diff options
Diffstat (limited to 'tests/hol4/polonius_list')
-rw-r--r-- | tests/hol4/polonius_list/Holmakefile | 5 | ||||
-rw-r--r-- | tests/hol4/polonius_list/poloniusListScript.sml | 37 | ||||
-rw-r--r-- | tests/hol4/polonius_list/poloniusListTheory.sig | 120 |
3 files changed, 162 insertions, 0 deletions
diff --git a/tests/hol4/polonius_list/Holmakefile b/tests/hol4/polonius_list/Holmakefile new file mode 100644 index 00000000..3c4b8973 --- /dev/null +++ b/tests/hol4/polonius_list/Holmakefile @@ -0,0 +1,5 @@ +# This file was automatically generated - modify ../Holmakefile.template instead +INCLUDES = ../../../backends/hol4 + +all: $(DEFAULT_TARGETS) +.PHONY: all diff --git a/tests/hol4/polonius_list/poloniusListScript.sml b/tests/hol4/polonius_list/poloniusListScript.sml new file mode 100644 index 00000000..06876ed4 --- /dev/null +++ b/tests/hol4/polonius_list/poloniusListScript.sml @@ -0,0 +1,37 @@ +(** THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS *) +(** [polonius_list] *) +open primitivesLib divDefLib + +val _ = new_theory "poloniusList" + + +Datatype: + (** [polonius_list::List] *) + list_t = | ListCons 't list_t | ListNil +End + +val [get_list_at_x_fwd_def] = DefineDiv ‘ + (** [polonius_list::get_list_at_x]: forward function *) + get_list_at_x_fwd (ls : u32 list_t) (x : u32) : u32 list_t result = + (case ls of + | ListCons hd tl => + if hd = x then Return (ListCons hd tl) else get_list_at_x_fwd tl x + | ListNil => Return ListNil) +’ + +val [get_list_at_x_back_def] = DefineDiv ‘ + (** [polonius_list::get_list_at_x]: backward function 0 *) + get_list_at_x_back + (ls : u32 list_t) (x : u32) (ret : u32 list_t) : u32 list_t result = + (case ls of + | ListCons hd tl => + if hd = x + then Return ret + else (do + tl0 <- get_list_at_x_back tl x ret; + Return (ListCons hd tl0) + od) + | ListNil => Return ret) +’ + +val _ = export_theory () diff --git a/tests/hol4/polonius_list/poloniusListTheory.sig b/tests/hol4/polonius_list/poloniusListTheory.sig new file mode 100644 index 00000000..41f21df7 --- /dev/null +++ b/tests/hol4/polonius_list/poloniusListTheory.sig @@ -0,0 +1,120 @@ +signature poloniusListTheory = +sig + type thm = Thm.thm + + (* Definitions *) + val get_list_at_x_back_def : thm + val get_list_at_x_fwd_def : thm + val list_t_TY_DEF : thm + val list_t_case_def : thm + val list_t_size_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 poloniusList_grammars : type_grammar.grammar * term_grammar.grammar +(* + [divDef] Parent theory of "poloniusList" + + [get_list_at_x_back_def] Definition + + ⊢ ∀ls x ret. + get_list_at_x_back ls x ret = + case ls of + ListCons hd tl => + if hd = x then Return ret + else + do + tl0 <- get_list_at_x_back tl x ret; + Return (ListCons hd tl0) + od + | ListNil => Return ret + + [get_list_at_x_fwd_def] Definition + + ⊢ ∀ls x. + get_list_at_x_fwd ls x = + case ls of + ListCons hd tl => + if hd = x then Return (ListCons hd tl) + else get_list_at_x_fwd tl x + | ListNil => Return ListNil + + [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 + + [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 |