Isabelle Tutorial: System, HOL and Proofs

Transcription

1 Isabelle Tutorial: System, HOL and Proofs Burkhart Wolff, Makarius Wenzel Université Paris-Sud

2 What we will talk about

3 What we will talk about Isabelle with: its System Framework the Logical Framework the Isabelle/HOL Environment Proof Contexts and Structured Proof Tactic Proofs ( apply style )

4 The Isabelle System Framework

5 Isabelle Architecture Modern Isabelle Architecture consists of 5 identifyable layers SML layer Kernel & Proof Object Layer Tactic Layer and decision procedures Isar Engine PIDE Framework and Interface Layer

6 Isabelle Architecture Observation: Effective parallelization is a PERVASIVE PROBLEM, that must be addressed PIDE jedit Scala System Interface records decision procedures datatypes kernel PO multi-core PolySML C1 C2 C3 C4

7 Isabelle Architecture In detail: PIDE jedit Scala System Interface records decision procedures datatypes kernel PO on the execution platform layer multi-core PolySML C1 C2 C3 C4

8 Isabelle Architecture In detail: PIDE jedit Scala System Interface decision procedures datatypes on the kernel layer kernel PO multi-core PolySML C1 C2 C3 C4

9 Isabelle Architecture In detail: PIDE jedit on layer of procedures and packages Scala System Interface decision procedures datatypes kernel PO multi-core PolySML C1 C2 C3 C4

10 Isabelle Architecture In detail: on the interface layer PIDE framework + Editor PIDE jedit Scala System Interface decision procedures datatypes kernel PO multi-core PolySML C1 C2 C3 C4

11 PIDE - GUI - Architecture (see PIDE - Project: u s e r Swing library installation manager src distribution server π de domain edit plugin domain view plugin integration layer JVM/ Scala inter face SML/ Scala inter face prover π de (Java / Scala) eg Isabelle (SML)

12 What is Isabelle as a System? A Document Processor where documents have a unique name may acyclicly import documents and consists of an command sequence where new commands may be intro duced on the fly (ie the system framework is extensible) A session (a collection of documents organized in a hierachy) may be frozen to a session (or configuration)

13 What is Isabelle as a System? Global View of a session Document / Theory A B C D

14 What is Isabelle as a System? Global View Document / Theory A atom detailed view: B C token token token D

15 What is Isabelle as a System? Document positions were evaluated to an implicit state, the theory context T Document / A Theory B C Θ 0 Θ 3-1 Θ 3-2 Θ 3 semantic evaluation as SML function D

16 What is Isabelle as a System? Document positions were evaluated to an implicit state, the theory context T Document / A Note: Theory stateless command evaluation No-sideeffects apart from state managed by Isabelle B C Θ 0 Θ 3-1 Θ 3-2 Θ semantic evaluation as SML function D

17 What is Isabelle as a System? Document positions were evaluated to an implicit state, the theory context T Document / A Theory B C Note: the theory context T can contain a type signature and a term signature, axioms, but also system configuration information etc Θ 0 Θ 3-1 Θ 3-2 Θ 3 semantic evaluation as SML function D

18 What is Isabelle as a System? Document positions were evaluated to an implicit state, the theory context T Note: Document / A and this is at the Theory beginning a minimal intuitionistic logic called in Isabelle/Pure B C Θ 0 Θ 3-1 Θ 3-2 Θ 3 semantic evaluation as SML function D

19 What is Isabelle as a System? Example theory D imports B C begin section{* First Section *} text{* Some mathematical \<alpha>}*} ML{* fun fac x = if x = 0 then 1 else x*fac(x-1) *} ML{* fac 10 *} end

20 What is Isabelle as a System? Example theory D imports B C begin section{* First Section *} text{* Some mathematical \<alpha>}*} ML{* fun fac x = if x = 0 then 1 else x*fac(x-1) *} ML{* fac 10 *} end

21 What is Isabelle as a System? Example theory D imports B C begin section{* First Section *} text{* Some mathematical \<alpha>}*} ML{* fun fac x = if x = 0 then 1 else x*fac(x-1) *} ML{* fac 10 *} end fac visible here because the ML environment is part of T

22 Demo I Start Isabelle (via the PIDE jedit) Browse demo1thy Commands: " text, section, subsection " ML " value " a browser for theorems: find_theorems Capabilities: hovering, jump-link,

23 Demo I

24 Main (Editing) Panel Demo I

25 Output Panel Demo I

26 Sidekick Panel/ [Documentation Panel Theories Panel] Demo I

27 Exercises Start Isabelle (via the PIDE/jEdit: isabelle jedit demo1thy) Explore Demo1thy: Set output window, modify texts and value-computations, ML-code Browse Editorthy ; Edit a (brief) document with mathematical notation Edit and evaluate a small SML program (see as primer)

28 Parallel Nano-Kernel LCF-Architecture in the jedit - GUI (PIDE) fine-grained, asynchronous parallelism (Isabelle2009-2)