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73 lines
1.6 KiB
Coq
73 lines
1.6 KiB
Coq
(** Formal Reasoning About Programs <http://adam.chlipala.net/frap/>
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* Supplementary Coq material: first-class functions and continuations
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* Author: Adam Chlipala
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* License: https://creativecommons.org/licenses/by-nc-nd/4.0/ *)
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Require Import Frap.
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Set Implicit Arguments.
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(** * Classic list functions *)
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Fixpoint map {A B : Set} (f : A -> B) (ls : list A) : list B :=
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match ls with
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| nil => nil
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| x :: ls' => f x :: map f ls'
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end.
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Fixpoint filter {A : Set} (f : A -> bool) (ls : list A) : list A :=
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match ls with
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| nil => nil
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| x :: ls' => if f x then x :: filter f ls' else filter f ls'
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end.
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Fixpoint foldl {A B : Set} (f : A -> B -> B) (acc : B) (ls : list A) : B :=
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match ls with
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| nil => acc
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| x :: ls' => foldl f (f x acc) ls'
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end.
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Record programming_languages := {
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Name : string;
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PurelyFunctional : bool;
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AppearedInYear : nat
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}.
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Definition pascal := {|
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Name := "Pascal";
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PurelyFunctional := false;
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AppearedInYear := 1970
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|}.
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Definition c := {|
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Name := "C";
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PurelyFunctional := false;
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AppearedInYear := 1972
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|}.
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Definition gallina := {|
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Name := "Gallina";
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PurelyFunctional := true;
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AppearedInYear := 1989
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|}.
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Definition haskell := {|
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Name := "Haskell";
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PurelyFunctional := true;
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AppearedInYear := 1990
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|}.
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Definition ocaml := {|
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Name := "OCaml";
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PurelyFunctional := false;
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AppearedInYear := 1996
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|}.
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Definition languages := [pascal; c; gallina; haskell; ocaml].
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Compute map Name languages.
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Compute map Name (filter PurelyFunctional languages).
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Compute foldl max 0 (map AppearedInYear languages).
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Compute foldl max 0 (map AppearedInYear (filter PurelyFunctional languages)).
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