Maxima 5.44.0 Manual: Macros

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### 36.3 Macros

Function: buildq (L, expr)

  Substitutes variables named by the list L into the expression expr, in parallel, without evaluating expr. The resulting expression is simplified, but not evaluated, after `buildq` carries out the substitution.

  The elements of L are symbols or assignment expressions `symbol: value`, evaluated in parallel. That is, the binding of a variable on the right-hand side of an assignment is the binding of that variable in the context from which `buildq` was called, not the binding of that variable in the variable list L. If some variable in L is not given an explicit assignment, its binding in `buildq` is the same as in the context from which `buildq` was called.

  Then the variables named by L are substituted into expr in parallel. That is, the substitution for every variable is determined before any substitution is made, so the substitution for one variable has no effect on any other.

  If any variable x appears as `splice (x)` in expr, then x must be bound to a list, and the list is spliced (interpolated) into expr instead of substituted.

  Any variables in expr not appearing in L are carried into the result verbatim, even if they have bindings in the context from which `buildq` was called.

  Examples

  `a` is explicitly bound to `x`, while `b` has the same binding (namely 29) as in the calling context, and `c` is carried through verbatim. The resulting expression is not evaluated until the explicit evaluation `''%`.

      (%i1) (a: 17, b: 29, c: 1729)$

      (%i2) buildq ([a: x, b], a + b + c);
      (%o2)                      x + c + 29

      (%i3) ''%;
      (%o3)                       x + 1758

  `e` is bound to a list, which appears as such in the arguments of `foo`, and interpolated into the arguments of `bar`.

      (%i1) buildq ([e: [a, b, c]], foo (x, e, y));
      (%o1)                 foo(x, [a, b, c], y)

      (%i2) buildq ([e: [a, b, c]], bar (x, splice (e), y));
      (%o2)                  bar(x, a, b, c, y)

  The result is simplified after substitution. If simplification were applied before substitution, these two results would be the same.

      (%i1) buildq ([e: [a, b, c]], splice (e) + splice (e));
      (%o1)                    2 c + 2 b + 2 a

      (%i2) buildq ([e: [a, b, c]], 2 * splice (e));
      (%o2)                        2 a b c

  The variables in L are bound in parallel; if bound sequentially, the first result would be `foo (b, b)`. Substitutions are carried out in parallel; compare the second result with the result of `subst`, which carries out substitutions sequentially.

      (%i1) buildq ([a: b, b: a], foo (a, b));
      (%o1)                       foo(b, a)

      (%i2) buildq ([u: v, v: w, w: x, x: y, y: z, z: u],
                    bar (u, v, w, x, y, z));
      (%o2)                 bar(v, w, x, y, z, u)

      (%i3) subst ([u=v, v=w, w=x, x=y, y=z, z=u],
                   bar (u, v, w, x, y, z));
      (%o3)                 bar(u, u, u, u, u, u)

  Construct a list of equations with some variables or expressions on the left-hand side and their values on the right-hand side. `macroexpand` shows the expression returned by `show_values`.

      (%i1) show_values ([L]) ::= buildq ([L], map ("=", 'L, L));
      (%o1)   show_values([L]) ::= buildq([L], map("=", 'L, L))

      (%i2) (a: 17, b: 29, c: 1729)$

      (%i3) show_values (a, b, c - a - b);
      (%o3)          [a = 17, b = 29, c - b - a = 1683]

      (%i4) macroexpand (show_values (a, b, c - a - b));
      (%o4)    map(=, '([a, b, c - b - a]), [a, b, c - b - a])

  Given a function of several arguments, create another function for which some of the arguments are fixed.

      (%i1) curry (f, [a]) :=
              buildq ([f, a], lambda ([[x]], apply (f, append (a, x))))$

      (%i2) by3 : curry ("*", 3);
      (%o2)        lambda([[x]], apply(*, append([3], x)))

      (%i3) by3 (a + b);
      (%o3)                       3 (b + a)

  ·

  Categories: Function definition

Function: macroexpand (expr)

  Returns the macro expansion of expr without evaluating it, when `expr` is a macro function call. Otherwise, `macroexpand` returns expr.

  If the expansion of expr yields another macro function call, that macro function call is also expanded.

  `macroexpand` quotes its argument. However, if the expansion of a macro function call has side effects, those side effects are executed.

  See also `::=`, `macros`, and `macroexpand1`..

  Examples

      (%i1) g (x) ::= x / 99;
                                          x
      (%o1)                      g(x) ::= --
                                          99

      (%i2) h (x) ::= buildq ([x], g (x - a));
      (%o2)            h(x) ::= buildq([x], g(x - a))

      (%i3) a: 1234;
      (%o3)                         1234

      (%i4) macroexpand (h (y));
                                    y - a
      (%o4)                         -----
                                     99

      (%i5) h (y);
                                  y - 1234
      (%o5)                       --------
                                     99

  ·

  Categories: Function application

Function: macroexpand1 (expr)

  Returns the macro expansion of expr without evaluating it, when `expr` is a macro function call. Otherwise, `macroexpand1` returns expr.

  `macroexpand1` quotes its argument. However, if the expansion of a macro function call has side effects, those side effects are executed.

  If the expansion of expr yields another macro function call, that macro function call is not expanded.

  See also `::=`, `macros`, and `macroexpand`.

  Examples

      (%i1) g (x) ::= x / 99;
                                          x
      (%o1)                      g(x) ::= --
                                          99

      (%i2) h (x) ::= buildq ([x], g (x - a));
      (%o2)            h(x) ::= buildq([x], g(x - a))

      (%i3) a: 1234;
      (%o3)                         1234

      (%i4) macroexpand1 (h (y));
      (%o4)                       g(y - a)

      (%i5) h (y);
                                  y - 1234
      (%o5)                       --------
                                     99

  ·

  Categories: Function application

Global variable: macros

  Default value: `[]`

  `macros` is the list of user-defined macro functions. The macro function definition operator `::=` puts a new macro function onto this list, and `kill`, `remove`, and `remfunction` remove macro functions from the list.

  See also `infolists`.

  ·

  Categories: Function definition ·Global variables

Function: splice (a)

  Splices (interpolates) the list named by the atom a into an expression, but only if `splice` appears within `buildq`; otherwise, `splice` is treated as an undefined function. If appearing within `buildq` as a alone (without `splice`), a is substituted (not interpolated) as a list into the result. The argument of `splice` can only be an atom; it cannot be a literal list or an expression which yields a list.

  Typically `splice` supplies the arguments for a function or operator. For a function `f`, the expression `f (splice (a))` within `buildq` expands to `f (a[1], a[2], a[3], ...)`. For an operator `o`, the expression `"o" (splice (a))` within `buildq` expands to `"o" (a[1], a[2], a[3], ...)`, where `o` may be any type of operator (typically one which takes multiple arguments). Note that the operator must be enclosed in double quotes `"`.

  Examples

      (%i1) buildq ([x: [1, %pi, z - y]], foo (splice (x)) / length (x));
                             foo(1, %pi, z - y)
      (%o1)                -----------------------
                           length([1, %pi, z - y])

      (%i2) buildq ([x: [1, %pi]], "/" (splice (x)));
                                      1
      (%o2)                          ---
                                     %pi

      (%i3) matchfix ("<>", "<>");
      (%o3)                          <>

      (%i4) buildq ([x: [1, %pi, z - y]], "<>" (splice (x)));
      (%o4)                   <>1, %pi, z - y<>

  ·

  Categories: Function definition

Next: Functions and Variables for Function Definition, Previous: Function, Up: Function Definition [Contents][Index]