diff options
Diffstat (limited to 'Prod.thy')
| -rw-r--r-- | Prod.thy | 13 |
1 files changed, 9 insertions, 4 deletions
@@ -75,7 +75,12 @@ section \<open>Function composition\<close> definition compose :: "[t, t, t] \<Rightarrow> t" where "compose A g f \<equiv> \<lambda>x: A. g`(f`x)" -syntax "_compose" :: "[t, t] \<Rightarrow> t" (infixr "o" 110) +syntax "_compose" :: "[t, t, t] \<Rightarrow> t" ("(2_ o[_]/ _)" [111, 0, 110] 110) +translations "g o[A] f" \<rightleftharpoons> "(CONST compose) A g f" + +text \<open>The composition @{term "g o[A] f"} is annotated with the domain @{term A} of @{term f}.\<close> + +syntax "_compose'" :: "[t, t] \<Rightarrow> t" (infixr "o" 110) text \<open>Pretty-printing switch for composition; hides domain type information.\<close> @@ -84,7 +89,7 @@ ML \<open>val pretty_compose = Attrib.setup_config_bool @{binding "pretty_compos print_translation \<open> let fun compose_tr' ctxt [A, g, f] = if Config.get ctxt pretty_compose - then Syntax.const @{syntax_const "_compose"} $ g $ f + then Syntax.const @{syntax_const "_compose'"} $ g $ f else @{const compose} $ A $ g $ f in [(@{const_syntax compose}, compose_tr')] @@ -93,12 +98,12 @@ end lemma compose_assoc: assumes "A: U i" and "f: A \<rightarrow> B" and "g: B \<rightarrow> C" and "h: \<Prod>x: C. D x" - shows "compose A (compose B h g) f \<equiv> compose A h (compose A g f)" + shows "(h o[B] g) o[A] f \<equiv> h o[A] g o[A] f" unfolding compose_def by (derive lems: assms cong) lemma compose_comp: assumes "A: U i" and "\<And>x. x: A \<Longrightarrow> b x: B" and "\<And>x. x: B \<Longrightarrow> c x: C x" - shows "compose A (\<lambda>x: B. c x) (\<lambda>x: A. b x) \<equiv> \<lambda>x: A. c (b x)" + shows "(\<lambda>x: B. c x) o[A] (\<lambda>x: A. b x) \<equiv> \<lambda>x: A. c (b x)" unfolding compose_def by (derive lems: assms cong) declare compose_comp [comp] |