diff options
| author | Josh Chen | 2020-05-28 14:08:26 +0200 |
|---|---|---|
| committer | Josh Chen | 2020-05-28 14:08:26 +0200 |
| commit | 1ccd93665a01acdc25b37409e94b71615ced5393 (patch) | |
| tree | 450284e77c40512408b0849f3ca2b12367aa4b90 | |
| parent | 6ff59c83de9ce7d5715fae19f50d94b0b973414a (diff) | |
more List and Maybe
| -rw-r--r-- | spartan/data/List.thy | 20 | ||||
| -rw-r--r-- | spartan/data/Maybe.thy | 6 | ||||
| -rw-r--r-- | spartan/data/More_Types.thy | 3 |
3 files changed, 22 insertions, 7 deletions
diff --git a/spartan/data/List.thy b/spartan/data/List.thy index 52f042b..c581019 100644 --- a/spartan/data/List.thy +++ b/spartan/data/List.thy @@ -50,19 +50,29 @@ lemmas abbreviation "ListRec A C \<equiv> ListInd A (\<lambda>_. C)" +Lemma (derive) ListCase: + assumes + "A: U i" "\<And>xs. xs: List A \<Longrightarrow> C xs: U i" and + nil_case: "c\<^sub>0: C (nil A)" and + cons_case: "\<And>x xs. \<lbrakk>x: A; xs: List A\<rbrakk> \<Longrightarrow> f x xs: C (cons A x xs)" and + "xs: List A" + shows "?List_cases A (\<lambda>xs. C xs) c\<^sub>0 (\<lambda>x xs. f x xs) xs: C xs" + by (elim xs) (fact nil_case, rule cons_case) + +lemmas List_cases [cases] = ListCase[rotated 4] + + +section \<open>Notation\<close> + definition nil_i ("[]") where [implicit]: "[] \<equiv> nil ?" -definition cons_i (infixr "#" 50) +definition cons_i (infixr "#" 120) where [implicit]: "x # xs \<equiv> cons ? x xs" translations "[]" \<leftharpoondown> "CONST List.nil A" "x # xs" \<leftharpoondown> "CONST List.cons A x xs" - - -section \<open>List notation\<close> - syntax "_list" :: \<open>args \<Rightarrow> o\<close> ("[_]") translations diff --git a/spartan/data/Maybe.thy b/spartan/data/Maybe.thy index 98f5283..1efbb95 100644 --- a/spartan/data/Maybe.thy +++ b/spartan/data/Maybe.thy @@ -55,8 +55,10 @@ Lemma Maybe_comp_some: lemmas [intros] = MaybeF Maybe_none Maybe_some and - MaybeE [elims "?m"] = MaybeInd and - [comps] = Maybe_comp_none Maybe_comp_some + [comps] = Maybe_comp_none Maybe_comp_some and + MaybeE [elims "?m"] = MaybeInd[rotated 4] +lemmas + Maybe_cases [cases] = MaybeE abbreviation "MaybeRec A C \<equiv> MaybeInd A (K C)" diff --git a/spartan/data/More_Types.thy b/spartan/data/More_Types.thy index fecf378..625f639 100644 --- a/spartan/data/More_Types.thy +++ b/spartan/data/More_Types.thy @@ -48,6 +48,9 @@ lemmas [elims ?s] = SumE and [comps] = Sum_comp_inl Sum_comp_inr +method left = rule Sum_inl +method right = rule Sum_inr + section \<open>Empty and unit types\<close> |