prolog-clp-constraintslisted

# Constraint Logic Programming (CLP) Guidelines Use this skill when designing, solving, or refactoring combinatorial optimization problems, integer constraints, symbolic arithmetic, or scheduling tasks in Prolog. ## 1. Module Declarations & Engine Compatibility Always import the appropriate constraint library based on the target engine: - **Scryer Prolog (Default)**: Use `library(clpz)` ```prolog :- use_module(library(clpz)). ``` - **SWI-Prolog**: Use `library(clpfd)` ```prolog :- use_module(library(clpfd)). ``` - **Trealla Prolog**: Use `library(clpz)` ```prolog :- use_module(library(clpz)). ``` --- ## 2. Separation of Concerns: Declaration vs Search Structure constraint programs into two distinct phases: 1. **Constraint Declaration**: Declare variables, domains (`ins`, `in`), and relations (`#=`, `#\=`, `all_different/1`). This phase must remain purely declarative without triggering premature search. 2. **Search (`labeling/2`)**: Bind variables to concrete values using search strategies (`labeling/2` or `label/1`). ```prolog % Example: N-Queens problem n_queens(N, Qs) :- length(Qs, N), Qs ins 1..N, all_different(Qs), safe_diagonals(Qs), labeling([ff], Qs). % Search heuristic: First-Fail (ff) ``` --- ## 3. Constraint Operators & Reification Prefer CLP constraints over imperative `(is)/2` arithmetic to maintain bidirectionality: - **Arithmetic Constraints**: `#=`, `#\=`, `#>`, `#>=`, `#<`, `#=<` - **Domain Declarations**: `X