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Questions tagged [isabelle]

Isabelle is a generic proof assistant, with Isabelle/HOL as main instance.

Isabelle is a generic proof assistant, which is best-known for its Isabelle/HOL instance. It allows mathematical formulas to be expressed in a formal language and provides tools for proving those formulas in a logical calculus. HOL specifications may be turned into program code in SML, OCaml, Haskell, or Scala. Isabelle includes many add-on tools like CVC4, Z3, SPASS, E prover.

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whats the standard way of stating that some sets partition another

I would write {1, 2} + {3} + {4} = {1, 2, 3, 4} in maths to say that the sets on LHS partition that of RHS. Is there something similar in isabelle so I don't need to go through all the permutations {1, 2} intersect {3} = {} etc. [EDIT] I've found…
simonzack
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Isabelle: new axiom for undefined functions

I am working on a theory where I use extensional functions defined in the Funcset theory quite heavily. I need to work with function valued functions where both the function, and the values are extensional. It is quite annoying that some of my…
Dávid Kertész
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Automated tools for applying formal methods to verify security policy in existing software

I am new to the Formal Methods arena, but I feel I have an educated grasp on its applications. However, I only seem to encounter formal methods as applied to the development process, as the software is created. I'd like to be able to apply formal…
Methmal Forods
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Using type classes to overload notation for constructors (now a namespace issue)

This is a derivative question of Existing constants (e.g. constructors) in type class instantiations. The short question is this: How can I prevent the error that occurs due to free_constructors, so that I can combine the two theories that I include…
user4655408
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I need a working tutorial on Isabelle and Sledgehammer

I installed the latest Isabelle/jEdit package to my Windows computer. I used the official package from the Isabelle website. Then I opened tutorials which are on the Isabelle webpage and I started computer experiments. I realized immediately that…
Amateur
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How to invoke functions in Isabelle/HOL?

Here is a theory I've taken from Isabelle Tutorial. It has ways to prove theorems but I was wondering how one would call the app function below with two lists. theory ToyList imports Main begin datatype 'a list = Nil | Cons 'a "'a list" …
bazinga
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how to make an example to test the rev_app immediately after lemma proved. an starting example for custom lemma

expect to use the subgoal to run the list which defined by let? aa = [1,2] and run rev_app on this aa and show the value as [2,1] theory Scratch2 imports Datatype begin datatype 'a list = Nil ("[]") | Cons 'a "'a list" (infixr "#"…
Ho Yeung Lee
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Isabelle: locale interpration about record fails in proof

Using the Algebra library, I encountered the following problem. In a proof I wanted to interpret the additive structure of a ring as a group. Here is a sample code: theory aaa imports "~~/src/HOL/Algebra/Ring" begin lemma assumes "ring R" shows…
Dávid Kertész
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Doing this proof automatically on Isabelle

I satarted to work with Isabelle a few weeks ago and it's hard to me to do some proves automatically. I've just use the rule "less_induct" to show a property on a list. theorem cuenta_ordena_1: "cuenta (ordena xs) y = cuenta xs y" proof(induct…
MaríaCC
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Proving topology statement in Isabelle

I have been working with limits and topology in and I want to prove the following lemma: lemma fixes f g :: "real ⇒ real" assumes "open S" "∀a b. a < b <--> f a < f b" "∀a. (f a)>0" "continuous_on UNIV (f)" "∀w∈S. ∀h. (w+h)∈S --> h * (f w) ≤ g (w+h)…
A K
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Ignoring a case to prove a goal through elimination

I have the following lemma to show the derivative of f at x is D. lemma lm1: assumes "(∀h. (f (x + h) - f x) = D*h)" shows "DERIV f x :> D" proof cases assume notzero: "∀h. h ≠ 0" have cs1: "(λh. (f (x + h) - f x) / h) -- 0 --> D" using assms…
A K
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Create a quotient-lifted type with polymorphism over working set and equivalence relation in Isabelle/HOL

I would like to create a quotient type with quotient_type in Isabelle/HOL in which I would left "non-constructed" the non-empty set S and the equivalence relation ≡. The goal is for me to derive generic properties w.r.t. S and ≡ over the…
Hai Nguyen Van
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Function definition with index/subscripts

I am trying to define the function: Fi(xi) = real However I am finding it hard to implement subscripts into my function. The subscript i has to be a natural number, whereas x is a real number, and the output is also real. I have tried defining the…
A K
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Declaring a coercion from a record type

I have a record type record foo = main_stuff :: "nat list" other_stuff :: "int" If f has type foo, I would like to be able to have f automatically coerced to the nat list in the main_stuff field, when necessary. For instance, I would like to be…
John Wickerson
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Customize proof-general's dark theme for Isabelle

I'm a novice in both Isabelle and Proof General. I am trying to set a dark theme in Proof General to use with Isabelle, but no matter what theme I choose (e.g. tango-dark, ample, monokai, etc.), the untouched inner syntax is highlighted in a very…
Phil
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