Implementation of Finite Field Class for GF(27)

docs/source/frame/environments.rst

@@ -7,5 +7,6 @@ FRAME environments define the context in which concepts and conjectures are gene
    :maxdepth: 1
    :caption: Contents:
 
+   environments/ground_truth_entities
+   environments/ground_truth_types
    environments/math_env
-   environments/name_overrides

docs/source/frame/environments/ground_truth_types.rst

@@ -0,0 +1,7 @@
+Ground Truth Types Environment
+==============================
+
+.. automodule:: frame.environments.ground_truth_types
+   :members:
+   :undoc-members:
+   :show-inheritance:

docs/source/frame/interestingness.rst

@@ -7,6 +7,3 @@ FRAME interestingness metrics are used to evaluate the quality and importance of
    :maxdepth: 1
    :caption: Contents:
 
-   interestingness/base
-   interestingness/comprehensibility
-   interestingness/parsimony

docs/source/frame/policies.rst

@@ -9,5 +9,5 @@ FRAME policies determine how conjectures and concepts are selected during theory
 
    policies/base
    policies/concept_biased_random_policy
-   policies/heuristic_policy
+   policies/interestingness_guided_policy
    policies/rule_balanced_random_policy

docs/source/frame/productions/conjecture_rules.rst

@@ -6,5 +6,6 @@ Conjecture Production Rules
    :caption: Conjecture Production Rules:
 
    conjectures/equivalence
+   conjectures/exclusivity
    conjectures/implication
    conjectures/nonexistence

frame/knowledge_base/entities.py

@@ -48,7 +48,7 @@
 import typing
 from frame.utils.logging import logger
 from frame.tools.z3_template import Z3Template
-
+import galois
 
 # Default timeout for example verification (in seconds)
 # This can be overridden by the configuration
@@ -532,6 +532,34 @@ def evaluate(self) -> int:
         return self.value
 
 
+class FiniteFieldOfOrder27(Expression):
+    """
+    Finite field of order 27. 
+    The elements are: 
+
+   [            0,             1,             2,             α,
+            α + 1,         α + 2,            2α,        2α + 1,
+           2α + 2,           α^2,       α^2 + 1,       α^2 + 2,
+          α^2 + α,   α^2 + α + 1,   α^2 + α + 2,      α^2 + 2α,
+     α^2 + 2α + 1,  α^2 + 2α + 2,          2α^2,      2α^2 + 1,
+         2α^2 + 2,      2α^2 + α,  2α^2 + α + 1,  2α^2 + α + 2,
+        2α^2 + 2α, 2α^2 + 2α + 1, 2α^2 + 2α + 2]
+    """
+    def __init__(self):
+        self.field = galois.GF(27)
+        self.field.repr("poly")
+
+
+class ElementOfFiniteFieldOfOrder27(Expression):
+    """
+    Represents a finite field element.
+    """
+    def __init__(self, value: int, field: FiniteFieldOfOrder27):
+        assert 0 <= value < 27, f"Value {value} must be between 0 and 26"
+        self.value = field.field(value)
+        self.field = field
+
+
 class NatDomain(Expression):
     """Represents the domain/type of natural numbers"""
 

pyproject.toml

@@ -31,7 +31,9 @@ dependencies = [
     "sphinx-rtd-theme (<2.0.0)",
     "rich (>=13.7.0,<14.0.0)",
     "parglare (>=0.16.1)",
-    "pebble"
+    "pebble",
+    "pyfinite (>=1.9.1,<2.0.0)",
+    "galois (>=0.4.6,<0.5.0)"
 ]