diff options
Diffstat (limited to 'tests/hol4/paper/paperTheory.sig')
| -rw-r--r-- | tests/hol4/paper/paperTheory.sig | 210 |
1 files changed, 210 insertions, 0 deletions
diff --git a/tests/hol4/paper/paperTheory.sig b/tests/hol4/paper/paperTheory.sig new file mode 100644 index 00000000..2da80da1 --- /dev/null +++ b/tests/hol4/paper/paperTheory.sig @@ -0,0 +1,210 @@ +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 |