If proofs are equivalent to programs

If proofs are equivalent to programs (in a precise sense!), then how ...

In proofs there is no such jerry rigging, your proof is either correct or it is not. I'd say proofs are more similar to algorithms than programs ...

How does the “proofs as programs” correspondence work for equality?

A proof of a=b is a program that transforms a and b into a common expression using some given rewriting rules.

What goes into proving two complicated programs are equivalent?

Formal analysis today is usually done on module or unit level. Unfortunately I'm not aware of a common metric which allows to predict if a ...

Proofs are Programs: A Few Examples of the Curry-Howard ...

Proofs can be transformed in programs, and programs can be transformed into proofs. If you have a proof, you can get a program out of it for free.

Proving equivalence of programs - Stack Overflow

To prove this across many optimizations (i.e. at scale), typically you might first throw some random inputs at both sequences. If they're not ...

Analogies between programs and proofs

It should help you see some of the similarities between the two processes, writing a program and writing a proof, and help you apply some of what you have ...

The Deep Link Equating Math Proofs and Computer Programs

Simply stated, the Curry-Howard correspondence posits that two concepts from computer science (types and programs) are equivalent, respectively, ...

Writing code in a functional programming language is equal to writing math proofs since program you are writing is a proof.

Curry–Howard correspondence - Wikipedia

In programming language theory and proof theory, the Curry–Howard correspondence is the direct relationship between computer programs and mathematical ...

How to determine whether two programs are 'algorithmically ... - Quora

Proof of algorithm equivalence involves rigorous mathematical proofs that may be concise and clear , or labyrinthine and murky. All such ...

Lab: Program Equivalence Proofs

The equivalence symbol (≡), LaTeX: \equiv ) acts like equality in that it asserts that the left- and right-hand sides of the symbol are equivalent. We say that ...

Proving Equivalence - Functional Programming in Lean

In other words, f=g can be proved by proving that f(x)=g(x) for all possible inputs x. This principle is called function extensionality. Function extensionality ...

Equiv: Program Equivalence - Software Foundations

Proof: Suppose b is equivalent to b' and c is equivalent to c'. We must show, for every st and st', that st =[ ...

Proofs about Programs - Princeton University

Idea 1: The fundamental definition of when programs are equal. Idea 2: A fundamental proof principle. two expressions are equal if and only if: • they both ...

Proofs as Programs - CMU School of Computer Science

In this chapter we investigate a computational interpretation of constructive proofs and relate it to functional programming. On the propositional fragment.

A Language-Independent Proof System for Full Program Equivalence

not; nevertheless, our proof system shows that the two programs are fully equivalent (even if we cannot establish termination or divergence of either one).

Proofs, Programs, and Pontification - cadlag dot org - Home

The “programs are proofs” correspondence links certain proof calculi, such as natural deduction, to certain models of computation, such as the ...

Programming Proofs and Proving Programs - YouTube

... of proofs, programs, and the correspondence between them, is one of the most significant intellectual developments of the 20th century. That ...

So proofs and programs are isomorphic. We know there are ...

To a first approximation, the Curry–Howard correspondence says that programming and proving are the same. This is literally true if "programming" and "proving" ...

When are two proofs of the same theorem really different proofs

A possible definition, which unfortunately only covers a portion of cases, is the following: two proofs are non-equivalent if one generalizes ...