This tutorial gives a motivation-driven introduction to a generic code generator framework in Isabelle for generating executable code in functional programming languages from logical specifications.

Emerging trends in proof styles and new applications of interactive proof assistants exploit the computational facilities of the provided proof language, reaping enormous benefits in proof size and convenience to the user. However, the resulting proof objects really put the proof assistant to the test in terms of computational time required to check them. We present a novel translation of the terms of the full Calculus of (Co)Inductive Constructions to OCAML programs. Building on this translation, we further present a new fully featured version of COQ that offloads much of the computation required during proof checking to a vanilla, state of the art and fine tuned compiler. This modular scheme yields substantial performance improvements over existing systems at a reduced implementation cost. The work presented here builds on previous work described in [GL02], but we place particular emphasis in this paper on the fact that this scheme is in fact an instance of untyped normalization by evaluation [FR04, Lin05, AHN08, Boe10].

HOL-TestGen is a specification and test case generation environment extending the interactive theorem prover Isabelle/HOL. As such, HOL-TestGen allows for an integrated workflow supporting interactive theorem proving, test case generation, and test data generation. The HOL-TestGen method is two-staged: first, the original formula is partitioned into test cases by transformation into a normal form called test theorem. Second, the test cases are analyzed for ground instances (the test data) satisfying the constraints of the test cases. Particular emphasis is put on the control of explicit test-hypotheses which can be proven over concrete programs. Due to the generality of the underlying framework, our system can be used for black-box unit, sequence, reactive sequence and white-box test scenarios. Although based on particularly clean theoretical foundations, the system can be applied for substantial case-studies.

We use higher-order logic to verify a quantifier elimination procedure for linear arithmetic over ordered fields, where the coefficients of variables are multivariate polynomials over another set of variables, we call parameters. The procedure generalizes Ferrante and Rackoff’s algorithm for the non-parametric case. The formalization is based on axiomatic type classes and automatically carries over to e.g. the rational, real and non-standard real numbers. It is executable, can be applied to HOL formulae by reflection and performs well on practical examples.

This article formalizes normalization by evaluation as implemented in Isabelle. Lambda calculus plus term rewriting is compiled into a functional program with pattern matching. It is proved that the result of a successful evaluation is a) correct, i.e. equivalent to the input, and b) in normal form. An earlier version of this theory is described in a paper by Aehlig et al. [1]. The normal form proof is not in that paper. 1

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