Const (Int 3))))))))))))) +#+end_src + +With the current single-binding ~Exists~, this requires nesting. With the proposed n-ary form, +it becomes flat and the quantifier chain is explicit: + +#+begin_src lisp +;; Proposed n-ary Exists (not yet implemented) +(RegisterConstraint + (constraint_name "suite_in_tall_building") + (relation_name "Suite") + (body + (Exists + (bindings ((r "Room") (b "Building"))) + (body + (And + ((MemberOf (target "Room") + (binding ((room_id (Var "room_id"))))) + (MemberOf (target "Building") + (binding ((building_id (Var "r.building_id"))))) + (MemberOf (target "greater_than_natural") + (binding ((left (Var "b.floors")) (right (Const (Int 3)))))))))))) +#+end_src + +* Namespacing + +Attributes from quantifier rows are namespaced by the variable name in ~extend_tuple~, +so that same-named attributes from different scopes do not overwrite each other. +~Var "attr"~ without a namespace refers to the tuple being checked (the relation the +constraint is registered on). ~Var "x.attr"~ refers to attribute ~attr~ from the row +bound to variable ~x~. + +| Expression | Resolves to | +|-------------------------+-----------------------------------------------| +| ~(Var "room_id")~ | ~suite.room_id~ (the incoming tuple) | +| ~(Var "r.building_id")~ | ~building_id~ from the ~r~ (Room) quantifier | +| ~(Var "b.floors")~ | ~floors~ from the ~b~ (Building) quantifier | + +Without namespacing, ~extend_tuple~ would overwrite the incoming tuple's attributes +with same-named attributes from the quantifier row, silently making ~Var~ resolve to +the wrong scope. See ~lib/constraint.ml~ and ~docs/dcl-quantification.org~ for a full +account of this failure mode and the provenance TODO. |