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Add another example

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-09-04 05:39:35 -07:00
parent 7a8d15e282
commit 9f34f96b08
3 changed files with 40 additions and 1 deletions
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13
examples/lean/ex2.lean
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@ -1,6 +1,17 @@
Theorem simple (p q r : Bool) : (p ⇒ q) ∧ (q ⇒ r) ⇒ p ⇒ r :=
Discharge (λ H1, Discharge (λ H2, MP (Conjunct2 H1) (MP (Conjunct1 H1) H2)))
Discharge (λ H_pq_qr, Discharge (λ H_p,
let P_pq := Conjunct1 H_pq_qr,
P_qr := Conjunct2 H_pq_qr,
P_q := MP P_pq H_p
in MP P_qr P_q))
Set pp::implicit true
Show Environment 1
Theorem simple2 (a b c : Bool) : (a ⇒ b ⇒ c) ⇒ (a ⇒ b) ⇒ a ⇒ c :=
Discharge (λ H_abc, Discharge (λ H_ab, Discharge (λ H_a,
let P_b := (MP H_ab H_a),
P_bc := (MP H_abc H_a)
in MP P_bc P_b)))
Show Environment 1

27
examples/lean/ex3.lean Normal file
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@ -0,0 +1,27 @@
Theorem and_comm (a b : Bool) : (a ∧ b) ⇒ (b ∧ a) :=
Discharge (λ H_ab, Conj (Conjunct2 H_ab) (Conjunct1 H_ab))
Theorem or_comm (a b : Bool) : (a ∨ b) ⇒ (b ∨ a) :=
Discharge (λ H_ab, DisjCases H_ab
(λ H_a, Disj2 b H_a)
(λ H_b, Disj1 a H_b))
(* ---------------------------------
(EM a) is the excluded middle a ∨ ¬a
(MT H H_na) is Modus Tollens with
H : (a ⇒ b) ⇒ a)
H_na : ¬a
produces
¬(a ⇒ b)
NotImp1 applied to
(MT H H_na) : ¬(a ⇒ b)
produces
a
----------------------------------- *)
Theorem pierce (a b : Bool) : ((a ⇒ b) ⇒ a) ⇒ a :=
Discharge (λ H, DisjCases (EM a)
(λ H_a, H_a)
(λ H_na, NotImp1 (MT H H_na)))
Show Environment 3

1
src/shell/CMakeLists.txt
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@ -4,6 +4,7 @@ add_executable(lean lean.cpp)
target_link_libraries(lean ${EXTRA_LIBS})
add_test(example1 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/lean/ex1.lean")
add_test(example2 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/lean/ex2.lean")
add_test(example3 ${CMAKE_CURRENT_BINARY_DIR}/lean "${LEAN_SOURCE_DIR}/../examples/lean/ex3.lean")
add_test(NAME leantests
WORKING_DIRECTORY "${LEAN_SOURCE_DIR}/../tests/lean"
COMMAND "./test.sh" "${CMAKE_CURRENT_BINARY_DIR}/lean")