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-#+TITLE: Constraints
-
-* Preamble
-Under an ontological commitment to objects, with an objects-properties
-modeling in a conceptual model, there are primitive and compound objects:
-
-** Primitive objects
-These are things we directly observe their existence independent of their individual properties
-
-** Compound objects
-These are collective properties observed through their relationships in groups or multigroups
-
-* Entity Properties
-These are the properties derived by observation or measurement
-procedures. They can be further divided in:
-- Quantitative :: which include ordinal and cardinal properties; for
-  example, customer rating and price of a product.
-- Qualitative :: observed only, for example an enum
-
-* 1st Order Properties
-They are inferred properties not directly observable in entities. They
-are abstractions generalized from multiple observed or measured
-properties that share:
-- The same kind of values;
-- The same allowable manipulations, and;
-- Meaningful comparability.
-
-They arise when several concrete properties, for example salary,
-commission and department budget, meet the above criteria. They are
-understood as deriving from a more general underlying property, in the
-example aforementioned, compensation, budget or whatever. That
-underlying abstraction is the 1OP.
-
-** 1st Order Properties in Context
-These are directly observed or measured properties of entities that
-appear in a specific group in context. In other words, they are
-concrete properties associated with entities of a particular type
-whithin a context of a specific group or multigroup. The context is
-essential because the underlying 1OP may manifest as different 1OPiCs
-depending on the entity type (employee VS department) or group
-membership (sales employees VS marketing employees).
-
-They are related to 1OPs insofar as they are contextual instantiations
-of a 1OP, therefore, all 1OPiCs of the same kind share comparable
-value sets and allow operations because they derive from the same
-root. To illustrate with one example: salary and commission are 1OPiC
-of the 1OP Compensation in the context of employees.
-
-* Constraint Algebra
-The costrait module attempts to implement constraints as relations, in
-other words, it follows the principle that Entity/1OPs/1OPiCs should
-be a relation or domain.
-
-** Core Distinction: Domains vs Relations
-- Domain (#domain{}): A VALUE SET with membership criteria (e.g., integers, rationals)
-- Relation (#relation{}): A SET OF TUPLES
-`less_than` is NOT a domain. It is a binary relation (subset of D × D).
-
-** 1st Order Properties (1OPs)
-A 1OP is a direct property (attribute) of individual entities. 1OPs can be:
-- Observed/measured: directly observed from entities (e.g., `salary`, `commission`)
-- Derived/inferred: computed from other 1OPs (e.g., `compensation` = salary + commission)
-
-** Types
-Domain constraints: ARE the domains themselves (membership criteria)
-- `integer` domain: membership test is_integer/1
-- `rational` domain: numerator, denominator (integers), denominator ≠ 0
-Attribute constraints (1OP constraints): Restrict attribute values
-- Specify which domain the attribute draws from
-- Add constraints beyond domain membership
-- Example: `salary` draws from `rational` + [gt(0), lt(1000000)]
-
-** 1st Order Properties in Context (1OPiCs)
-A 1OPiC is a 1OP that is DERIVED from other observed/measured 1OPs within
-the context of a specific relation.
-Examples in `employees` relation:
-- `salary`: observed/measured 1OP (draws from `money` domain)
-- `commission`: observed/measured 1OP (draws from `money` domain)
-- `compensation`: 1OPiC derived as salary + commission in context of employees
-The schema entry `#{compensation => money}` declares which domain the
-derived 1OPiC draws its values from.
-
-** Binary Relations
-Comparisons are proper relations (not domains!):
-```
-Less_Than_Integer = {(a, b) | a, b in Z, a < b}
-```
-To express "x < 5", we check: `(x, 5) in Less_Than_Integer`
-
-** First-Order Logic Interface
-Constraints become membership tests in relations:
-- `x < 5` becomes `(x, 5) in less_than`
-- `x > 3 AND x < 10` becomes `(3, x) in less_than AND (x, 10) in less_than`
-
-** Negation
-Negation requires an explicit universe: `not(R, Universe)` computes
-the complement of R within Universe.