With

Status: Stable

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

Description

With[{x = x0, ...}, expr]

specifies that x should be replaced by x0 throughout expr.

Examples (5)

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

Basic examples (1)

In[1]:= x = 10; With[{x = 5}, x^2]
Out[1]= 25

Applications (4)

In[2]:= With[{a = 2, b = 3}, a^2 + b^2]
Out[2]= 13

In[3]:= With[{phi = (1 + Sqrt[5])/2}, Simplify[phi^2 - phi - 1]]
Out[3]= 0

In[4]:= With[{n = 20}, N[Sum[1/k^2, {k, 1, n}], 30]]
Out[4]= 1.596163243913023316640878872058

In[5]:= With[{x = 1 + I}, x^2]
Out[5]= 2*I

Implementation notes

Algorithm. builtin_with (in src/modular.c) implements lexical constants by literal substitution — no renaming and no symbol-table mutation (contrast Module/Block). With carries HoldAll | Protected (set in src/attr.c). Each binding must be x = val (value evaluated immediately in the outer scope) or x := val (RHS substituted verbatim, unevaluated); the handler collects these into a ScopingEnv linked list mapping the constant name to its replacement expression.

The body is rewritten by substitute_scoping, the same recursive, shadow-aware tree walk used by Module: it replaces free occurrences of each constant, drops a name from the environment when descending into a nested scoping construct that rebinds it, and substitutes into nested binding RHSs (so With[{q=12}, With[{k=q}, k]] resolves k to 12) without touching binding LHS names. The substituted body is then evaluated; Return[v]/Return[v, With] is trapped via eval_classify_return. Because substitution is structural, the constants vanish before evaluation and leave no trace in the symbol table.

• HoldAll, Protected.
• Replaces occurrences of symbols in the body before evaluation.

Attributes: HoldAll, Protected.

References

See also: HoldAll

• Source: src/modular.c
• Specification: docs/spec/builtins/scoping-constructs.md
• Tests: tests/test_autocompile.c
• Tests: tests/test_blas.c
• Tests: tests/test_cherry_dilog.c
• Tests: tests/test_cherry_dilog_exp.c

Notes & additional examples

Notes

With[{x = x0, ...}, expr] replaces each x by its value x0 throughout expr and then evaluates the result. Unlike Module, the substitution is literal and immediate, making With ideal for inlining constants and parameters.