wl-init

Some Wolfram Language (a.k.a. Mathematica) packages that make things easier

• AllowTrailingComma.m: Drop every trailing comma in RowBox. Only boxes interface. For some reason, $PreRead doesn’t work in text-based interface at all! Also, the package allows some constructs (Module, With, Block, Function) have empty (Null) elements in their first argument. In particular, trailing and leading commas are ignored.

• RangeSyntax.m: Interpret (in boxes) x = a … b as {x, a, b} and x = a … b … d as {x, a, b, d} to be used in range specification.

• DifferentialD.m: Prettyprint Dt[x] as ⅆx. Conversely, interpret ⅆx as Dt[x].

• ForEach.m: Another syntax for Do loop or Table list comprehension with an iterator in the first argument.

• FormatUsage.m: A Private`FormatUsage function that is used in other packages to, yes, format usage messages. Later, I found Macros`SetUsage but it didn’t satisfy me.

• UsageOnly.m: A Private`UsageOnly[symb] auxiliary function that is used in some packages to indicate that the symbol does nothing but holds symb::usage message. It may be used in a package that does not introduce valuable eponymous symbol.

• IfThenElse.m: The If’s syntax makes code be very confusing when used not as ternary operator with several-word branches but as conditional statement with large branches. Else branch starts somewhere below with a tiny comma (one of many). If [test] Then [ifTrue] Else [ifFalse] is much easier to read. Also, IfQ is added to surely choose between branches; it is guaranteed to be evaluated to one of the branches, unlike If which stays unevaluated unless test evaluates to boolean.

• QuantityInput.m: Simple input of Quantity[5, "cm"] as 5::cm.

• MethodCall.m: OO-style syntactic sugar: expr::foo[args…] evaluates to foo[expr, args…]. Some functions like Map, Apply, Nest, etc. are treated with first two arguments reversed. Method calls may be chained, thus

      l = {{1, 2, 3}, {4, 5, 6}};
      (l ::Append[{7, 8, 9}]
         ::Apply[Plus, {1}]
         ::Riffle[", and "]
         ::Map[ToString]
         ::StringJoin[])
  

  gives "6, and 15, and 24".
  The package may conflict with the QuantityInput` package, so the code above works only due to l being not explicitly (in its unevaluated form) a number or a list of numbers. (Also note the parentheses: without them, newlines would terminate expression leading to a syntax error.) expr //$@ foo[args…] is a version with very low precedence.

• ScopeExit.m: Write here, defer evaluation until end of block. Useful for assured resources release. Inspired by scope(exit) in D language.

• SequenceParse.m: When in boxes interface, Sequences may be entered in parentheses separated by comma: () is empty Sequence[], (1,) is unary Sequence[1], (1,2,3) is Sequence[1,2,3]. ∅∅ interprets as (not evaluates to) Sequence[] even in text interface.

• SwitchPattern.m (maybe not the best name, couldn’t think up better): System Switch function compares its first argument to several pattern forms, and evaluates to the value corresponding to the first match. The problem is, values cannot use variables (named patterns) bound in pattern forms. The SwitchPattern function solves this problem.

• HeldPureFunction.m: Easily construct anonymous functions with HoldAllComplete attribute. E.g. List @@ (Length[Unevaluated@#]&!) /@ Hold[1+1+1, 2+2] gives {3, 2}.

• ThrowGeneral.m: Two different forms of Throw & Catch — tagged and untagged — is a headache. They are unrelated: tagged Catch can’t catch untagged Throw and vice versa. So, both Catch[ Throw[expr, tag] ] and Catch[ Throw[expr] , _] catch nothing! This package makes a tag be used implicitly: the untagged versions are simply redirected to the tagged ones. Catch[expr] catches any thrown thing; Throw[expr] uses General tag.

• TypeSystemEither.m: TypeSystem`Either union type is declared but not working (at least, in 10.0.1). This is a minor fix just to type check via TypeSystem`ConformsQ. Complex things with Dataset are not considered.

• IsQ.m: IsQ[expr, head] or IsQ[head][expr] is equivalent to Head[expr] === head. The same way, IsntQ[expr, head] or IsntQ[head][expr] is a negation of that.

• WithNest.m: The package provide versions of With and Module — WithNest and ModuleNest in which each local-variable initialisations may refer to previously defined ones. E.g. WithNest[{a = 1, b = -a, c = 42}, b + c] gives 41. Braces are optional, i.e. one can write WithNest[a = 1, b = -a, c = 42, b + c]. System`Block already has the property of consecutive initialisers, so BlockNest is provided just in consistency and for a braceless form. The *Nest names are for historical reasons; now I doubt they are good enough, but cannot think up better ones. GeneralUtilities`Where provides the same behavior as WithNest in a braceless form.

• TheSymbol.m: Some single-letter system symbols — E, I, O, D, K, C, N, π — are protected. TheSymbolE, TheSymbolI, …, TheSymbolPi are provided that are displayed as a letter and are assignable. TheSymbol[⟨symbol or string⟩] can be used to be evaluated to one of the above symbols.

• Associate.m: Association has an undocumented usage as a replace-value/add-key function. There’s no need to use this Associate since its functionality is exactly in Assiciation.

• Second.m: Convenient functions Second, Third, …, Tenth — wrappers of Part.