Text.Parse.Units

This module defines a parser for unit expressions. The syntax for these expressions is like F#'s. There are four arithmetic operators (*, /, ^, and juxtaposition). Exponentiation binds the tightest, and it allows an integer to its right (possibly with minus signs and parentheses). Next tightest is juxtaposition, which indicates multiplication. Because juxtaposition binds tighter than division, the expressions m/s^2 and m/s s are equivalent. Multiplication and division bind the loosest and are left-associative, meaning that m/s*s is equivalent to (m/s)*s, probably not what you meant. Parentheses in unit expressions are allowed, of course.

Within a unit string (that is, a unit with an optional prefix), there may be ambiguity. If a unit string can be interpreted as a unit without a prefix, that parsing is preferred. Thus, min would be minutes, not milli-inches (assuming appropriate prefixes and units available.) There still may be ambiguity between unit strings, even interpreting the string as a prefix and a base unit. If a unit string is amiguous in this way, it is rejected. For example, if we have prefixes da and d and units m and am, then dam is ambiguous like this.

Parsing units

data UnitExp pre u

Parsed unit expressions, parameterized by a prefix identifier type and a unit identifier type

Constructors

Unity

"1"

Unit (Maybe pre) u

a unit with, perhaps, a prefix

Mult (UnitExp pre u) (UnitExp pre u)

Div (UnitExp pre u) (UnitExp pre u)

Pow (UnitExp pre u) Integer

Instances

(Show pre, Show u) => Show (UnitExp pre u)

parseUnit :: (Show pre, Show u) => SymbolTable pre u -> String -> Either String (UnitExp pre u)

Parse a unit expression, interpreted with respect the given symbol table. Returns either an error message or the successfully-parsed unit expression.

Symbol tables

data SymbolTable pre u

A "symbol table" for the parser, mapping prefixes and units to their representations.

Constructors

SymbolTable

Fields

prefixTable :: PrefixTable pre

unitTable :: UnitTable u

type PrefixTable pre = Map String pre

A finite mapping from prefix spellings to prefix identifiers (of unspecified type pre). All prefix spellings must be strictly alphabetic.

type UnitTable u = String -> Maybe u

A mapping from unit spellings to unit identifiers (of unspecified type u). All unit spellings must be strictly alphabetic.

mkSymbolTable

Arguments

:: (Show pre, Show u)

=> [(String, pre)]

Association list of prefixes

-> [(String, u)]

Association list of units

-> Either String (SymbolTable pre u)

Build a symbol table from prefix mappings and unit mappings. The prefix mapping can be empty. This function checks to make sure that the strings are not inherently ambiguous and are purely alphabetic.

unsafeMkSymbolTable :: PrefixTable pre -> UnitTable u -> SymbolTable pre u

Make a symbol table without checking for ambiguity or non-purely alphabetic strings. The prefixes must be a (potentially empty) finite map, but the units mapping need not be finite. Note that this is unsafe in that the resulting parser may behave unpredictably. It surely won't launch the rockets, though.

universalSymbolTable :: SymbolTable a String

A symbol table that accepts all unit strings, but supports no prefixes.

Testing only

lex :: String -> Either ParseError [Token]

unitStringParser :: UnitStringParser_UnitExp