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test(lean): add 'let' expression test

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura 2014-06-16 14:11:26 -07:00
parent 21c54755a9
commit 873a5c8605
2 changed files with 28 additions and 0 deletions
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23
tests/lean/let1.lean Normal file
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-- Correct version
check let bool : Type.{1} := Type.{0},
and (p q : bool) : bool := ∀ c : bool, (p → q → c) → c,
infixl `∧` 25 := and,
and_intro (p q : bool) (H1 : p) (H2 : q) : p ∧ q
:= λ (c : bool) (H : p → q → c), H H1 H2,
and_elim_left (p q : bool) (H : p ∧ q) : p
:= H p (λ (H1 : p) (H2 : q), H1),
and_elim_right (p q : bool) (H : p ∧ q) : q
:= H q (λ (H1 : p) (H2 : q), H2)
in and_intro
check let bool : Type.{1} := Type.{0},
and (p q : bool) : bool := ∀ c : bool, (p → q → c) → c,
infixl `∧` 25 := and,
and_intro (p q : bool) (H1 : p) (H2 : q) : q ∧ p
:= λ (c : bool) (H : p → q → c), H H1 H2,
and_elim_left (p q : bool) (H : p ∧ q) : p
:= H p (λ (H1 : p) (H2 : q), H1),
and_elim_right (p q : bool) (H : p ∧ q) : q
:= H q (λ (H1 : p) (H2 : q), H2)
in and_intro

5
tests/lean/let1.lean.expected.out Normal file
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let bool : Type := Bool in (let and : bool -> bool -> bool := fun (p : bool) (q : bool), (Pi (c : bool) (a : p -> q -> c), c) in (let and_intro : Pi (p : bool) (q : bool) (H1 : p) (H2 : q), (and p q) := fun (p : bool) (q : bool) (H1 : p) (H2 : q) (c : bool) (H : p -> q -> c), (H H1 H2) in (let and_elim_left : Pi (p : bool) (q : bool) (H : and p q), p := fun (p : bool) (q : bool) (H : and p q), (H p (fun (H1 : p) (H2 : q), H1)) in (let and_elim_right : Pi (p : bool) (q : bool) (H : and p q), q := fun (p : bool) (q : bool) (H : and p q), (H q (fun (H1 : p) (H2 : q), H2)) in and_intro)))) : Pi (p : Bool) (q : Bool) (H1 : p) (H2 : q) (c : Bool) (H : p -> q -> c), c
let1.lean:16:10: error: type mismatch at definition 'and_intro', expected type
Pi (p : Bool) (q : Bool) (H1 : p) (H2 : q), ((fun (p : Bool) (q : Bool), (Pi (c : Bool) (a : p -> q -> c), c)) q p)
given type:
Pi (p : Bool) (q : Bool) (H1 : p) (H2 : q) (c : Bool) (H : p -> q -> c), c