<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Hi James, <div class=""><br class=""></div><div class="">mathematician lurker here. This is interesting:<br class=""><div class="">
<div dir="auto" style="color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); font-variant-ligatures: normal; font-variant-position: normal; font-variant-caps: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); font-variant-ligatures: normal; font-variant-position: normal; font-variant-caps: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); font-variant-ligatures: normal; font-variant-position: normal; font-variant-caps: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="color: rgb(0, 0, 0); font-variant-ligatures: normal; font-variant-position: normal; font-variant-caps: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><br class=""></div></div></div></div></div></div></div></div></div></div></div><div><blockquote type="cite" class=""><div class="">On Aug 21, 2020, at 12:47, James Wood <<a href="mailto:james.wood.100@strath.ac.uk" class="">james.wood.100@strath.ac.uk</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><span style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Most other areas of maths traditionally don't resemble this</span><br style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">type-directed style of programming. There are few, small, inductive</span><br style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">types, and a lot of reasoning is done at the level of algebraic axioms</span><br style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">(with no inductive types in sight). These features largely nullify</span><br style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Agda's advantages, and instead the advantages of Lean and Coq in the</span><br style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: AgmenaPro-Regular; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">field of proving shine through.</span></div></blockquote></div><br class=""></div><div class="">Can you elaborate a bit?</div><div class=""><br class=""></div><div class="">Thanks,</div><div class=""><br class=""></div><div class="">—Ettore</div><div class=""><div class=""><div dir="auto" style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="font-variant-ligatures: normal; font-variant-position: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; line-height: normal; orphans: 2; text-align: -webkit-auto; widows: 2; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="font-variant-ligatures: normal; font-variant-position: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; line-height: normal; text-align: -webkit-auto; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="font-variant-ligatures: normal; font-variant-position: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; line-height: normal; text-align: -webkit-auto; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="font-variant-ligatures: normal; font-variant-position: normal; font-variant-numeric: normal; font-variant-alternates: normal; font-variant-east-asian: normal; line-height: normal; text-align: -webkit-auto; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><font face="Osaka" class=""><span style="font-size: 12px;" class="">Ettore Aldrovandi</span></font></div><div class=""><font face="Osaka" class=""><span style="font-size: 12px;" class="">Department of Mathematics, Florida State University</span></font></div><div class=""><font face="Osaka" class=""><span style="font-size: 12px;" class="">1017 Academic Way * <a href="http://www.math.fsu.edu/~ealdrov" class="">http://www.math.fsu.edu/~ealdrov</a></span></font></div><div class=""><font face="Osaka" class=""><span style="font-size: 12px;" class="">Tallahassee, FL 32306-4510, USA * * aldrovandi at math dot fsu dot edu</span></font></div><div class=""><font face="Osaka" class=""><span style="font-size: 12px;" class=""><br class=""></span></font></div></div></div></div></div></div></div></div></div></div></div></div></body></html>