Forgot to add formtest.py

Note: we need to implement FormatValues()

Author: rocky

test/formtest.py

@@ -0,0 +1,94 @@
+"""
+Example to show how new Format-directed Boxing might work.
+
+This is a minimal example so we can discuss feasiblity.
+"""
+from mathics.builtin.forms.base import box
+from mathics.core.atoms import IntegerM1, Integer1, Rational
+from mathics.core.expression import Expression
+from mathics.core.symbols import SymbolDivide
+from mathics.core.systemsymbols import (
+    SymbolMakeBoxes,
+    SymbolPower,
+    SymbolSqrt,
+    SymbolStandardForm,
+)
+from mathics.session import MathicsSession
+
+session = MathicsSession(character_encoding="ASCII")
+
+
+# Hacky pseudo boxing rules.
+# Currently in MakeBox rule rewriting occurs via MakeBox rewrite rules
+# which are attached to various Builtin classes.
+
+# The rewrite is performed as a part of rewriting portion of Expression evaluation.
+# We probably want to segregate these rules from other kinds of rules.
+#
+# The below hacky code is to simulate the rule behavior for
+# just a few kinds of things so we don't have to hook into the
+# complex rewrite mechanism in use in general evaluation. The implementation we use
+# is just good enough for the new kinds of things we need.
+# It is not intended to be used in a final implementation.
+
+
+def sqrt_boxform_fn(expr):
+    return Expression(SymbolSqrt, expr.elements[0])
+
+
+def power_boxform_fn(expr):
+    new_expr = expr.elements[0]
+    if new_expr.elements[-1] == IntegerM1:
+        return Expression(SymbolDivide, Integer1, new_expr.elements[0])
+    elif new_expr.elements[-1] == Rational(1, 2):
+        return Expression(SymbolSqrt, new_expr.elements[0])
+    return new_expr
+
+
+boxform_rules = {SymbolSqrt: sqrt_boxform_fn, SymbolPower: power_boxform_fn}
+
+
+def apply_formatvalues_rules(expr, evaluation):
+    """
+    Hacky replacement for rules() found in Expression rewrite_apply_eval().
+    Note, we need to add builtin FormatValues() and the internals that go with that.
+    """
+    if expr.elements[-1] not in (SymbolStandardForm,):  # Or more generally $BoxForms
+        # For other forms, there might be other transformations too, and this should
+        # be discussed.
+        # For simplicity, we will just handle a small number of $BoxForms rules
+        return expr
+
+    # Remove the Form from expression "expr"
+    unboxed_expr = expr.elements[0]
+
+    if unboxed_expr.head in boxform_rules:
+        new_expr = boxform_rules[unboxed_expr.head](expr)
+        return new_expr
+    return unboxed_expr
+
+
+# Begin demo code.
+
+for expr_str in (
+    "1 / x",  # Show off "Division" boxing
+    "a ^ b",  # Show off "Power" boxing
+    "Sqrt[a]",  # Show off "Square-root boxing"
+):
+    expr = session.evaluate(expr_str)
+    print("Input expression:  ", expr)
+
+    # Here is how Mathics currently evaluates MakeBoxes
+    boxed_expr = Expression(SymbolMakeBoxes, expr, SymbolStandardForm)
+    print("Mathics MakeBoxes: ", boxed_expr)
+    print("Eval'd Makeboxes:  ", boxed_expr.evaluate(session.evaluation))
+
+    # Here is how Mathics might better box an expression.
+    # First we apply MakeBox boxing transformation rules.
+    # This handles expression rewriting.
+    transformed_boxed_expr = apply_formatvalues_rules(boxed_expr, session.evaluation)
+
+    boxed_expr2 = box(transformed_boxed_expr, session.evaluation, SymbolStandardForm)
+    print("New    MakeBoxes:  ", boxed_expr2)
+    print("-" * 30)
+    print("")