A Simple Java Code Generator for ACL2 Based on a Deep Embedding of ACL2 in Java

2022

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This paper describes a code generator that translates ACL2 constructs to corresponding Java constructs, according to a shallow embedding of ACL2 in Java. Starting from purely functional ACL2 code, the generated Java code exhibits imperative and object-oriented features like destructive updates, loops, and overloading. The overall translation from ACL2 to Java is fairly elaborate, consisting of several ACL2-to-ACL2 pre-translation steps, an ACL2-to-Java proper translation step, and several Java-to-Java post-translation steps. Experiments suggest that the generated Java code is not much slower than the ACL2 code. The code generator can also recognize, and translate to Java, ACL2 representations of certain Java constructs, forerunning a code generation approach based on a shallow embedding of Java in ACL2 (i.e. going the other way). This code generator builds upon, and significantly extends, a simple Java code generator for ACL2 based on a deep embedding of ACL2 in Java.

Section: Introductionmentioning

confidence: 86%

A Complex Java Code Generator for ACL2 Based on a Shallow Embedding of ACL2 in Java

2022

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“…A large and interesting subset of data type refinements involves isomorphic mappings between abstract and concrete representations; examples are refining finite sets to duplicate-free ordered lists or to bit vectors, adding record components that are computable from the others for caching, and some perhaps less expected ones as in Section 4.2. Many other data type refinements do not involve isomorphic mappings; see Section 6. In an interactive theorem prover like ACL2, stepwise program refinement can be carried out using predicates over (deeply or shallowly embedded) implementations as specifications s i and (reversed) implication as ↝ (an approach called 'pop-refinement') [4,5]; and c ↦ may be realized either as a ↝ sequence entirely in the logic of the prover [4], or via a more typical code generator [6] [23,Topic ATJ]. The APT (Automated Program Transformations) library [23, Topic APT] provides tools to carry out derivation steps s i ↝ s i+1 via automated transformations (as outlined above) in ACL2.…”

Section: Background Motivation and Contributionmentioning

confidence: 99%

“…• osi, the isomorphism from new to old, like ξ −1 or υ −1 in Section 2. Defiso attempts to prove the following applicability conditions (assuming unary functions): 6 • (old o) ⇒ (new (iso o)), i.e. iso maps values in old to values in new.…”

Section: Establishing Isomorphic Mappingsmentioning

confidence: 99%

“…In an interactive theorem prover like ACL2, stepwise program refinement can be carried out using predicates over (deeply or shallowly embedded) implementations as specifications s i and (reversed) implication as ↝ (an approach called 'pop-refinement') [4,5]; and c ↦ may be realized either as a ↝ sequence entirely in the logic of the prover [4], or via a more typical code generator [6] [23,Topic ATJ]. The APT (Automated Program Transformations) library [23, Topic APT] provides tools to carry out derivation steps s i ↝ s i+1 via automated transformations (as outlined above) in ACL2.…”

mentioning

confidence: 99%

“…If X and Y are part of the required "interface" in s 0 of the program being derived, note that a wrapper f ≡ υ −1 ○ f ′ ○ ξ can be mechanically defined along with f ′ , provably satisfying f = f . This is different from the definition of f ′ that includes the isomorphic conversions: f only converts the input once and the output once, while the definition of f ′ that includes the isomorphic conversions performs several conversions at each recursive call 6. Sometimes this paper uses infix notations for logical connectives and equality 7.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Isomorphic Data Type Transformations

Westfold

2020

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In stepwise derivations of programs from specifications, data type refinements are common. Many data type refinements involve isomorphic mappings between the more abstract and more concrete data representations. Examples include refinement of finite sets to duplicate-free ordered lists or to bit vectors, adding record components that are functions of the other fields to avoid expensive recomputation, etc. This paper describes the APT (Automated Program Transformations) tools to carry out isomorphic data type refinements in the ACL2 theorem prover and gives examples of their use. Because of the inherent symmetry of isomorphisms, these tools are also useful to verify existing programs, by turning more concrete data representations into more abstract ones to ease verification. Typically, a data type will have relatively few interface functions that access the internals of the type. Once versions of these interface functions have been derived that work on the isomorphic type, higher-level functions can be derived simply by substituting the old functions for the new ones. We have implemented the APT transformations isodata to generate the former, and propagate-iso for generating the latter functions as well as theorems about the generated functions from the theorems about the original functions. Propagate-iso also handles cases where the type is a component of a more complex one such as a list of the type or a record that has a field of the type: the isomorphism on the component type is automatically lifted to an isomorphism on the more complex type. As with all APT transformations, isodata and propagate-iso generate proofs of the relationship of the transformed functions to the originals. Background, Motivation, and ContributionIn stepwise program refinement [10,24], an implementation is derived from a specification via a sequence of intermediate specifications. A derivation is a sequence s 0 ↝ s 1 ↝ ... ↝ s n c ↦ p, where: s 0 is a requirements specification in some specification language; s 1 ,...,s n are intermediate specifications in the same language; ↝ is a refinement relation (a preorder, i.e. reflexive and transitive); and p is an implementation in some programming language, obtained from s n via a code generator c

A Proof-Generating C Code Generator for ACL2 Based on a Shallow Embedding of C in ACL2

2022

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This paper describes a C code generator for ACL2 that recognizes ACL2 representations of C constructs, according to a shallow embedding of C in ACL2, and translates those representations to the represented C constructs. The code generator also generates ACL2 theorems asserting the correctness of the C code with respect to the ACL2 code. The code generator currently supports a limited but growing subset of C that already suffices for some interesting programs. This paper also offers a general perspective on language embedding and code generation.