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A Comparative Study of Formalisms for Programming Language
Definition.
A thesis presented in partial fulfilment of tho requirsments for the degree of Master. of Science in
Computer Science at Massey University.
Ian Joseph Thompson Janu~ry 1975
ii
Abstract
This sludy looks Rt a number of methods for defining the f u 11 syntax and s efl12.n ti cs of computer pro gr arnrni n g languages. The syntax, especially the nature of context- dependent conditions in it, is first oxamined, then some oxtensions of context-free grammars are compared to see to what cxt8nt they can encompass the full contGxt-
conditions of typicc1l programminy lnnguages. It is found that several syntax extensions are i11adequate in this r egard, and that tho ability to cnlculoto complicated functions and conditions , and to eventually delete the val ues of such functions, is needed. This ability may be obtained either by allowing unrestricted rules and rncta- vari ablos in the phrase- structure, or by associating roathematical functionc either with individual production r ules or with the whole contoxt--froe structure, to trL,ns- f orm it into an ' c.ibstrocl syntax ' .
Since the forrn of o definition of a progr2.r,1rnir19 J.,rngt1ar;e semantics de pen cJ s critical .l y on how one conceives II n: can i 11 y 11 ,
f ive mo.in tyf)es of semantics are considered: these are called I natural 1 , 1 pr of)osi t ional ' , 1 function8l' , snd ' structural' sem~ntics, as well as a semantics based on string rewriting rules. The five types are compared for their success in defining tho sornantics of computing l anguages, of the example Algal-like ~anguage ALEX in particular. Among othei conclusions, i t is found that the sen1antics of structures and computations on structures is the only type sufficiently comprehensive, precise, and r eadable.
I\ c know led genre n ts
In the preparation of this thesis, I wish particularly to thank Lloyd Thomas and
Professor Tate for many valuable discussions, suggestions 1 and criticisms, and also to
thank Bob Doran for help in his obtaining i mportant source materials.
i i i
Table of Contents
Acknowledgem8nts
1 The probl ems of programming l anguage definition.
2 Syntax
2 .1 Introduction
2.2 Context-dependent conditions 2.3 Extended grammars
2.3.1 Context-sensitive grammars 2. 3.2 Scattered-context grammars 2.3.3 Programmed grammars
2.4 Grammars with associated context- dependent conditions
2.4 .1 Property grammars
2.4. 2 Grammars using inherited and derived
iii
1
3 3 4
7 7 9 12
14 14
attributes, Production Systems 17 2.4.3 Conditions defined by functions on the
whole context-free syntactic structure 20 2.4.3.1 The Vienna Definition method 21
2.4.3.1 Objects and selectors and·
operations in VDL 21
2.4.3.2 Constructing the abstract syntax
in VOL 24
2.4.3.2 Linked-Forest Manipulation Sys tems 26 2.5 van Wijngaarden grammars 29 2. 5.1 Grammars with unrestricted rewriting rules 29 2.5.2 Grammars with metasyntactic variables 30
2. 5.2.1 An historical digression
2.5. 2.2 Context-dependencies defined by van Llijngaarden grammars
2.6 Conclusion
3 Semantics
3.1 Introduction
3. 2 ~atural semantics
3.2.1 Natural l anguage semantics
30
31
36 36
37 37 3.2.2 Semantics by compilers 39 3. 3 P,r oposi tional semantics 40
3. 4 .r unctional semantics 44
3. 4. 1 The l ambda cal culus 45
3 • 5 S e f! i an t i c s b as o d on s t r i n g r e w r i t i n g r u l o s 4 8 3. 5.1 Preprocessing semantics 48 3.5. 2 Data-processing semantics 51 3.6 Semantics with structures and computations
on structures 54
3 • 6 • 1 I n f o r rn :q t.i. o 11 s t r u c t u 1· e s 3.'1.2 Sornentic 01etaJ.angu2ges
3.6.2.1 The Vienna Definition Language 3. G. 2.2 The OASIS/1 definition of PL/I
f O r [ [ U\/ /'. r~ S J
3. G. 2. 3 The Algal 60 method
3 • G • 2 • I~ L i n l<G d- ~-or e s t r:i an i p u l a t i on S y s t ems as semanti c met al anguoges
3. 6. 3 Hypothetical machines 3.G.3.1 Machine structures 3.7 Conclusion
References Bibliography
Appendices
A Concrete syntax of ALEX: a context-free
54 57 57
59 60
62 , 6G (;7 71
73 79
83
covering grammar 83
8 Abstract represent ation of .the concrete
syntax in VDL 85
C Abstract syntax for the VDL definition of ALEX 88 D Translation from concrete to abstract syntax 89
E Definition of ALEX syntax by a Production System
F Definition of ALEX syntax by ~ van Llijngaarden grammar
G Definition of ALEX syntax by a Linked-Forest Manipulation System
H f'iachine states for the VDL definition of ALEX semantics
I Interpretation instructions for tho VOL
94
97
1 02
106
definition 107
J Abstract syntax for the BAS IS definition of
ALEX 112
K Machine states for the BASIS definition 113 L Interpretation program for the BASIS dofinition 114 M Abstract syntax tree-structures for the LFMS
definition of ALEX 120
N Transformation rules for the LFMS definition 121
1 The problems of proaramming lanquage definition
Defining a computing language is generally done in two stnges :
1) ~ntax : defining as rigorously as possible the set of all possible programs of the language, together with their formal structures and substructures.
1
2)
semantics : associating wi th each such program its meaning, so that the effects of executing the progr am with its data are as rigo rous- ly defined as possible.Details of definitions of these two stages will be discussed in the following two chapters (although t he exact dem2rcation between the stages has varied for different people; I shall discuss t his further in section
2.2) .
The aim is to be able to define a significantly l ar ge language,including both st ages of definition, 8nd to this end there are several criteria for
comparing the different systems examined l ater.
1) Scope of t he definition method
Is it applicable to all features of all progr amming languages, or are there some features that can be encompassed either not at all, only with great difficulty, or at the cost of breaking up a neat system?
2) Elegance
A general aim is for a definition as readable , concise, and 'trahsparent' as possible. A readable definitJon should be understandable even with only a short
initiation into the details of the formalism ; it should not be written in a wholly foreign language. A definition should al.so ·transparentl y follow the
language being defined; this means that small changes in the language should require only small changes in the formal definition. Concerning concisenes; one should
disti nguish between the method and its appl ication to specific l anguages: a very simpl e method wil l general ly lead t o a very compl i cated definition. 3 ) Rioour
Syntax definitions should dofine, ideall y, al l and only the proqr;-ims in the .lant_;uage, and assign correct formal structures to val id programs. They should avoid ovorlapping, incompatible, ambj guous, and/or missing specifications. Si mi larly wit h
semantics. Note, however, t hat i t i s occasionaJ Jy desi reab le to leavo certain parts of~ standar d
2
de fin j_ t .i on either corn p let e 1 y op on , or to de J. i berat e 1 y give only a pnrt i ol definition of t hem. r or example, the de ta .i l [; of re c1 l a r i t h m Ei ti c, beyond certain
basic conditions, may be postponed beyond the
standard defi nition; and i n any case the effect of merging p;:,ralJ.eJ. operations should i ntentionally be left undetermined.
4 ) Fur rn a J. is i.' t i on
The for111al jsts ' idec:il is th2t a ciefinition shouJ d
S8Y everything thnt can be sc1id about c1Jl programs i n the lc111guc1ge, a11d i n such a manner that mechan- i cal ~;b:1ternents r.,rn be rnarle 8hOut the proqri:lm wj thout either us.inq hum,:,n understand.ing at this point, or rL1nnin9 i t on a computer with specif ic data. Such statements, for exnmple, could concern the mechan- ioal design of impJ.oment~tjons , or the mechanical proofs of correctness , equival ence, etc., of
programs i n t he language.
Chapter 2 looks at lhe synlactic; and chapter 3 the
semant i c, components of definitions of progr amming l anguages , and in the appendi ces I have used those methods which ar e sufficiently powerful for the definition of "ALEX". ALEX i s the name which hencefort h I give to a certai n subset of Algal 60; i t does not include arrays ,. for-loops , conditional
expressions , or designational expressi ons , but i t does
incl ude mi~ed- mode arithmetic, procedures , functions, call- by-name and call-by-value parameters, 11goto11 and 11if11
statements, Rnd the implicit declaration of labels.
