An Eiffel Library for Units of Measurement

Transcription

1 An Eiffel Library for Units of Measurement Issues and approaches to the support of numerical values with physical dimensions Semester project Markus Keller 1 / 16

2 Schedule Short introduction to units: concepts & standards Previous work for other languages Requirements for a Base Library Architecture #1: Genericity-based, checks at compile time Discussion Architecture #2: Object-based, checks at run time (DbC) Discussion 2 / 16

3 The SI-System Why Units? - Unit of scale is a reference for comparison and measurement - Dimensional Analysis: helps detecting errors & gives insight - Assumption: Physical laws are dimensionally invariant. ISO 1000: "SI units and multiples (prefixes)" ISO 31:0-13: "Quantities and units of {field of use}" - 7 base units: m (length), kg (mass), s (time), A (electric current), K (temperature), mol (amount of substance), cd (luminous intensity) -- "orthogonal" dimensions - 2 supplementary units: rad, sr -- they couldn t decide... - Derived units: e.g. N, J, V, m/s -- from base units - Obsolete units -- everything before SI 3 / 16

4 some nasty cases absolute temperature: absolute or relative? coordinate - different origins of C and F - not automatically derivable, perhaps C C? relative measure db, neper: logarithmic density, loudness, currencies: not even constant time: s, min, h, d => calendar for m(onth), y(ear), time zone, plane and solid angles: rad and sr or dimensionless? dimensionless ratios: refractive index, particle density (ppm) not reducible quantities: car uses 3 l / 100 km = 0.03 mm 2? 4 / 16

5 Unit (of Measurement), Dimension, Quantity Adimension is a type. It denotes a class of similar scales. Aunit is an instance of a dimension type. Different units of the same dimension are isomorphic. -- a reference of scale Aquantity consists of a value and a unit. Conformance should be based on dimensions, not on units. Operations on Quantities - Addition (subtraction) of quantities: only equal dimensions - Multiplication (division): always OK from unit point of view - may result in composite dimensions which have to be resolved (brought to a canonical form) - q: only if q is power of 2. () int : always OK. sin, : [rad] -> [] 5 / 16

6 Previous Work Some activity in this field. Why not in broad use? Most common approach: extend compiler to include unit types - extended type system, static resolution at compile time Other approaches: - Type inference: guess who? ML & co. - Use runtime objects & throw exceptions: Smalltalk A general issue: How to build a customizable compiler? - Compile by Contract: How can we let programmers decide what to do at (compile assembly run) time? - manifest constants for complex types, (type-)checks, assertions 6 / 16

7 Requirements for a Base Library of Units user can add new units (even better: and new dimensions) automatic conversion and static unit-equality checks little/no overhead (execution time and syntactic) generic value representation (REAL, DOUBLE,, INTEGER?) - problem: how to represent conversion factors? accuracy & precision: unsolved (unsolvable) numeric problem - additional problems: prefixes & implicit conversion to internal representation can hamper precision Create/change units and dimensions at run time? - > static type checking impossible -- irreversible decision 7 / 16

8 Architecture #1: static unit checking class QUANTITY [V -> {NUMERIC, COMPARABLE}; D -> DIMENSION] inherit NUMERIC redefine infix "+", infix " ", infix "*", infix "/", COMPARABLE redefine feature value: expanded V infix "*" (other: QUANTITY [V; DIMENSION]):??? is do end end -- class QUANTITY DIMENSION [1, -2, 0, 0, 0, 0, 0]??? Eiffel lacks C++ s non-type template parameters. A complete unit library with dimensional analysis at compile time is not feasible. The problem is with the inability to reduce complex unit expressions to a canonical (normal) form. Since there s no way to compute generic type parameters in Eiffel, we cannot produce the correct result types for unit multiplication and division. In C++, the compiler can create new types by instantiating templates with (constant) non-type parameters. These "compile time calculations" are not possible in Eiffel. 8 / 16

9 Architecture #1: static unit checking (2) We could simulate non-type generic parameters by an explosion of hand-written generic classes and routines - classes (Px, Z, Mx) represent values (+x, 0, x), respectively: class FORCE [V -> {NUMERIC, COMPARABLE}; D -> DIMENSION [P1, P1, M2, Z, Z, Z, Z]] inherit NUMERIC redefine infix "+", infix " ", infix "*", infix "/", COMPARABLE redefine feature DIMENSION [L, M, T, I, Θ, N, J] value: expanded V infix "*" (other: QUANTITY [V; DIMENSION [Z, Z, Z, Z, Z, Z, Z]]): DIMENSION [P1, P1, M2, Z, Z, Z, Z]] is do end infix "*" (other: QUANTITY [V; DIMENSION [P1, Z, Z, Z, Z, Z, Z]]): DIMENSION [P2, P1, M2, Z, Z, Z, Z]] is do end end but that s neither object-oriented nor extensible. 9 / 16

10 Architecture #2: object-based UNITS [V ->...] QUANTITY [V -> {NUMERIC, COMPARABLE}] dimension DIMENSION DOUBLE_UNITS DOUBLE_ LENGTH_UNITS s, min, h DOUBLE_ TIME_UNITS COMPLEX_DIMENSION BASE_DIMENSION LENGTH TIME / 16

11 Architecture #2: object-based (2) class QUANTITY [V -> {NUMERIC, COMPARABLE}] inherit NUMERIC redefine infix "+", infix "-", infix "*", infix "/", COMPARABLE redefine create make (value: V; dimension: DIMENSION) is do end feature value: expanded V; dimension: expanded DIMENSION infix "+" (other: like Current): like Current is require dimension.commensurate_with (other.dimension) do create Result.make (value + other.value, dimension) end infix "*" (other: QUANTITY [V]): QUANTITY [V] is do create Result.make (value * other.value, dimension *other.dimension) end -- a candidate for target conversion from V item (unit: QUANTITY[V]): V is-- value in units unit require... commensurate_with... do Result := value / unit.value end 11 / 16

12 References Michael Karr and David B. Loveman: "Incorporation of Units into Programming languages". CACM Vol. 21, No. 5, May Compiler André van Delft: "A Java Extension with Support for Dimensions". Software Practice and Experience 29(7), (1999) -- Compiler Walter E. Brown: "The SI Library of Unit-Based Computation", CHEP 98, Chicago, SIunits: The reference implementation for C++ John J. Barton and Lee R Nackman: "Scientific and engineering C++". Addison Wesley, same idea as SIunits Paul N. Hilfinger: "An Ada Package for Dimensional Analysis". ACM Trans. on Progamming Lang. and Systems, Vol. 10, No. 2, April 1988, pp Andrew J. Kennedy: "Programming Languages and Dimensions". Diss. Univ. Cambridge, November 1995, -- ML, inference 12 / 16

13 Discussion Eiffel Unit Library Presentation style Language (Eiffel and mine ;-) - > Another topic to discuss (TUPLE conformance) 13 / 16

14 A TUPLE of problems Agent mechanism is not statically type safe: class C feature f (x1: T1; x2: T2) is do... end make is do use (agent f (?,?)) end --> PROCEDURE [C, TUPLE [T1, T2]] use (action: PROCEDURE [C, TUPLE [T1]] is do action.call ([a1]) -- call s argument type: TUPLE [T1] -- call fails at run time, even though end end -- openness of arguments is static issue Problem: TUPLE [T1, T2] conforms to TUPLE [T1] Solution: TUPLE [T1, T2,...] shall only conform to TUPLE 14 / 16

15 A TUPLE of problems (2) Today s definition implies: "agent f (?,?)": PROCEDURE [C, TUPLE [A, B]]... is-a-kind-of... "agent g (?)": PROCEDURE [C, TUPLE [A]] TUPLE TUPLE [A] TUPLE [A, B] Is there a convincing reason, why tuple type conformance rules are so loose? - Features with variable argument count can always use ARRAY [ANY] for their arguments. - Static typing => avoid avoidable run time exceptions 15 / 16

16 A TUPLE of problems (3) - Solution? Proposition: retain "inheritance" only from TUPLE - undefine TUPLE - TUPLE [] is the empty TUPLE - TUPLE [A, B,...] only conforms to TUPLE (not to TUPLE []) TUPLE * TUPLE [] TUPLE [A] TUPLE [A, B]... and BTW: rename agent as wrap -- agent is overloaded in class PROGRAMMING_CONSTRUCTS 16 / 16