Abstract
This chapter discusses language theory and includes a discussion on grammar, parse trees and derivations from grammar. The important area of programming language semantics is discussed, including axiomatic, denotational and operational semantics.
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Notes
- 1.
ε denotes the empty word.
- 2.
Recall from Chap. 6 that a monoid (M, *, e) is a structure that is closed and associative under the binary operation ‘*’, and it has an identity element ‘e’.
- 3.
Chomsky made important contributions to linguistics and the theory of grammars. He is more widely known today as a critic of United States foreign policy.
- 4.
Backus–Naur form is named after John Backus and Peter Naur. It was created as part of the design of the Algol 60 programming language, and is used to define the syntax rules of the language.
- 5.
It is possible that what the programmer has written is not be what the programmer had intended.
- 6.
There are attribute (or affix) grammars that extend the syntactic description of the language with supplementary elements covering the semantics. The process of adding semantics to the syntactic description is termed decoration.
- 7.
Hoare was influenced by earlier work by Floyd on assigning meanings to programs using flowcharts (Floyd 1967).
- 8.
Total correctness is expressed using {P}a{Q} and program fragment a is totally correct for precondition P and postcondition Q if and only if whenever a is executed in any state in which P is satisfied then execution terminates, and the resulting state satisfies Q.
- 9.
This virtual stack-based machine was originally designed by Peter Landin (a British computer scientist) to evaluate lambda calculus expressions, and it has since been used as a target for several compilers. Landin was influenced by McCarthy’s LISP.
- 10.
This is similar to what a compiler does in that if errors are found during the compilation phase, the compiler halts and displays the errors and does not continue with code generation.
- 11.
This essentially expresses that the names of bound variables are unimportant.
- 12.
This essentially expresses the idea of function application.
- 13.
This essentially expresses the idea that two functions are equal if and only if they give the same results for all arguments.
References
Floyd R (1967) Assigning meanings to programs. Proc Symp Appl Math (19):19–32
Hoare CAR (1969) An axiomatic basis for computer programming. Commun ACM 12(10):576–585
Meyer (1990) Introduction to the theory of programming languages. Prentice Hall
Naur P (ed) (1960) Report on the algorithmic language, ALGOL 60. Commun ACM 3(5):299–314
O’Regan G (2006) Mathematical approaches to software quality. Springer, Berlin
O’Regan G (2016) Introduction to the history of computing. Springer, Berlin
Plotkin G (1981) A structural approach to operational semantics. Technical Report DAIM FN-19. Computer Science Department. Aarhus University, Denmark
Stoy J (1977) Denotational semantics. the scott-strachey approach to programming language theory. MIT Press
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O’Regan, G. (2020). Language Theory and Semantics. In: Mathematics in Computing. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-34209-8_12
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DOI: https://doi.org/10.1007/978-3-030-34209-8_12
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