Logic for exact real arithmetic

Continuing earlier work of the first author with U. Berger, K. Miyamoto and H. Tsuiki, it is shown how a division algorithm for real numbers given as a stream of signed digits can be extracted from an appropriate formal proof. The property of being a real number represented as a stream is formulated by means of coinductively defined predicates, and formal proofs involve coinduction. The proof assistant Minlog is used to generate the formal proofs and extract their computational content as terms of the underlying theory, a form of type theory for finite or infinite data. Some experiments with running the extracted term are described, after its translation to Haskell

Butter Mountains, Milk Lakes and Optimal Price Limiters

It is known that simple price limiters may have unexpected consequences in irregular commodity price fluctuations between bull and bear markets and complicated impacts on the size of buffer stocks. In particular, imposing a lower price boundary may lead to a huge buffer stock, e.g. to a ?butter mountain? or a ?milk lake? and this is a real problem for regulators since storage costs may become impossible to finance over time. The relation between price limiters and the size of buffer stocks is nontrivial and there may exist some optimal price limiters which require only weak market interventions and thus provide a rather inexpensive option to regulate commodity markets. In this paper, we use a simple commodity market model to explore the relation between price limiters and the average growth rate of the buffer stocks. It is found that these optimal price limiter levels are simply the minimum values of unstable periodic orbits of the underlying deterministic system.commodity markets; price stabilization; limiter control; butter mountains and milk lakes

Internalising modified realisability in constructive type theory

A modified realisability interpretation of infinitary logic is formalised and proved sound in constructive type theory (CTT). The logic considered subsumes first order logic. The interpretation makes it possible to extract programs with simplified types and to incorporate and reason about them in CTT.Comment: 7 page

Extracting verified decision procedures: DPLL and Resolution

This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we formalize a completeness proof for the DPLL proof system and extract a SAT solver from it. When applied to a propositional formula in conjunctive normal form the program produces either a satisfying assignment or a DPLL derivation showing its unsatisfiability. We use non-computational quantifiers to remove redundant computational content from the extracted program and translate it into Haskell to improve performance. We also prove the equivalence between the resolution proof system and the DPLL proof system with a bound on the size of the resulting resolution proof. This demonstrates that it is possible to capture quantitative information about the extracted program on the proof level. The formalization is carried out in the interactive proof assistant Minlog

Extracting Imperative Programs from Proofs: In-place Quicksort

The process of program extraction is primarily associated with functional programs with less focus on imperative program extraction. In this paper we consider a standard problem for imperative programming: In-place Quicksort. We formalize a proof that every array of natural numbers can be sorted and apply a realizability interpretation to extract a program from the proof. Using monads we are able to exhibit the inherent imperative nature of the extracted program. We see this as a first step towards an automated extraction of imperative programs. The case study is carried out in the interactive proof assistant Minlog

PENGADAAN GURU SEKOLAH DASARDI YAYASAN HANG TUAH CABANG SURABAYA

Keberhasilan lembaga pendidikan dalam meningkatkan mutu pendidikan dipengaruhi oleh kualitas guru di lembaga. Pengadaan guru mempunyai peran menyediakan guru yang berkualitas dan sesuai dengan kebutuhan lembaga. Pengadaan guru sekolah dasar di Yayasan Hang Tuah Cabang Surabaya terdiri dari rekrutmen dan seleksi. Penelitian ini bertujuan untuk mendeskripsikan rekrutmen guru SD di Yayasan Hang Tuah Cabang Surabaya yang meliputi sumber internal dan eksternal dan proses seleksi guru SD di Yayasan Hang Tuah Cabang Surabaya yang meliputi seleksi administratif, wawancara, tes mengajar dan keputusan seleksi. Penelitian ini menggunakan pendekatan kualitatif dengan metode deskriptif dan rancangan penelitian studi kasus. Teknik pengumpulan data menggunakan wawancara, observasi dan studi dokumentasi. Data dianalisis dengan melakukan reduksi data, penyajian data dan verifikasi data. Pengecekan keabsahan data dilakukan dengan kredibilitas, transferabilitas, dependabilitas, dan konfirmabilitas Hasil dari penelitian ini yaitu: (1) pengadaan guru SD di Yayasan Hang Tuah cabang Surabaya adalah kegiatan yang dilakukan untuk memperoleh guru yang bermutu pada jenjang SD melalui rekrutmen dan proses seleksi guru; (2) pengadaan guru SD di Yayasan Hang Tuah Cabang Surabaya telah dilakukan sesuai dengan proses pengadaan yang terdiri dari rekrutmen dan seleksi untuk memperoleh guru yang bermutu dalam mendukung peningkatan mutu pendidikan SD di Yayasan Hang Tuah Cabang Surabaya; (3) rekrutmen guru SD di Yayasan Hang Tuah Cabang Surabaya adalah proses pencarian pelamar dari sumber internal dan eksternal. Proses pencarian pelamar dari sumber internal meliputi Kepala sekolah mencari pelamar, melakukan penilaian, merekomendasikan ke yayasan, yayasan menerima surat lamaran, dan melakukan instruksi. Proses pencarian pelamar dari sumber eksternal meliputi penerimaan surat lamaran, pengklasifikasian surat lamaran dan pengarsipan surat lamaran; (4) proses seleksi guru SD di Yayasan Hang Tuah Cabang Surabaya adalah tahap-tahap memilih dan menentukan pelamar yang akan diterima melalui serangkaian kegiatan yaitu seleksi administratif, wawancara, tes mengajar dan keputusan seleksi dengan memegang kriteria yang telah ditetapkan lembaga pada setiap tahapan; dan (5) Data rekrutmen dan seleksi pelamar yang telah diterima sebagai guru SD di Yayasan Hang Tuah Cabang Surabaya diarsipkan di ruang Seksi Administrasi dan Logistik dan digunakan untuk analisis pengadaan guru SD berikutnya serta pembinaan karir guru.Kata Kunci: pengadaan guru, rekrutmen guru, seleksi gur