소프트웨어 기초(Software Foundations)

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lazyswamp 2017. 9. 11. 11:55

소프트웨어 기초 (Software Foundations) 번역

- 2017년 9월 대학원 강의로 소프트웨어 기초를 진행하면서 번역한 것을 위 웹 주소에 올려놓았습니다.

[ 교재 ]

New volumes : Vol 1. Logical Foundations, Vol 2. Programming Language Foundations

- https://softwarefoundations.cis.upenn.edu/

[ 강의 로드맵 ]

Vol 1. Logical Foundations : Preface

Vol 1. Logical Foundations : Functional Programming in Coq (Basics)

Vol 1. Logical Foundations : Proof by Induction (Induction)

Vol 1. Logical Foundations : Working with Structured Data (Lists)

Vol 1. Logical Foundations : Polymorphism and Higher-Order Functions (Poly)

Vol 1. Logical Foundations : Logic in Coq (Logic)

Vol 1. Logical Foundations : Inductive Defined Propositions (IndProp)

Vol 1. Logical Foundations : Simple Imperative Programs (Imp)

Vol 2. Programming Language Foundations : Program Equivalence (Equiv)

Vol 2. Programming Language Foundations : Hoare Logic, Part I (Hoare)

[ 전술 목록 : Ch. More Basic Tactics in Volume 1 ]

intros: move hypotheses/variables from goal to context
reflexivity: finish the proof (when the goal looks like e = e)
apply: prove goal using a hypothesis, lemma, or constructor
apply... in H: apply a hypothesis, lemma, or constructor to a hypothesis in the context (forward reasoning)
apply... with...: explicitly specify values for variables that cannot be determined by pattern matching
simpl: simplify computations in the goal
simpl in H: ... or a hypothesis
rewrite: use an equality hypothesis (or lemma) to rewrite the goal
rewrite ... in H: ... or a hypothesis
symmetry: changes a goal of the form t=u into u=t
symmetry in H: changes a hypothesis of the form t=u into u=t
unfold: replace a defined constant by its right-hand side in the goal
unfold... in H: ... or a hypothesis
destruct... as...: case analysis on values of inductively defined types
destruct... eqn:...: specify the name of an equation to be added to the context, recording the result of the case analysis
induction... as...: induction on values of inductively defined types
inversion: reason by injectivity and distinctness of constructors
assert (H: e) (or assert (e) as H): introduce a "local lemma" e and call it H
generalize dependent x: move the variable x (and anything else that depends on it) from the context back to an explicit hypothesis in the goal formula

[전술 목록 : Ch.3 from Coq in a Hurry ]