120 lines
2.6 KiB
Plaintext
120 lines
2.6 KiB
Plaintext
(*
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* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*)
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theory ML_Goal_Test
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imports
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ML_Goal
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ML_Utils.ML_Utils
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begin
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experiment begin
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\<comment>\<open>
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Basic usage.
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\<close>
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ML_goal test: \<open>
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[@{term "(P \<longrightarrow> Q) \<and> P \<longrightarrow> Q"}]
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\<close>
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apply clarsimp
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done
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thm test
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\<comment>\<open>
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A goal that we definitely don't want to write out by hand.
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In this case, we're going to show that if x is less than 10,
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we "only" need to consider the cases when x = 0, or x = 1, or...
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\<close>
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ML_goal big_goal: \<open>
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let
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val var_x = Free ("x", @{typ nat});
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val var_P = Free ("P", @{typ bool});
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val max = 10;
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\<comment>\<open>
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@{ML "HOLogic.mk_nat"} produces nested Suc's, which are pretty
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ugly, so we use this instead.
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\<close>
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val mk_nat = HOLogic.mk_number @{typ nat};
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\<comment>\<open>
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Turns (i: int) into @{term "x = i \<Longrightarrow> P"}.
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\<close>
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fun mk_case i =
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let
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val prem = HOLogic.mk_eq (var_x, mk_nat i) |> HOLogic.mk_Trueprop;
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val conc = var_P |> HOLogic.mk_Trueprop;
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in Logic.mk_implies (prem, conc) end
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val x_cases =
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ListExtras.range 0 max
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|> map mk_case;
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val assm =
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HOLogic.mk_binrel @{const_name "less"}
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(var_x,
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(mk_nat max))
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|> HOLogic.mk_Trueprop;
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val goal =
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Logic.list_implies (assm :: x_cases, var_P |> HOLogic.mk_Trueprop)
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in [goal] end
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\<close>
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by force
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\<comment>\<open>
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Names are optional.
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\<close>
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ML_goal \<open>
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[@{term "True"}]
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\<close>
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by (rule TrueI)
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\<comment>\<open>
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Multiple goals are supported, and result in similar
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"list of fact" lemmas
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\<close>
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ML_goal multiple_goals: \<open>
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[@{term "(P \<Longrightarrow> Q \<Longrightarrow> P)"}, @{term "(P \<Longrightarrow> Q \<Longrightarrow> Q)"}]
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\<close>
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by simp+
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thm multiple_goals[OF TrueI]
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\<comment>\<open>
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Handles mixes of @{typ bool} and @{typ prop}.
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\<close>
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ML_goal \<open>
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[@{term "PROP A \<Longrightarrow> PROP A"}, @{term "B \<longrightarrow> B"}]
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\<close>
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by simp+
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\<comment>\<open>
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Turns out a lemma name can refer to nothing as well!
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\<close>
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ML_goal nothing: \<open>[]\<close>
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done
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thm nothing[OF TrueI]
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\<comment>\<open>
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Attributes can be applied, just like normal lemmas.
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\<close>
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definition magic where "magic = (5 :: nat)"
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ML_goal declared_with_an_attribute[folded magic_def, simp]: \<open>
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[@{term "(5 :: nat) = 2 + 3"}]
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\<close>
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by simp
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lemma uses_our_new_magic_simp_rule:
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"magic = 1 + 4"
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by simp
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end
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end |