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Diffstat (limited to 'tests/hol4/misc-paper/paperTheory.sig')
| -rw-r--r-- | tests/hol4/misc-paper/paperTheory.sig | 210 |
1 files changed, 0 insertions, 210 deletions
diff --git a/tests/hol4/misc-paper/paperTheory.sig b/tests/hol4/misc-paper/paperTheory.sig deleted file mode 100644 index 2da80da1..00000000 --- a/tests/hol4/misc-paper/paperTheory.sig +++ /dev/null @@ -1,210 +0,0 @@ -signature paperTheory = -sig - type thm = Thm.thm - - (* Definitions *) - val call_choose_fwd_def : thm - val choose_back_def : thm - val choose_fwd_def : thm - val list_nth_mut_back_def : thm - val list_nth_mut_fwd_def : thm - val list_t_TY_DEF : thm - val list_t_case_def : thm - val list_t_size_def : thm - val ref_incr_fwd_back_def : thm - val sum_fwd_def : thm - val test_choose_fwd_def : thm - val test_incr_fwd_def : thm - val test_nth_fwd_def : thm - - (* Theorems *) - val datatype_list_t : thm - val list_t_11 : thm - val list_t_Axiom : thm - val list_t_case_cong : thm - val list_t_case_eq : thm - val list_t_distinct : thm - val list_t_induction : thm - val list_t_nchotomy : thm - - val paper_grammars : type_grammar.grammar * term_grammar.grammar -(* - [divDef] Parent theory of "paper" - - [call_choose_fwd_def] Definition - - ⊢ ∀p. call_choose_fwd p = - (let - (px,py) = p - in - do - pz <- choose_fwd T px py; - pz0 <- u32_add pz (int_to_u32 1); - (px0,_) <- choose_back T px py pz0; - Return px0 - od) - - [choose_back_def] Definition - - ⊢ ∀b x y ret. - choose_back b x y ret = - if b then Return (ret,y) else Return (x,ret) - - [choose_fwd_def] Definition - - ⊢ ∀b x y. choose_fwd b x y = if b then Return x else Return y - - [list_nth_mut_back_def] Definition - - ⊢ ∀l i ret. - list_nth_mut_back l i ret = - case l of - ListCons x tl => - if i = int_to_u32 0 then Return (ListCons ret tl) - else - do - i0 <- u32_sub i (int_to_u32 1); - tl0 <- list_nth_mut_back tl i0 ret; - Return (ListCons x tl0) - od - | ListNil => Fail Failure - - [list_nth_mut_fwd_def] Definition - - ⊢ ∀l i. - list_nth_mut_fwd l i = - case l of - ListCons x tl => - if i = int_to_u32 0 then Return x - else - do - i0 <- u32_sub i (int_to_u32 1); - list_nth_mut_fwd tl i0 - od - | ListNil => Fail Failure - - [list_t_TY_DEF] Definition - - ⊢ ∃rep. - TYPE_DEFINITION - (λa0'. - ∀ $var$('list_t'). - (∀a0'. - (∃a0 a1. - a0' = - (λa0 a1. - ind_type$CONSTR 0 a0 - (ind_type$FCONS a1 (λn. ind_type$BOTTOM))) - a0 a1 ∧ $var$('list_t') a1) ∨ - a0' = - ind_type$CONSTR (SUC 0) ARB (λn. ind_type$BOTTOM) ⇒ - $var$('list_t') a0') ⇒ - $var$('list_t') a0') rep - - [list_t_case_def] Definition - - ⊢ (∀a0 a1 f v. list_t_CASE (ListCons a0 a1) f v = f a0 a1) ∧ - ∀f v. list_t_CASE ListNil f v = v - - [list_t_size_def] Definition - - ⊢ (∀f a0 a1. - list_t_size f (ListCons a0 a1) = 1 + (f a0 + list_t_size f a1)) ∧ - ∀f. list_t_size f ListNil = 0 - - [ref_incr_fwd_back_def] Definition - - ⊢ ∀x. ref_incr_fwd_back x = i32_add x (int_to_i32 1) - - [sum_fwd_def] Definition - - ⊢ ∀l. sum_fwd l = - case l of - ListCons x tl => do i <- sum_fwd tl; i32_add x i od - | ListNil => Return (int_to_i32 0) - - [test_choose_fwd_def] Definition - - ⊢ test_choose_fwd = - do - z <- choose_fwd T (int_to_i32 0) (int_to_i32 0); - z0 <- i32_add z (int_to_i32 1); - if z0 ≠ int_to_i32 1 then Fail Failure - else - do - (x,y) <- choose_back T (int_to_i32 0) (int_to_i32 0) z0; - if x ≠ int_to_i32 1 then Fail Failure - else if y ≠ int_to_i32 0 then Fail Failure - else Return () - od - od - - [test_incr_fwd_def] Definition - - ⊢ test_incr_fwd = - do - x <- ref_incr_fwd_back (int_to_i32 0); - if x ≠ int_to_i32 1 then Fail Failure else Return () - od - - [test_nth_fwd_def] Definition - - ⊢ test_nth_fwd = - (let - l = ListNil; - l0 = ListCons (int_to_i32 3) l; - l1 = ListCons (int_to_i32 2) l0 - in - do - x <- - list_nth_mut_fwd (ListCons (int_to_i32 1) l1) (int_to_u32 2); - x0 <- i32_add x (int_to_i32 1); - l2 <- - list_nth_mut_back (ListCons (int_to_i32 1) l1) - (int_to_u32 2) x0; - i <- sum_fwd l2; - if i ≠ int_to_i32 7 then Fail Failure else Return () - od) - - [datatype_list_t] Theorem - - ⊢ DATATYPE (list_t ListCons ListNil) - - [list_t_11] Theorem - - ⊢ ∀a0 a1 a0' a1'. - ListCons a0 a1 = ListCons a0' a1' ⇔ a0 = a0' ∧ a1 = a1' - - [list_t_Axiom] Theorem - - ⊢ ∀f0 f1. ∃fn. - (∀a0 a1. fn (ListCons a0 a1) = f0 a0 a1 (fn a1)) ∧ - fn ListNil = f1 - - [list_t_case_cong] Theorem - - ⊢ ∀M M' f v. - M = M' ∧ (∀a0 a1. M' = ListCons a0 a1 ⇒ f a0 a1 = f' a0 a1) ∧ - (M' = ListNil ⇒ v = v') ⇒ - list_t_CASE M f v = list_t_CASE M' f' v' - - [list_t_case_eq] Theorem - - ⊢ list_t_CASE x f v = v' ⇔ - (∃t l. x = ListCons t l ∧ f t l = v') ∨ x = ListNil ∧ v = v' - - [list_t_distinct] Theorem - - ⊢ ∀a1 a0. ListCons a0 a1 ≠ ListNil - - [list_t_induction] Theorem - - ⊢ ∀P. (∀l. P l ⇒ ∀t. P (ListCons t l)) ∧ P ListNil ⇒ ∀l. P l - - [list_t_nchotomy] Theorem - - ⊢ ∀ll. (∃t l. ll = ListCons t l) ∨ ll = ListNil - - -*) -end |