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Questions tagged [logical-foundations]

Questions related to Logical Foundations course from the University of Pennsylvania

Logical Foundations course covers functional programming, basic concepts of logic, computer-assisted theorem proving, and Coq. First volume of the Software Foundations series.

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Logic: In_app_iff exercize

Trying to solve In_app_iff excersize from Logic chapter I came to this monstrosity: (* Lemma used later *) Lemma list_nil_app : forall (A : Type) (l : list A), l ++ [] = l. Proof. intros A l. induction l as [| n l' IHl']. - simpl.…
user4035
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Tactics: filter_exercise

(** **** Exercise: 3 stars, advanced (filter_exercise) This one is a bit challenging. Pay attention to the form of your induction hypothesis. *) Theorem filter_exercise : forall (X : Type) (test : X -> bool) …
user4035
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Logical foundations errors

I am passing through Logical foundations course and is facing the following errors: Strings undefined Lists.v, code: Definition manual_grade_for_rev_injective : option (nat*string) := None. Response: Error: The reference string was not found in…
user4035
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Require Export changes requirements in every file

I'm new to Coq, and currently going through the Software Foundations series of tutorials. However, I keep finding myself struggling with getting the Require Export part working on the first try, every file seemingly requiring a new strategy to work.…
Electric Coffee
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Software Foundations: apply ... with ... tactic

I'm try to run some simple examples on apply ... with ... tactic from Pierce's "Software Foundations". It seems that examples from book doesn't work for me: Theorem trans_eq: forall (X: Type) (n m o: Type), n = m -> m = o -> n =…
John Ostin
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Logic: excluded_middle_irrefutable

Here is the task from the book: Proving the consistency of Coq with the general excluded middle axiom requires complicated reasoning that cannot be carried out within Coq itself. However, the following theorem implies that it is always safe …
user4035
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Logic: evenb_double_conv

Theorem evenb_double_conv : forall n, exists k, n = if evenb n then double k else S (double k). Proof. (* Hint: Use the [evenb_S] lemma from [Induction.v]. *) intros n. induction n as [|n' IHn']. - simpl. exists O. simpl.…
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