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09:00-10:30 Session 125M
Students' Proof Assistant (SPA)

ABSTRACT. The Students' Proof Assistant (SPA) aims to both teach how to use a proof assistant like Isabelle but also to teach how reliable proof assistants are built. Technically it is a miniature proof assistant inside the Isabelle proof assistant. In addition we conjecture that a good way to teach structured proving is with a concrete prover where the connection between semantics, proof system, and prover is clear. In fact, the proofs in Lamport's TLAPS proof assistant have a very similar structure to those in the declarative prover SPA. To illustrate this we compare a proof of Pelletier's problem 43 in TLAPS, Isabelle/Isar and SPA.

Natural Deduction Assistant (NaDeA)

ABSTRACT. We present the Natural Deduction Assistant (NaDeA) and discuss its advantages and disadvantages as a tool for teaching logic. In particular we compare our approach to natural deduction in the Isabelle proof assistant. NaDeA is available online: https://nadea.compute.dtu.dk/

Rating of Geometric Automated Theorem Provers

ABSTRACT. The field of geometric automated theorem provers has a long and rich history, form the early synthetic provers in the 50th of last century to nowadays provers.

Establishing a rating among them will be useful for the improvement of the current methods/implementations. With wider scope, more efficient, with readable proofs and with trustworthy proofs.

We need a common test bench: a common language to describe the geometric problems; a large set of problems and a set of measures to achieve such goal.

10:30-11:00Coffee Break
11:00-12:30 Session 127M
Lucas Interpretation from Programmers’ Perspective

ABSTRACT. Within the process of pushing the ISAC prototype towards maturity for service in engineering courses one of the most crucial points is to make programming convenient in ISAC . Programming means to describe mathematical algorithms (a functional program without input/output, so no concern with didactics and dialogues, which are handled by a separate component not discussed here) of engineering problems by use of libraries of methods and specifications as well as of respective theories. ISAC builds upon the theorem prover Isabelle, which offers a convenient programming environment and a specific function package. This is considered an appropriate means to improve programming in ISAC as required. The first steps of improvement are described in this paper and the other steps are listed in detail.

GeoCoq: formalized foundations of geometry

ABSTRACT. Geometry is central in both the history and teaching of the structure of mathematical proofs and the axiomatic method.

In this talk, we will give an overview of the GeoCoq library. The library developed in collaboration with P.Boutry, G. Braun, C. Gries and P. Schreck consists in a formalization of geometry using the Coq proof assistant.

Starting from the foundations based on either Euclid’s, Tarski’s, or Hilbert’s axiom systems, we formalized the traditional results which can be used for high-school exercises.

We will discuss the axiomatizations and the automation necessary for use in the classroom.

Based on some examples taken from highschool exercices, we will revisit some traditional proofs from a formal point of view.

12:30-14:00Lunch Break
14:00-15:30 Session 128M
Towards intuitive reasoning in axiomatic geometry

ABSTRACT. Proving lemmas in synthetic geometry is an often time-consuming endeavour - many intermediate lemmas need to be proven before interesting results can be obtained. Automated theorem provers (ATP) made much progress in the recent years and can prove many of these intermediate lemmas automatically. The interactive theorem prover Elfe accepts mathematical texts written in fair English and verifies the text with the help of ATP. Geometrical texts can thereby easily be formalized in Elfe, leaving only the cornerstones of a proof to be derived by the user. This allows for teaching axiomatic geometry to students without prior experience in formal mathematics.

Proving in the Isabelle Proof Assistant that the Set of Real Numbers is not Countable

ABSTRACT. We present a new succinct proof of the uncountability of the real numbers – optimized for clarity – based on the proof by Benjamin Porter in the Isabelle Analysis theory.

15:30-16:00Coffee Break
16:00-18:00 Session 130L

ThEdu Business Meeting

ThEdu'18 business meeting

ABSTRACT. ThEdu'18 business meeting

ThEdu'18 post proceedings at EPTCS

ThEdu'19 - where, when and other organizational issues.

19:15-21:30 Workshops dinner at Magdalen College

Workshops dinner at Magdalen College. Drinks reception from 7.15pm, to be seated by 7:45 (pre-booking via FLoC registration system required; guests welcome).