Abstract
An interpreter for an imperative programming language called Minila has been formally specified in CafeOBJ, an executable specification language, and so have a virtually machine (VM) and a compiler. The compiler transforms a Minila program into an instruction sequence processed by the VM. Since the formal specifications are executable, it is doable to test if for any concrete terminating program p the result of interpreting p is the same as the one of processing by the VM the instruction sequence generated from p by the compiler, where the result is an environment, a variable-value pair collection. The equivalence is called the Minila compiler correctness with respect to p. In addition to test, properties of CafeOBJ specifications can be theorem proved by writing what are called proof scores in CafeOBJ and executing them with CafeOBJ. The Minila compiler correctness for all terminating programs in Minila has been theorem proved.
The research was first conducted by the second author (A2) [1] partially supervised by the third author (A3) when A2 was a Master’s student of JAIST and then reconducted by the first author (A1) [2] supervised by A3 totally independent from A2 when A1 was an internship student of JAIST. The paper is based on the first author’s achievement. This work was partially supported by JSPS KAKENHI Grant Number 26240008.
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Notes
- 1.
Minila consists of a minimal essence of procedural programming languages, such as C, and has been used by the third author, et al. for educational purposes (www.jaist.ac.jp/~ogata/lecture/i217/).
- 2.
A set of trans rules could be included in a CafeOBJ specification, but trans rules are not used in this paper.
- 3.
The terminology “proof score” has been coined by Joseph Goguen [5]. The authors suppose that since he was very enthusiastic to music, the terminology came from “music score”.
- 4.
\((\forall y:T2)(\forall z:T3)((\exists x:T1)p(x,y) \Rightarrow q(y,z))\) is equivalent to \((\forall x:T1)(\forall y:T2)(\forall z:T2)(p(x,y) \Rightarrow q(y,z))\).
- 5.
Some descriptions on the proof score are inserted.
- 6.
The slides used are available at http://www.jaist.ac.jp/~kokichi/class/TUW1207+08/.
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Daudier, D., Ngoc Quoc Bao, T., Ogata, K. (2018). A Proof Score Approach to Formal Verification of an Imperative Programming Language Compiler. In: Tian, C., Nagoya, F., Liu, S., Duan, Z. (eds) Structured Object-Oriented Formal Language and Method. SOFL+MSVL 2017. Lecture Notes in Computer Science(), vol 10795. Springer, Cham. https://doi.org/10.1007/978-3-319-90104-6_13
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