96 lines
3.4 KiB
Plaintext
96 lines
3.4 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 Guess_ExI
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imports
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Eisbach_Tools.Eisbach_Methods
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Eisbach_Tools.Apply_Debug
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begin
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(*
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This file contains the experimental methods guess_exI and guess_spec. Each, as the name suggests,
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attempts to guess an instantiation for their respective rules. It does so by looking
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for a matching premise for the quantifying binder, checking that
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this could be the only match for safety.
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*)
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method abs_used for P = (match (P) in "\<lambda>s. ?P" \<Rightarrow> \<open>fail\<close> \<bar> _ \<Rightarrow> \<open>-\<close>)
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method in_conj for P Q = (
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match (Q) in "P" \<Rightarrow> \<open>-\<close>
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| match (Q) in "\<lambda>y. A y \<and> B y" for A B \<Rightarrow>
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\<open> match (A) in "(Q' :: 'b)" for Q' \<Rightarrow> \<open>match (B) in "(Q'' :: 'b)" for Q'' \<Rightarrow>
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\<open> in_conj P Q' | in_conj P Q''\<close>\<close>\<close>
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)
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method guess_exI =
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(require_determ \<open>(match conclusion in "\<exists>x. Q x" for Q \<Rightarrow>
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\<open>match premises in "P y" for P y \<Rightarrow>
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\<open>abs_used P, in_conj P Q, rule exI[where x=y]\<close>\<close>)\<close>)
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lemma fun_uncurry:
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"(P \<longrightarrow> Q \<longrightarrow> R) \<longleftrightarrow> (P \<and> Q) \<longrightarrow> R"
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by auto
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method guess_spec_inner for P uses I =
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((match I in "\<forall>x. C x \<longrightarrow> _ x" for C \<Rightarrow> \<open>in_conj P C\<close> ))
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method guess_spec =
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(require_determ \<open>(match premises in I:"\<forall>x. _ x \<longrightarrow> _ x" \<Rightarrow>
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\<open>match premises in "P y" for P y \<Rightarrow>
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\<open>abs_used P, guess_spec_inner P I:I[simplified fun_uncurry],
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insert I, drule spec[where x=y]\<close>\<close>)\<close>)
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text \<open>Tests and examples\<close>
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experiment begin
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lemma
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assumes Q: "Q x"
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shows "P x \<Longrightarrow> \<forall>x. Q x \<longrightarrow> P x \<longrightarrow> R \<Longrightarrow> R"
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by (guess_spec, blast intro: Q)
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(* Conflicting premises are checked *)
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lemma
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assumes Q: "Q x"
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shows "\<lbrakk> P x; P y \<rbrakk> \<Longrightarrow> \<forall>x. Q x \<longrightarrow> P x \<longrightarrow> R \<Longrightarrow> R"
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apply (fails \<open>guess_spec\<close>)
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by (blast intro: Q)
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(* Conflicts between different conjuncts are checked *)
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lemma
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assumes Q: "Q x"
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shows "\<lbrakk> P x; Q y \<rbrakk> \<Longrightarrow> \<forall>x. Q x \<longrightarrow> P x \<longrightarrow> R \<Longrightarrow> R"
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apply (fails \<open>guess_spec\<close>)
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by (blast intro: Q)
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end
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text \<open>Tests and examples\<close>
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experiment begin
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lemma "P x \<Longrightarrow> \<exists>x. P x"
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by guess_exI
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lemma
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assumes Q: "Q x"
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shows "P x \<Longrightarrow> \<exists>x. Q x \<and> P x"
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apply guess_exI
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by (blast intro: Q)
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(* Conflicting premises are checked *)
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lemma
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assumes Q: "Q x"
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shows "\<lbrakk> P x; P y \<rbrakk> \<Longrightarrow> \<exists>x. Q x \<and> P x"
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apply (fails \<open>guess_exI\<close>)
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by (blast intro: Q)
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(* Conflicts between different conjuncts are checked *)
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lemma
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assumes Q: "Q x"
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shows "\<lbrakk> P x; Q y \<rbrakk> \<Longrightarrow> \<exists>x. Q x \<and> P x"
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apply (fails \<open>guess_exI\<close>)
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by (blast intro: Q)
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end
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end |