fix: support between predicate in FOL dense DSL

- grammar.ts: add 'between' to isKeywordThatCanBePredicate() so the parser
  recognizes it as a valid predicate keyword in forall/exists formula bodies
- compiler.ts: add special case in compileDenseFOLToFormula for
  between(, min, max, dimension?) that extracts numeric args into
  options ({min, max, dimension}) instead of dropping them in the generic
  arg loop. The existing betweenPredicate evaluator already handles these.
- fol-dense-combinations.test.ts: replace GAP test with two verified-working
  tests for between and between with dimension

packages/imhotep-dsl/src/compiler.ts

@@ -801,6 +801,35 @@ export function compileDenseFOLToFormula(dslFormula: DslFormulaNode): FormulaNod
       }
       case 'PredicateCall': {
         const pc = node as DslPredicateCall
+
+        // between($x, min, max, dimension?): extract numeric args into
+        // options so the betweenPredicate evaluator can consume them.
+        // The generic arg loop drops numbers, so we handle this up-front.
+        if (pc.name === 'between') {
+          const options: Record<string, number | string> = {}
+          const compiledArgs: VariableRef[] = []
+
+          for (let i = 0; i < pc.args.length; i++) {
+            const arg = pc.args[i]
+            if (i === 0) {
+              compiledArgs.push(convertTerm(arg) as VariableRef)
+            } else if (typeof arg === 'number') {
+              if (i === 1) options.min = arg
+              else if (i === 2) options.max = arg
+            } else if (typeof arg === 'string') {
+              options.dimension = arg
+            }
+          }
+
+          return {
+            type: 'FormulaNode',
+            kind: 'predicate',
+            predicate: 'between',
+            args: compiledArgs,
+            ...(Object.keys(options).length > 0 ? { options } : {}),
+          } as FormulaNode
+        }
+
         const implicitBindings: TupleBinding[] = []
         const compiledArgs: VariableRef[] = []
 

packages/imhotep-dsl/src/fol-dense-combinations.test.ts

@@ -436,13 +436,24 @@ describe('FOL Dense DSL - Solver Formula Lowering', () => {
 describe('FOL Dense DSL - Gap Detection', () => {
   // These tests document known gaps in the dense DSL FOL support
 
-  it('GAP: dense DSL does not support size between assertions', () => {
+  it('between parses as predicate in dense DSL', () => {
-    // between is only in fluent API, not dense DSL grammar
     const source = `forall $btn in elements('.button'):\n  between($btn, 44, 100)`
     const result = parseSpec(source)
-    // May parse as predicate call or fail
+    assert.strictEqual(result.diagnostics.length, 0, `Expected no diagnostics but got: ${result.diagnostics.map(d => d.message).join(', ')}`)
-    assert.ok(result.diagnostics.length > 0 || result.ast.children.length === 0,
+    const formula = getFormula(result.ast)
-      'Expected parse failure or no formula for between in dense DSL')
+    assert.ok(formula, 'Expected formula for between in dense DSL')
+    const compiled = compileDenseFOLToFormula(formula!)
+    assert.ok(compiled, 'Expected compiled formula for between')
+  })
+
+  it('between with dimension parses as predicate in dense DSL', () => {
+    const source = `forall $btn in elements('.button'):\n  between($btn, 44, 100, 'width')`
+    const result = parseSpec(source)
+    assert.strictEqual(result.diagnostics.length, 0, `Expected no diagnostics but got: ${result.diagnostics.map(d => d.message).join(', ')}`)
+    const formula = getFormula(result.ast)
+    assert.ok(formula, 'Expected formula for between with dimension in dense DSL')
+    const compiled = compileDenseFOLToFormula(formula!)
+    assert.ok(compiled, 'Expected compiled formula for between with dimension')
   })
 
   it('separatedFrom parses as relation predicate in dense DSL', () => {

packages/imhotep-dsl/src/grammar.ts

@@ -665,7 +665,7 @@ export class GrammarParser {
       // Spatial aliases
       'beside', 'nextTo', 'adjacent', 'touching', 'near', 'under', 'within',
       // Size predicates that can appear in FOL formula bodies
-      'width', 'height', 'size',
+      'width', 'height', 'size', 'between',
     ]
     return predicateKinds.includes(kind)
   }