diff options
Diffstat (limited to 'backends/hol4')
| -rw-r--r-- | backends/hol4/divDefLib.sml | 9 | ||||
| -rw-r--r-- | backends/hol4/divDefLibTestTheory.sig | 116 |
2 files changed, 65 insertions, 60 deletions
diff --git a/backends/hol4/divDefLib.sml b/backends/hol4/divDefLib.sml index 80f47f65..f53ef6f8 100644 --- a/backends/hol4/divDefLib.sml +++ b/backends/hol4/divDefLib.sml @@ -896,9 +896,14 @@ fun DefineDiv (def_qt : term quotation) = (* Prove the final equations *) val def_eqs = prove_def_eqs body_is_valid def_tms raw_defs - (* Save the definitions *) + (* Save the final equations as definitions. + + Note that because we use the same names, doing this overrides the "raw" + definitions, which are then forgotten, which means we don't need to + manually delete them. + *) val thm_names = map (fn x => x ^ "_def") fnames - val _ = map save_thm (zip thm_names def_eqs) + val _ = map store_definition (zip thm_names def_eqs) in def_eqs end diff --git a/backends/hol4/divDefLibTestTheory.sig b/backends/hol4/divDefLibTestTheory.sig index 8da736ab..526f74a6 100644 --- a/backends/hol4/divDefLibTestTheory.sig +++ b/backends/hol4/divDefLibTestTheory.sig @@ -5,14 +5,20 @@ sig (* Definitions *) val btree_TY_DEF : thm val btree_case_def : thm + val btree_height_def : thm val btree_size_def : thm + val even_def : thm val list_t_TY_DEF : thm val list_t_case_def : thm val list_t_size_def : thm val node_TY_DEF : thm val node_case_def : thm + val nth_def : thm + val odd_def : thm val tree_TY_DEF : thm val tree_case_def : thm + val tree_height_def : thm + val tree_nodes_height_def : thm val tree_size_def : thm (* Theorems *) @@ -21,13 +27,11 @@ sig val btree_case_cong : thm val btree_case_eq : thm val btree_distinct : thm - val btree_height_def : thm val btree_induction : thm val btree_nchotomy : thm val datatype_btree : thm val datatype_list_t : thm val datatype_tree : thm - val even_def : thm val list_t_11 : thm val list_t_Axiom : thm val list_t_case_cong : thm @@ -41,17 +45,13 @@ sig val node_case_eq : thm val node_induction : thm val node_nchotomy : thm - val nth_def : thm - val odd_def : thm val tree_11 : thm val tree_Axiom : thm val tree_case_cong : thm val tree_case_eq : thm val tree_distinct : thm - val tree_height_def : thm val tree_induction : thm val tree_nchotomy : thm - val tree_nodes_height_def : thm val tree_size_eq : thm val divDefLibTest_grammars : type_grammar.grammar * term_grammar.grammar @@ -83,6 +83,19 @@ sig ⊢ (∀a f f1. btree_CASE (BLeaf a) f f1 = f a) ∧ ∀a0 a1 f f1. btree_CASE (BNode a0 a1) f f1 = f1 a0 a1 + [btree_height_def] Definition + + ⊢ ∀tree. + btree_height tree = + case tree of + BLeaf v => Return 1 + | BNode l r => + do + hl <- btree_height l; + hr <- btree_height r; + Return (hl + hr) + od + [btree_size_def] Definition ⊢ (∀f a. btree_size f (BLeaf a) = 1 + f a) ∧ @@ -90,6 +103,10 @@ sig btree_size f (BNode a0 a1) = 1 + (btree_size f a0 + btree_size f a1) + [even_def] Definition + + ⊢ ∀i. even i = if i = 0 then Return T else odd (i − 1) + [list_t_TY_DEF] Definition ⊢ ∃rep. @@ -163,6 +180,20 @@ sig ⊢ ∀a f. node_CASE (Node a) f = f a + [nth_def] Definition + + ⊢ ∀ls i. + nth ls i = + case ls of + ListCons x tl => + if u32_to_int i = 0 then Return x + else do i0 <- u32_sub i (int_to_u32 1); nth tl i0 od + | ListNil => Fail Failure + + [odd_def] Definition + + ⊢ ∀i. odd i = if i = 0 then Return F else even (i − 1) + [tree_TY_DEF] Definition ⊢ ∃rep. @@ -208,6 +239,27 @@ sig ⊢ (∀a f f1. tree_CASE (TLeaf a) f f1 = f a) ∧ ∀a f f1. tree_CASE (TNode a) f f1 = f1 a + [tree_height_def] Definition + + ⊢ ∀tree. + tree_height tree = + case tree of + TLeaf v => Return 1 + | TNode (Node ls) => tree_nodes_height ls + + [tree_nodes_height_def] Definition + + ⊢ ∀ls. + tree_nodes_height ls = + case ls of + [] => Return 0 + | t::tl => + do + h1 <- tree_height t; + h2 <- tree_nodes_height tl; + Return (h1 + h2) + od + [tree_size_def] Definition ⊢ (∀f a. tree_size f (TLeaf a) = 1 + f a) ∧ @@ -244,19 +296,6 @@ sig ⊢ ∀a1 a0 a. BLeaf a ≠ BNode a0 a1 - [btree_height_def] Theorem - - ⊢ ∀tree. - btree_height tree = - case tree of - BLeaf v => Return 1 - | BNode l r => - do - hl <- btree_height l; - hr <- btree_height r; - Return (hl + hr) - od - [btree_induction] Theorem ⊢ ∀P. (∀a. P (BLeaf a)) ∧ (∀b b0. P b ∧ P b0 ⇒ P (BNode b b0)) ⇒ @@ -278,10 +317,6 @@ sig ⊢ DATATYPE (tree TLeaf TNode ∧ node Node) - [even_def] Theorem - - ⊢ ∀i. even i = if i = 0 then Return T else odd (i − 1) - [list_t_11] Theorem ⊢ ∀a0 a1 a0' a1'. @@ -350,20 +385,6 @@ sig ⊢ ∀nn. ∃l. nn = Node l - [nth_def] Theorem - - ⊢ ∀ls i. - nth ls i = - case ls of - ListCons x tl => - if u32_to_int i = 0 then Return x - else do i0 <- u32_sub i (int_to_u32 1); nth tl i0 od - | ListNil => Fail Failure - - [odd_def] Theorem - - ⊢ ∀i. odd i = if i = 0 then Return F else even (i − 1) - [tree_11] Theorem ⊢ (∀a a'. TLeaf a = TLeaf a' ⇔ a = a') ∧ @@ -392,14 +413,6 @@ sig ⊢ ∀a' a. TLeaf a ≠ TNode a' - [tree_height_def] Theorem - - ⊢ ∀tree. - tree_height tree = - case tree of - TLeaf v => Return 1 - | TNode (Node ls) => tree_nodes_height ls - [tree_induction] Theorem ⊢ ∀P0 P1 P2. @@ -412,19 +425,6 @@ sig ⊢ ∀tt. (∃a. tt = TLeaf a) ∨ ∃n. tt = TNode n - [tree_nodes_height_def] Theorem - - ⊢ ∀ls. - tree_nodes_height ls = - case ls of - [] => Return 0 - | t::tl => - do - h1 <- tree_height t; - h2 <- tree_nodes_height tl; - Return (h1 + h2) - od - [tree_size_eq] Theorem ⊢ tree1_size f = list_size (tree_size f) |