Theory Eval_Examples

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theory Eval_Examples
imports Eval Rational
begin

(*  ID:         $Id: Eval_Examples.thy,v 1.10 2008/01/31 10:44:43 haftmann Exp $
    Author:     Florian Haftmann, TU Muenchen
*)

header {* Small examples for evaluation mechanisms *}

theory Eval_Examples
imports Eval "~~/src/HOL/Real/Rational"
begin

text {* evaluation oracle *}

lemma "True ∨ False" by eval
lemma "¬ (Suc 0 = Suc 1)" by eval
lemma "[] = ([]:: int list)" by eval
lemma "[()] = [()]" by eval
lemma "fst ([]::nat list, Suc 0) = []" by eval

text {* SML evaluation oracle *}

lemma "True ∨ False" by evaluation
lemma "¬ (Suc 0 = Suc 1)" by evaluation
lemma "[] = ([]:: int list)" by evaluation
lemma "[()] = [()]" by evaluation
lemma "fst ([]::nat list, Suc 0) = []" by evaluation

text {* normalization *}

lemma "True ∨ False" by normalization
lemma "¬ (Suc 0 = Suc 1)" by normalization
lemma "[] = ([]:: int list)" by normalization
lemma "[()] = [()]" by normalization
lemma "fst ([]::nat list, Suc 0) = []" by normalization

text {* term evaluation *}

value "(Suc 2 + 1) * 4"
value (code) "(Suc 2 + 1) * 4"
value (SML) "(Suc 2 + 1) * 4"
value ("normal_form") "(Suc 2 + 1) * 4"

value "(Suc 2 + Suc 0) * Suc 3"
value (code) "(Suc 2 + Suc 0) * Suc 3"
value (SML) "(Suc 2 + Suc 0) * Suc 3"
value ("normal_form") "(Suc 2 + Suc 0) * Suc 3"

value "nat 100"
value (code) "nat 100"
value (SML) "nat 100"
value ("normal_form") "nat 100"

value "(10::int) ≤ 12"
value (code) "(10::int) ≤ 12"
value (SML) "(10::int) ≤ 12"
value ("normal_form") "(10::int) ≤ 12"

value "max (2::int) 4"
value (code) "max (2::int) 4"
value (SML) "max (2::int) 4"
value ("normal_form") "max (2::int) 4"

value "of_int 2 / of_int 4 * (1::rat)"
value (code) "of_int 2 / of_int 4 * (1::rat)"
value (SML) "of_int 2 / of_int 4 * (1::rat)"
value ("normal_form") "of_int 2 / of_int 4 * (1::rat)"

value "[]::nat list"
value (code) "[]::nat list"
value (SML) "[]::nat list"
value ("normal_form") "[]::nat list"

value "[(nat 100, ())]"
value (code) "[(nat 100, ())]"
value (SML) "[(nat 100, ())]"
value ("normal_form") "[(nat 100, ())]"


text {* a fancy datatype *}

datatype ('a, 'b) bair =
    Bair "'a::order" 'b
  | Shift "('a, 'b) cair"
  | Dummy unit
and ('a, 'b) cair =
    Cair 'a 'b

value "Shift (Cair (4::nat) [Suc 0])"
value (code) "Shift (Cair (4::nat) [Suc 0])"
value (SML) "Shift (Cair (4::nat) [Suc 0])"
value ("normal_form") "Shift (Cair (4::nat) [Suc 0])"

end

lemma

  True ∨ False  [!]

lemma

  Suc 0  Suc 1  [!]

lemma

  [] = []  [!]

lemma

  [()] = [()]  [!]

lemma

  fst ([], Suc 0) = []  [!]

lemma

  True ∨ False  [!]

lemma

  Suc 0  Suc 1  [!]

lemma

  [] = []  [!]

lemma

  [()] = [()]  [!]

lemma

  fst ([], Suc 0) = []  [!]

lemma

  True ∨ False  [!]

lemma

  Suc 0  Suc 1  [!]

lemma

  [] = []  [!]

lemma

  [()] = [()]  [!]

lemma

  fst ([], Suc 0) = []  [!]