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Definition

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Definition[s]

prints the own-, down- and up-values associated with s.

Examples (10)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (3)

In[1]:= g /: f[g[x_]] := h[x]; Definition[g]
Out[1]= g /: f[g[x_]] := h[x]

In[2]:= c0 = 3; Definition[c0]
Out[2]= c0 = 3

Display only

In[3]:= fd[x_] := x^2; FullForm[Definition[fd]]
Out[3]= Definition[fd]

Applications (7)

An OwnValue

In[4]:= c0 = 3; Definition[c0]
Out[4]= c0 = 3

DownValues, the special case first; the immediate fd[0] = 1 is shown with :=

In[5]:= fd[x_] := x^2; fd[0] = 1; Definition[fd]
Out[5]= fd[0] := 1
fd[x_] := x^2

An UpValue, shown in tag form

In[6]:= g /: f[g[x_]] := h[x]; Definition[g]
Out[6]= g /: f[g[x_]] := h[x]

All three kinds: own, then down, then up

In[7]:= gq = 7; gq[0] = z; gq /: f[gq[x_]] := h[x]; Definition[gq]
Out[7]= gq = 7
gq[0] := z
gq /: f[gq[x_]] := h[x]

Nothing defined

In[8]:= Definition[neverdefined]

The head is only displayed this way; the expression is still Definition[fd]

In[9]:= FullForm[Definition[fd]]
Out[9]= Definition[fd]

Attributes are not listed, unlike Mathematica

In[10]:= SetAttributes[fl, Listable]; fl[x_] := x + 1; Definition[fl]
Out[10]= fl[x_] := x + 1

Implementation notes

Algorithm. Definition has no evaluator builtin: Definition[s] (attributes HoldAll, Protected) stays as an inert expression, and the printer renders it. In print_standard, a Definition[sym] node calls print_definition_body, which reads symtab_get_own_values, symtab_get_down_values and symtab_get_up_values and prints one line per rule: OwnValues as lhs = rhs, DownValues as lhs := rhs, UpValues as s /: lhs := rhs, in that order and in each list's stored order. A symbol with no values prints Null. render_definitions in src/core.c builds the same text into a string for ?s / Information[s], which appends it after the usage message.

Data structures. It reads the three Rule lists on the SymbolDef directly and does not copy them. The patterns are printed with the ordinary print_standard, so a conditioned rule shows its Condition on the left (lhs /; test := rhs). DownValues come out in add_rule's specificity order, so a literal fd[0] rule appears before the general fd[x_] one.

Complexity / limits. Linear in the total number of rules. Display only: FullForm[Definition[s]] is Definition[s]. The rule store has no immediate/delayed flag, so every down- and up-value prints with := and every own-value with =. Attributes, Options, messages, NValues and SubValues are not printed (Mathematica includes Attributes[s] = {...} lines). Compiled in under UP_VALUES.

Attributes: HoldAll, Protected.

References

See also: FullForm

Notes & additional examples

Notes

  • Definition[s] stays unevaluated and is displayed as one line per stored rule: OwnValues as s = v, DownValues as lhs := rhs, UpValues as s /: lhs := rhs. With no rules it prints Null. ?s and Information[s] add the same lines after the usage message.
  • The rule store does not record immediate versus delayed, so every down- and up-value is shown with :=.
  • Unlike Mathematica, it does not print Attributes[s] = {...}, Options, messages, NValues or SubValues.
  • Attributes {HoldAll, Protected}.
  • See also: OwnValues, DownValues, UpValues, Information, Attributes.