FUNCTION substitute

(* SCHEMA mathematical_functions_schema; *)

FUNCTION substitute(expr : generic_expression;
                    vars : LIST [1:?] OF generic_variable;
                    vals : LIST [1:?] OF maths_value) : generic_expression;
  LOCAL
    types : SET OF STRING := stripped_typeof(expr);
    opnds : LIST OF generic_expression;
    op1, op2 : generic_expression;
    qvars : LIST OF generic_variable;
    srcdom : maths_space_or_function;
    prpfun : LIST [1:?] OF maths_function;
    finfun : maths_function_select;
  END_LOCAL;
  IF SIZEOF (vars) <> SIZEOF (vals) THEN  RETURN (?);  END_IF;
  IF 'GENERIC_LITERAL' IN types THEN  RETURN (expr);  END_IF;
  IF 'GENERIC_VARIABLE' IN types THEN
    REPEAT i := 1 TO SIZEOF (vars);
      IF expr :=: vars[i] THEN  RETURN (vals[i]);  END_IF;
    END_REPEAT;
    RETURN (expr);
  END_IF;
  IF 'QUANTIFIER_EXPRESSION' IN types THEN
    qvars := expr\quantifier_expression.variables;
    -- Variables subject to a quantifier do not participate in this kind of
    -- substitution process.
    REPEAT i := SIZEOF (vars) TO 1 BY -1;
      IF vars[i] IN qvars THEN
        REMOVE (vars, i);
        REMOVE (vals, i);
      END_IF;
    END_REPEAT;
    opnds := expr\multiple_arity_generic_expression.operands;
    REPEAT i := 1 TO SIZEOF (opnds);
      IF NOT (opnds[i] IN qvars) THEN
        expr\multiple_arity_generic_expression.operands[i] :=
          substitute(opnds[i],vars,vals);
        -- This technique will not work on subtypes of quantifier_expression
        -- which derive their operands from other attributes!
      END_IF;
    END_REPEAT;
    RETURN (expr);  -- operands modified!
  END_IF;
  IF 'UNARY_GENERIC_EXPRESSION' IN types THEN
    op1 := expr\unary_generic_expression.operand;
    expr\unary_generic_expression.operand := substitute(op1, vars, vals);
    -- This technique will not work on subtypes of unary_generic_expression
    -- which derive their operands from other attributes!
  END_IF;
  IF 'BINARY_GENERIC_EXPRESSION' IN types THEN
    op1 := expr\binary_generic_expression.operands[1];
    expr\binary_generic_expression.operands[1] := substitute(op1, vars, vals);
    op2 := expr\binary_generic_expression.operands[2];
    expr\binary_generic_expression.operands[2] := substitute(op2, vars, vals);
    -- This technique will not work on subtypes of binary_generic_expression
    -- which derive their operands from other attributes!
  END_IF;
  IF 'PARALLEL_COMPOSED_FUNCTION' IN types THEN
    -- Subtype of multiple_arity_generic_expression which derives its operands.
    srcdom := expr\parallel_composed_function.source_of_domain;
    prpfun := expr\parallel_composed_function.prep_functions;
    finfun := expr\parallel_composed_function.final_function;
    srcdom := substitute(srcdom,vars,vals);
    REPEAT i := 1 TO SIZEOF (prpfun);
      prpfun[i] := substitute(prpfun[i],vars,vals);
    END_REPEAT;
    IF 'MATHS_FUNCTION' IN stripped_typeof(finfun) THEN
      finfun := substitute(finfun,vars,vals);
    END_IF;
    RETURN (make_parallel_composed_function(srcdom,prpfun,finfun));
  END_IF;
  IF 'MULTIPLE_ARITY_GENERIC_EXPRESSION' IN types THEN
    opnds := expr\multiple_arity_generic_expression.operands;
    REPEAT i := 1 TO SIZEOF (opnds);
      expr\multiple_arity_generic_expression.operands[i] :=
        substitute(opnds[i],vars,vals);
        -- This technique will not work on subtypes of multiple_arity_generic_
        -- expression which derive their operands from other attributes!
    END_REPEAT;
  END_IF;
  RETURN (expr);
END_FUNCTION;  -- substitute

Referenced By

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2012-03-27T17:13:59-04:00